Damage Mechanism of Ultra-thin Asphalt Overlay(UTAO) based on Discrete Element Method

Aiming to analyze the damage mechanism of UTAO from the perspective of meso-mechanical mechanism using discrete element method(DEM),we conducted study of diseases problems of UTAO in several provinces in China,and found that aggregate spalling was one of the main disease types of UTAO.A discrete element model of UTAO pavement structure was constructed to explore the meso-mechanical mechanism of UTAO damage under the influence of layer thickness,gradation,and bonding modulus.The experimental results show that,as the thickness of UTAO decreasing,the maximum value and the mean value of the contact force between all aggregate particles gradually increase,which leads to aggregates more prone to spalling.Compared with OGFC-5 UTAO,AC-5 UTAO presents smaller maximum and average values of all contact forces,and the loading pressure in AC-5 UTAO is fully diffused in the lateral direction.In addition,the increment of pavement modulus strengthens the overall force of aggregate particles inside UTAO,resulting in aggregate particles peeling off more easily.The increase of bonding modulus changes the position where the maximum value of the tangential force appears,whereas has no effect on the normal force.

Investigation of the block toppling evolution of a layered model slope by centrifuge test and discrete element modeling

Primary toppling usually occurs in layered rock slopes with large anti-dip angles.In this paper,the block toppling evolution was explored using a large-scale centrifuge system.Each block column in the layered model slope was made of cement mortar.Some artificial cracks perpendicular to the block column were prefabricated.Strain gages,displacement gages,and high-speed camera measurements were employed to monitor the deformation and failure processes of the model slope.The centrifuge test results show that the block toppling evolution can be divided into seven stages,i.e.layer compression,formation of major tensile crack,reverse bending of the block column,closure of major tensile crack,strong bending of the block column,formation of failure zone,and complete failure.Block toppling is characterized by sudden large deformation and occurs in stages.The wedge-shaped cracks in the model incline towards the slope.Experimental observations show that block toppling is mainly caused by bending failure rather than by shear failure.The tensile strength also plays a key factor in the evolution of block toppling.The simulation results from discrete element method(DEM)is in line with the testing results.Tensile stress exists at the backside of rock column during toppling deformation.Stress concentration results in the fragmented rock column and its degree is the most significant at the slope toe.

Nonlinear wave dispersion in monoatomic chains with lumped and distributed masses:discrete and continuum models

The main objective of this paper is to investigate the influence of inertia of nonlinear springs on the dispersion behavior of discrete monoatomic chains with lumped and distributed masses.The developed model can represent the wave propagation problem in a non-homogeneous material consisting of heavy inclusions embedded in a matrix.The inclusions are idealized by lumped masses,and the matrix between adjacent inclusions is modeled by a nonlinear spring with distributed masses.Additionally,the model is capable of depicting the wave propagation in bi-material bars,wherein the first material is represented by a rigid particle and the second one is represented by a nonlinear spring with distributed masses.The discrete model of the nonlinear monoatomic chain with lumped and distributed masses is first considered,and a closed-form expression of the dispersion relation is obtained by the second-order Lindstedt-Poincare method(LPM).Next,a continuum model for the nonlinear monoatomic chain is derived directly from its discrete lattice model by a suitable continualization technique.The subsequent use of the second-order method of multiple scales(MMS)facilitates the derivation of the corresponding nonlinear dispersion relation in a closed form.The novelties of the present study consist of(i)considering the inertia of nonlinear springs on the dispersion behavior of the discrete mass-spring chains;(ii)developing the second-order LPM for the wave propagation in the discrete chains;and(iii)deriving a continuum model for the nonlinear monoatomic chains with lumped and distributed masses.Finally,a parametric study is conducted to examine the effects of the design parameters and the distributed spring mass on the nonlinear dispersion relations and phase velocities obtained from both the discrete and continuum models.These parameters include the ratio of the spring mass to the lumped mass,the nonlinear stiffness coefficient of the spring,and the wave amplitude.

Discrete Element Modelling of Damage Evolution of Concrete Considering Meso-Structure of ITZ

The mechanical properties of interfacial transition zones(ITZs)have traditionally been simplified by reducing the stiffness of cement in previous simulation methods.A novel approach based on the discrete element method(DEM)has been developed for modeling concrete.This new approach efficiently simulates the meso-structure of ITZs,accurately capturing their heterogeneous properties.Validation against established uniaxial compression experiments confirms the precision of thismodel.The proposedmodel canmodel the process of damage evolution containing cracks initiation,propagation and penetration.Under increasing loads,cracks within ITZs progressively accumulate,culminating in macroscopic fractures that traverse themortarmatrix,forming the complex,serpentine path of cracks.This study reveals four distinct displacement patterns:tensile compliant,tensile opposite,mixed tensile-shear,and shear opposite patterns,each indicative of different stages in concrete’s damage evolution.The widening angle of these patterns delineates the progression of cracks,with the tensile compliant pattern signaling the initial crack appearance and the shear opposite pattern indicating the concrete model’s ultimate failure.

Correlations between mineral composition and mechanical properties of granite using digital image processing and discrete element method

This study investigated the correlations between mechanical properties and mineralogy of granite using the digital image processing(DIP) and discrete element method(DEM). The results showed that the X-ray diffraction(XRD)-based DIP method effectively analyzed the mineral composition contents and spatial distributions of granite. During the particle flow code(PFC2D) model calibration phase, the numerical simulation exhibited that the uniaxial compressive strength(UCS) value, elastic modulus(E), and failure pattern of the granite specimen in the UCS test were comparable to the experiment. By establishing 351 sets of numerical models and exploring the impacts of mineral composition on the mechanical properties of granite, it indicated that there was no negative correlation between quartz and feldspar for UCS, tensile strength(σ_(t)), and E. In contrast, mica had a significant negative correlation for UCS, σ_(t), and E. The presence of quartz increased the brittleness of granite, whereas the presence of mica and feldspar increased its ductility in UCS and direct tensile strength(DTS) tests. Varying contents of major mineral compositions in granite showed minor influence on the number of cracks in both UCS and DTS tests.

Computational fluid dynamics-discrete element method simulation of stirred tank reactor for graphene production

Liquid phase exfoliation(LPE)process for graphene production is usually carried out in stirred tank reactor and the interactions between the solvent and the graphite particles are important as to improve the production efficiency.In this paper,these interactions were revealed by computational fluid dynamics–discrete element method(CFD-DEM)method.Based on simulation results,both liquid phase flow hydrodynamics and particle motion behavior have been analyzed,which gave the general information of the multiphase flow behavior inside the stirred tank reactor as to graphene production.By calculating the threshold at the beginning of graphite exfoliation process,the shear force from the slip velocity was determined as the active force.These results can support the optimization of the graphene production process.

Capability of discrete element method to investigate the macro-micro mechanical behaviours of granular soils considering different stress conditions and morphological gene mutation

Discrete element method(DEM)has been widely utilised to model the mechanical behaviours of granular materials.However,with simplified particle morphology or rheology-based rolling resistance models,DEM failed to describe some responses,such as the particle kinematics at the grain-scale and the principal stress ratio against axial strain at the macro-scale.This paper adopts a computed tomography(CT)-based DEM technique,including particle morphology data acquisition from micro-CT(mCT),spherical harmonic-based principal component analysis(SH-PCA)-based particle morphology reconstruction and DEM simulations,to investigate the capability of DEM with realistic particle morphology for modelling granular soils’micro-macro mechanical responses with a consideration of the initial packing state,the morphological gene mutation degree,and the confining stress condition.It is found that DEM with realistic particle morphology can reasonably reproduce granular materials’micro-macro mechanical behaviours,including the deviatoric stressevolumetric straineaxial strain response,critical state behaviour,particle kinematics,and shear band evolution.Meanwhile,the role of multiscale particle morphology in granular soils depends on the initial packing state and the confining stress condition.For the same granular soils,rougher particle surfaces with a denser initial packing state and a higher confining stress condition result in a higher degree of shear strain localisation.

Effect of heterogeneity on mechanical and micro-seismic behaviors of sandstone subjected to multi-level cyclic loading: A discrete element method investigation

In numerical simulation of the mechanical responses and acoustic emission(AE)characteristics of rocks under cyclic loading,the impacts of compositional heterogeneities of mineral grains have barely been considered.This will lead to a poor reproduction of rock’s behaviors in terms of stress-strain relationship and micro-seismic characteristics in numerical simulation.This work aims to analyze and reveal the impact of parameter heterogeneity on the rock’s fatigue and micro-seismic properties based on PFC3D.Two distribution patterns(uniform and Weibull distributions),are implemented to assign four critical parameters(i.e.tensile strength,cohesion,parallel bond stiffness and linear stiffness)for 32 sets of numerical schemes.The results show that the models with high heterogeneity of tensile strength and cohesion can better reproduce the stress-strain relationship as well as the patterns of cumulative AE counts and energy magnitude.The evolution of the proportion of three-level AE events in the laboratory test is consistent with the numerical results when the highly heterogeneous tensile strength and cohesion are distributed.The numerical results can provide practical guidance to the PFC-based modeling of rock heterogeneity when exposed to multi-level cyclic loading and AE monitoring.

Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations

We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.

Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model

The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.

Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity,geometrical heterogeneity,weak grain boundaries and micro-defects.Microcracks are usually observed in crystalline rocks in two forms:natural and stress-induced;the amount of stressinduced microcracking increases with depth and in-situ stress.Laboratory results indicate that the physical properties of rocks such as strength,deformability,P-wave velocity and permeability are influenced by increase in miciocrack intensity.In this study,the finite-discrete element method(FDEM)is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network(μDFN) approach.The characteristics of the microcracks required to create μDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature.A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-μDFN models indicate that micro-heterogeneity has a profound influence on both the mechanical behavior and resultant fracture pattern.An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope.Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement.Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone,and the frictional strength component remains unaffected.Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks,with a reduction in tensile strength as microcrack intensity increases.The importance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and its effects on the mechanisms leading to spalling damage near an underground opening are also discussed.

Understanding roof deformation mechanics and parametric sensitivities of coal mine entries using the discrete element method

Although conventional coal mine designs are conservative regarding pillar strength,local failures such as roof-falls and pillar bursts still affect mine safety and operations.Previous studies have identified that discontinuous,layered roof materials have some self-supporting capacity.This research is a preliminary step towards understanding these mechanics in coal-measure rocks.Although others have considered broad conceptual models and simplified analogs for mine roof behavior,this study presents a unique numerical model that more completely represents in-situ roof conditions.The discrete element method(DEM)is utilized to conduct a parametric analysis considering a range of in-situ stress ratios,material properties,and joint networks to determine the parameters controlling the stability of single-entries modeled in two-dimensions.Model results are compared to empirical observations of roof-support effectiveness(ARBS)in the context of the coal mine roof rating(CMRR)system.Results such as immediate roof displacement,overall stability,and statistical relationships between model parameters and outcomes are presented herein.Potential practical applications of this line of research include:(1)roof-support optimization for a range of coal-measure rocks,(2)establishment of a relationship between roof stability and pillar stress,and(3)determination of which parameters are most critical to roof stability and therefore require concentrated evaluation.

Numerical investigations on mechanical characteristics and failure mechanism of outwash deposits based on random meso-structures using discrete element method

Outwash deposit is a unique type of geological materials, and its features such as heterogeneity, discontinuity and nonlinearity determine the complexity of mechanical characteristics and failure mechanism. In this work, random meso-structure of outwash deposits was constructed by the technique of computer random simulation based on characteristics of its meso-structure in the statistical sense and some simplifications, and a series of large direct shear tests on numerical samples of outwash deposits with stone contents of 15%, 30%, 45% and 60% were conducted using the discrete element method to further investigate its mechanical characteristics and failure mechanism under external load. The results show that the deformation characteristics and shear strength of outwash deposits are to some extent improved with the increase of stone content, and the shear stress–shear displacement curves of outwash deposits show great differences at the post-peak stage due to the random spatial distribution and content of stones. From the mesoscopic view, normal directions of contacts between "soil" and "stone" particles undergo apparent deflection as the shear displacement continues during the shearing process, accompanying redistribution of the magnitude of contact forces during the shearing process. For outwash deposits, the shear zone formed after shear failure is an irregular stripe due to the movements of stones near the shear zone, and it expands gradually with the increase of stone content. In addition, there is an approximately linear relation between the mean increment of internal friction angle and the stone content lying between 30% and 60%, and a concave nonlinear relation between the mean increment of cohesion and stone content, which are in good agreement with the existing research results.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.

A discrete Boltzmann model with symmetric velocity discretization for compressible flow

A discrete Boltzmann model(DBM) with symmetric velocity discretization is constructed for compressible systems with an adjustable specific heat ratio in the external force field. The proposed two-dimensional(2D) nine-velocity scheme has better spatial symmetry and numerical accuracy than the discretized velocity model in literature [Acta Aerodyn. Sin.40 98108(2022)] and owns higher computational efficiency than the one in literature [Phys. Rev. E 99 012142(2019)].In addition, the matrix inversion method is adopted to calculate the discrete equilibrium distribution function and force term, both of which satisfy nine independent kinetic moment relations. Moreover, the DBM could be used to study a few thermodynamic nonequilibrium effects beyond the Euler equations that are recovered from the kinetic model in the hydrodynamic limit via the Chapman–Enskog expansion. Finally, the present method is verified through typical numerical simulations, including the free-falling process, Sod’s shock tube, sound wave, compressible Rayleigh–Taylor instability,and translational motion of a 2D fluid system.

A review of methods,applications and limitations for incorporating fluid flow in the discrete element method

The past decade has witnessed the substantial growth in research interests and progress on the subject of coupled hydro-mechanical processes in rocks and soils,driven mainly by the surge of research in unconventional hydrocarbon reservoirs and associated hazards.Many coupling techniques have been developed to include the effects of fluid flow in the discrete element method(DEM),and the techniques have been applied to a variety of geomechanical problems.Although these coupling methods have been successfully applied in various engineering fields,no single fluid/DEM coupling method is universal due to the complexity of engineering problems and the limitations of the numerical methods.For researchers and engineers,the key to solve a specific problem is to select the most appropriate fluid/DEM coupling method among these modeling technologies.The purpose of this paper is to give a comprehensive review of fluid flow/DEM coupling methods and relevant research.Given their importance,the availability or unavailability of best practice guidelines is outlined.The theoretical background and current status of DEM are introduced first,and the principles,applications,and advantages and disadvantages of different fluid flow/DEM coupling methods are discussed.Finally,a summary with speculation on future development trends is given.

A new method to simulate irregular particles by discrete element method

Granular materials are ubiquitous in nature and important in various applications such as road and railway engineering. Granular materials exhibit complicated mechanical behaviors, which are affected significantly by the irregular shape of particles. Currently, the discrete element method (DEM) has been accepted as an effective approach to investigate the mechanical behaviors of granular materials. However, there are scarce simulations based on DEM in literatures considering the irregularity of particle shape. A new method is proposed to simulate individual real particle with irregular shape using clump constituted by overlapping spheres. First, the geometric model of real particle with surface nodes and inner nodes is established through digitally processing the computerized tomography (CT) scanning data. Second, a clump consisting of spheres is generated to simulate the real particle using a minimum distance criterion. The criterion is implemented by tree optimization algorithm. Influential factors are also introduced to balance the model accuracy and computing cost. Effects of the influential factors, including the density of geometric grid and the minimum distance, on simulations are discussed. Results show that this new method is simpler and more efficient than the previous methods in terms of the model accuracy and computing cost.

Parallel Computing of Discrete Element Method on GPU

General purpose computing on GPU for scientific computing has been rapidly growing in recent years. We investigate the applicability of GPU to discrete element method (DEM) often used in particle motion simulation. NVIDIA provides a sample code for this type of simulation, which obtained superior performance than CPU in computational time. A computational model of the contact force in NVIDIA’s sample code is, however, too simple to use in practice. This paper modifies the NVIDIA’s simple model by replacing it with the practical model. The computing speed of the practical model on GPU is compared with the simple one on GPU and with the practical one on CPU in numerical experiments. The result shows that the practical model on GPU obtains the computing speed 6 times faster than the practical one on CPU while 7 times slower than that of the simple one on GPU. The effects of the GPU architectures on the computing speed are analyzed.