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.

Discrete element modeling of migration and evolution rules of coarse aggregates in the static compaction process

To investigate migration and evolution rules of coarse aggregates in the static compaction process, an algorithm of generating digital coarse aggregates that can reflect real morphology（ such as shape, size and fracture surface） of aggregate particles, is represented by polyhedral particles based on the discrete element method（ DEM）. A digital specimen comprised of aggregates and air voids is developed. In addition,a static compaction model consisting of a digital specimen and three plates is constructed and a series of evaluation indices such as mean contact force σMCF, wall stress in direction of zcoordinate σWSZZ, porosity and coordination numbers are presented to investigate the motion rules of coarse aggregates at different compaction displacements of 7. 5, 15 and 30 mm. The three-dimensional static compaction model is also verified with laboratory measurements. The results indicate that the compaction displacements are positively related to σMCF and σWSZZ, which increase gradually with the increase in iterative steps. When the compaction proceeds, the digital specimen porosity decreases, but the coordination number increases. The variation ranges of these four indices are different at different compaction displacements. This study provides a method to analyze the compaction mechanism of particle materials such as asphalt mixture and graded broken stone.

A modified discrete element model for sea ice dynamics

Considering the discontinuous characteristics of sea ice on various scales,a modified discrete element model（DEM） for sea ice dynamics is developed based on the granular material rheology.In this modified DEM,a soft sea ice particle element is introduced as a self-adjustive particle size function.Each ice particle can be treated as an assembly of ice floes,with its concentration and thickness changing to variable sizes under the conservation of mass.In this model,the contact forces among ice particles are calculated using a viscous-elastic-plastic model,while the maximum shear forces are described with the Mohr-Coulomb friction law.With this modified DEM,the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths.The thicknesses,concentrations and velocities of ice particles are obtained,and then reasonable dynamic process is analyzed.The sea ice dynamic process is also simulated in a vortex wind field.Taking the influence of thermodynamics into account,this modified DEM will be improved in the future work.

Evaluating the mechanical properties of anisotropic shale containing bedding and natural fractures with discrete element modeling

Natural fracture data from one of the Carboniferous shale masses in the eastern Qaidam Basin were used to establish a stochastic model of a discrete fracture network and to perform discrete element simulation research on the size efect and mechanical parameters of shale.Analytical solutions of fctitious joints in transversely isotropic media were derived,which made it possible for the proposed numerical model to simulate the bedding and natural fractures in shale masses.The results indicate that there are two main factors infuencing the representative elementary volume(REV)size of a shale mass.The frst and most decisive factor is the presence of natural fractures in the block itself.The second is the anisotropy ratio:the greater the anisotropy is,the larger the REV.The bedding angle has little infuence on the REV size,whereas it has a certain infuence on the mechanical parameters of the rock mass.When the bedding angle approaches the average orientation of the natural fractures,the mechanical parameters of the shale blocks decrease greatly.The REV representing the mechanical properties of the Carboniferous shale masses in the eastern Qaidam Basin were comprehensively identifed by considering the infuence of bedding and natural fractures.When the numerical model size is larger than the REV,the fractured rock mass discontinuities can be transformed into equivalent continuities,which provides a method for simulating shale with natural fractures and bedding to analyze the stability of a borehole wall in shale.

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.

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method(DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil(e.g. cavity expansion),DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response.Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model,and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation(i.e. cavity expansion), a minimum distance of11 a(a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.

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.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Multi-scale Simulation Method with Coupled Finite/Discrete Element Model and Its Application

The existing research on continuous structure is usually analyzed with finite element method (FEM) and granular medium with discrete element method (DEM), but there are few researches on the coupling interaction between continuous structure and discrete medium. To the issue of this coupling interaction, a multi-scale simulation method with coupled finite/discrete element model is put forward, in their respective domains of discrete and finite elements, the nodes follow force law and motion law of their own method, and on the their interaction interface, the touch type between discrete and finite elements is distinguished as two types: full touch and partial touch, the interaction force between them is calculated with linear elastic model. For full touch, the contact force is proportional to the overlap distance between discrete element and finite element patch. For partial touch, first the finite element patch is extended on all sides indefinitely to be a complete plane, the full contact force can be obtained with the touch type between discrete element and plane being viewed as full touch, then the full overlap area between them and the actual overlap area between discrete element and finite element patch are computed, the actual contact force is obtained by scaling the full contact force with a factor which is determined by the ratio of the actual overlap area to the full overlap area. The contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the ideal simulation results can be got. This method has been used to simulate the cutter disk of the earth pressure balance shield machine (EPBSM) made in North Heavy Industry (NHI) with its excavation diameter of 6.28 m cutting and digging the sandy clay layer. The simulation results show that as the gradual increase of excavating depth of the cutter head, the maximum stress occurs at the roots of cutters on the cutter head, while for the soil, the largest stress is distributed at the region which directly contacted with the cutters. The proposed research can provide good solutions for correct design and installation of cutters, and it is necessary to design mounting bracket to fix cutters on cutter head.

Isotropic compression behavior of granular assembly with non-spherical particles by X-ray micro-computed tomography and discrete element modeling

The particle morphological properties,such as sphericity,concavity and convexity,of a granular assembly significantly affect its macroscopic and microscopic compressive behaviors under isotropic loading condition.However,limited studies on investigating the microscopic behavior of the granular assembly with real particle shapes under isotropic compression were reported.In this study,X-ray computed tomography(mCT)and discrete element modeling(DEM)were utilized to investigate isotropic compression behavior of the granular assembly with regard to the particle morphological properties,such as particle sphericity,concavity and interparticle frictions.The mCT was first used to extract the particle morphological parameters and then the DEM was utilized to numerically investigate the influences of the particle morphological properties on the isotropic compression behavior.The image reconstruction from mCT images indicated that the presented particle quantification algorithm was robust,and the presented microscopic analysis via the DEM simulation demonstrated that the particle surface concavity significantly affected the isotropic compression behavior.The observations of the particle connectivity and local void ratio distribution also provided insights into the granular assembly under isotropic compression.Results found that the particle concavity and interparticle friction influenced the most of the isotropic compression behavior of the granular assemblies.

Research regarding coal-bed wellbore stability based on a discrete element model

Wellbore instability is a key problem restricting efficient production of coal-bed methane. In order to perform thorough and systematic research regarding coal-bed wellbore stability problems, a new discrete element model which fully considers the features of cleat coal-beds is established based on the Kirsch equation. With this model, the safe pipe tripping speed, drilling fluid density window and coal- bed collapse/fracture pressure are determined; in addition, the relationships between pipe tripping speed and pipe size, cleat size, etc. and wellbore stability are analyzed in the coal-bed drilling and pipe tripping processes. The case studies show the following results： the wellbore collapses （collapse pressure： 4.33 MPa） or fractures （fracture pressure： 12.7 MPa） in certain directions as a result of swab or surge pressure when the pipe tripping speed is higher than a certain value; the cleat face size has a great influence on wellbore stability, and if the drilling fluid pressure is too low, the wellbore is prone to collapse when the ratio of the face cleat size to butt cleat size is reduced; however, if the drilling fluid pressure is high enough, the butt cleat size has no influence on the wellbore fracture; the factors influencing coal-bed stability include the movement length, pipe size, borehole size.

Numerical Analysis of Ice Rubble with a Freeze-Bond Model in Dilated Polyhedral Discrete Element Method

Freezing in ice rubble is a common phenomenon in cold regions,which can consolidate loose blocks and change their mechanical properties.To model the cohesive effect in frozen ice rubble,and to describe the fragmentation behavior with a large external forces exerted,a freeze-bond model based on the dilated polyhedral discrete element method(DEM)is proposed.Herein,imaginary bonding is initialized at the contact points to transmit forces and moments,and the initiation of the damage is detected using the hybrid fracture model.The model is validated through the qualitative agreement between the simulation results and the analytical solution of two bonding particles.To study the effect of freeze-bond on the floating ice rubble,punch-through tests were simulated on the ice rubble under freezing and nonfreezing conditions.The deformation and resistance of the ice rubble are investigated during indenter penetration.The influence of the internal friction coefficient on the strength of the ice rubble is determined.The results indicate that the proposed model can properly describe the consolidated ice rubble,and the freeze-bond effect is of great significance to the ice rubble properties.

A modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials.The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape.In this study,three dimentional(3D)modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles.The contact volumebased energy-conserving model is used to realize the contact detection between irregularly shaped particles,and the contact force model is refined and modified to describe the contact under real conditions.The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode.In addition,the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method(DEM)to illustrate the applicability of the method of complex problems.

Discrete Element Modeling of Tangjiagou Two-Branch Rock Avalanche Triggered by the 2013 Lushan MW6.6 Earthquake,China

Two branches of Tangjiagou rock avalanche were triggered by Lushan earthquake in Sichuan Province,China on April 20th,2013.The rock avalanche has transported about 1500000 m3 of sandstone from the source area.Based on discrete element modeling,this study simulates the deformation,failure and movement process of the rock avalanche.Under seismic loading,the mechanism and process of deformation,failure,and runout of the two branches are similar.In detail,the stress concentration occur firstly on the top of the mountain ridge,and accordingly,the tensile deformation appears.With the increase of seismic loading,the strain concentration zone extends in the forward and backward directions along the slipping surface,forming a locking segment.As a result,the slipping surface penetrates and the slide mass begin to slide down with high speed.Finally,the avalanche accumulates in the downstream and forms a small barrier lake.Modeling shows that a number of rocks on the surface exhibit patterns of horizontal throwing and vertical jumping under strong ground shaking.We suggest that the movement of the rock avalanche is a complicated process with multiple stages,including formation of the two branches,high-speed sliding,transformation into debris flows,further movement and collision,accumulation,and the final steady state.Topographic amplification effects are also revealed based on acceleration and velocity of special monitoring points.The horizontal and vertical runout distances of the surface materials are much greater than those of the internal materials.Besides,the sliding duration is also longer than that of the internal rock mass.

Simulation of a Laboratory Scale Ball Mill via Discrete Element Method Modelling

Discrete Element Method (DEM) is a powerful tool for simulating different types of mills. It also used for computing different types of particles such as rocks, grains, and molecules. DEM has been widely used in the field of rock mechanics. In the present work, DEM approach is applied to model the milling media (powder particles and balls) inside a planetary ball mill and to estimate the distribution of particles of a dry powder during milling. In fact, the efficiency of the DEM strongly depends on the input parameters. The DEM simulation results indicated that DEM is a promising tool for the simulation of the dynamic particles motion and interactions within planetary ball mill. These results could be utilized to further develop the synthesis performance, anticipate the reaction, and reduce the wear in the dry milling reactions.

Discrete Element Modeling of a Subduction Zone with a Seafloor Irregularity and its Impact on the Seismic Cycle

Seafloor irregularities influence rupture behavior along the subducting slab and in the overriding plate,thus affecting earthquake cycles.Whether seafloor irregularities increase the likelihood of large earthquakes in a subduction zone remains contested,partially due to focus put either on fault development or on rupture pattern.Here,we simulate a subducting slab with a seafloor irregularity and the resulting deformation pattern of the overriding plate using the discrete element method.Our simulations illustrate the rupture along three major fault systems:megathrust,splay and backthrust faults.Our results show different rupture dimensions of earthquake events varying from tens to ca.140 km.Our results suggest that the recurrence interval of megathrust events with rupture length of ca.100 km is ca.140 years,which is overall comparable to the paleoseismic records at the Mentawai area of the Sumatran zone.We further propose the coseismic slip amounts decrease and interseismic slip amounts increase from the surface downwards gradually.We conclude that the presence of seafloor irregularities significantly affects rupture events along the slab as well as fault patterns in the overriding plate.

Modeling calving process of glacier with dilated polyhedral discrete element method

Mass loss caused by glacier calving is one of the direct contributors to global sea level rise.Reliable calving laws are required for accurate modelling of ice sheet mass balance.Both continuous and discontinuous methods have been used for glacial calving simulations.In this study,the discrete element method(DEM)based on dilated polyhedral elements is introduced to simulate the calving process of a tidewater glacier.Dilated polyhedrons can be obtained from the Minkowski sum of a sphere and a core polyhedron.These elements can be utilized to generate a continuum ice material,where the interaction force between adjacent elements is modeled by constructing bonds at the joints of the common faces.A hybrid fracture model considering fracture energy is introduced.The viscous creep behavior of glaciers on long-term scales is not considered.By applying buoyancy and gravity to the modelled glacier,DEM results show that the calving process is caused by cracks which are initialized at the top of the glacier and spread to the bottom.The results demonstrate the feasibility of using the dilated polyhedral DEM method in glacier simulations,additionally allowing the fragment size of the breaking fragments to be counted.The relationship between crack propagation and internal stress in the glacier is analyzed during calving process.Through the analysis of the Mises stress and the normal stress between the elements,it is found that geometric changes caused by the glacier calving lead to the redistribution of the stress.The tensile stress between the elements is the main influencing factor of glacier ice failure.In addition,the element shape,glacier base friction and buoyancy are studied,the results show that the glacier model based on the dilated polyhedral DEM is sensitive to the above conditions.

Identification of the Discrete Element Model Parameters for Rock-Like Brittle Materials

An inverse method for parameters identification of discrete element model combined with experiment is proposed.The inverse problem of parameter identification is transmitted to solve an optimization problem by minimizing the distance between the numerical calculations and experiment responses.In this method,the discrete element method is employed as numerical calculator for the forward problem.Then,the orthogonal experiment design with range analysis was used to carry out parameters sensitivity analysis.In addition,to improve the computational efficiency,the approximate model technique is used to replace the actual computational model.The intergeneration projection genetic algorithm(IP-GA)is employed as the optimization algorithm.Consequently,the parameters of the discrete element model are determined.To verify the effectiveness and accuracy of the inverse results,the comparisons of shape deviation experiments with discrete element simulations are provided.It indicates that the effective and reliable discrete element model parameters can be quickly obtained through several sets of experimental data.Hence,this inverse method can be applied more widely to determine the parameters of discrete element model for other materials.

3D random Voronoi grain-based models for simulation of brittle rock damage and fabric-guided micro-fracturing

A grain-based distinct element model featuring three-dimensional （3D） Voronoi tessellations （randompoly-crystals） is proposed for simulation of crack damage development in brittle rocks. The grainboundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rockand allow for numerical replication of crack damage progression through initiation and propagation ofmicro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the pastfor brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi modelshas limited its application to two-dimensional （2D） codes. The proposed approach is implemented inNeper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files thatcan be read directly into 3DEC. A series of Unconfined Compressive Strength （UCS） tests are simulated in3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate therelationship between each micro-parameter and the model＇s macro-response. The possibility of numericalreplication of the classical U-shape strength curve for anisotropic rocks is also investigated innumerical UCS tests by using complex-shaped （elongated） grains that are cemented to one another alongtheir adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models foraccurate replication of the mechanical behaviour of isotropic and anisotropic （containing a fabric） rocks. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

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.