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.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

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.

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.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

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.

A Study on the Physical Properties of Banana Straw Based on the Discrete Element Method

To improve the application of discrete element models(DEM)to the design of agricultural crushers,in this study a new highly accurate model is elaborated.The model takes into account the fiber structure,porous nature of the material and the leaf sheath coating structure.Dedicated experimental tests are conducted to determine the required“intrinsic”and basic contact parameters of the considered banana straw materials.A large number of bonding parameters are examined in relation to the particle aggregation model in order to characterize different actual banana straws.Using the particle surface energy contact model,the viscosity characteristics of the crushed material are determined together with the related stacking angle(considered as the main response factor).Through single factor experiment analysis,it is found that when the surface energy is 0.9 J·m-2,the relative error between simulations and physical experiments is 5.288%.

A Consistent Time Level Implementation Preserving Second-Order Time Accuracy via a Framework of Unified Time Integrators in the Discrete Element Approach

In this work,a consistent and physically accurate implementation of the general framework of unified second-order time accurate integrators via the well-known GSSSS framework in the Discrete Element Method is presented.The improved tangential displacement evaluation in the present implementation of the discrete element method has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process in calculating the algorithmic tangential displacement.Several numerical examples have been used to validate the proposed tangential displacement evaluation;this is in contrast to past practices which only seem to attain the first-order time accuracy due to inconsistent time level implementation with different algorithms for normal and tangential directions.The comparisons with the existing implementation and the superiority of the proposed implementation are given in terms of the convergence rate with improved numerical accuracy in time.Moreover,several schemes via the unified second-order time integrators within the framework of the GSSSS family have been carried out based on the proposed correct implementation.All the numerical results demonstrate that using the existing state-of-the-art implementation reduces the time accuracy to be first-order accurate in time,while the proposed implementation preserves the correct time accuracy to yield second-order.

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.

GPU-Based Simulation of Dynamic Characteristics of Ballasted Railway Track with Coupled Discrete-Finite Element Method

Considering the interaction between a sleeper,ballast layer,and substructure,a three-dimensional coupled discrete-finite element method for a ballasted railway track is proposed in this study.Ballast granules with irregular shapes are constructed using a clump model using the discrete element method.Meanwhile,concrete sleepers,embankments,and foundations are modelled using 20-node hexahedron solid elements using the finite element method.To improve computational efficiency,a GPU-based(Graphics Processing Unit)parallel framework is applied in the discrete element simulation.Additionally,an algorithm containing contact search and transfer parameters at the contact interface of discrete particles and finite elements is developed in the GPU parallel environment accordingly.A benchmark case is selected to verify the accuracy of the coupling algorithm.The dynamic response of the ballasted rail track is analysed under different train speeds and loads.Meanwhile,the dynamic stress on the substructure surface obtained by the established DEM-FEM model is compared with the in situ experimental results.Finally,stress and displacement contours in the cross-section of the model are constructed to further visualise the response of the ballasted railway.This proposed coupling model can provide important insights into high-performance coupling algorithms and the dynamic characteristics of full scale ballasted rail tracks.

Discrete element modeling of ice loads on ship hulls in broken ice fields

Ice loads on a ship hull affect the safety of the hull structure and the ship maneuvering performance in ice-covered regions. A discrete element method （DEM） is used to simulate the interaction between drifting ice floes and a moving ship. The pancake ice floes are modelled with three-dimensional （3-D） dilated disk elements considering the buoyancy, drag force and additional mass induced by the current. The ship hull is modelled with 3D disks with overlaps. Ice loads on the ship hull are determined through the contact detection between ice floe element and ship hull element and the contact force calculation. The influences of different ice conditions （current velocities and directions, ice thicknesses, concentrations and ice floe sizes） and ship speeds are also examined on the dynamic ice force. The simulated results are compared qualitatively well with the existing field data and other numerical results. This work can be helpful in the shil3 structure design and the navigation securitv in ice-covered fields.

Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method (FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory (URL) Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks (DFNs) of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.

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.

PARALLEL ANALYSIS OF COMBINED FINITE/DISCRETE ELEMENT SYSTEMS ON PC CLUSTER

A computational strategy is presented for the nonlinear dynamic analysis of large- scale combined finite/discrete element systems on a PC cluster.In this strategy,a dual-level domain decomposition scheme is adopted to implement the dynamic domain decomposition.The domain decomposition approach perfectly matches the requirement of reducing the memory size per processor of the calculation.To treat the contact between boundary elements in neighbouring subdomains,the elements in a subdomain are classified into internal,interfacial and external elements.In this way,all the contact detect algorithms developed for a sequential computation could be adopted directly in the parallel computation.Numerical examples show that this implementation is suitable for simulating large-scale problems.Two typical numerical examples are given to demonstrate the parallel efficiency and scalability on a PC cluster.

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.

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.

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.

Discrete element crowd model for pedestrian evacuation through an exit

A series of accidents caused by crowds within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on the discrete element method, a granular dynamic model, in which the human body is simplified as a self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of the human body is simulated by applying the second Newton＇s law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, the clogging phenomenon occurs more easily when the desired velocity is high and the exit may as a result be totally blocked at a desired velocity of 1.6 m/s or above, leading to faster-to-frozen effect.