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.

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.

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.

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.

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.

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%.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.

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.

Discrete element method analysis of lateral resistance of fouled ballast bed

The lateral resistance of sleeper plays an important role in ensuring the stability of a railway track, which may change in the operation of railway, due to the fouling in the ballast bed. In this work, discrete element method was adopted to investigate the effect of fouling on the lateral resistance of sleeper. The shape information of ballast was captured by method of three-dimensional vision reconstruction. In order to calibrate the mechanical parameters and verify the models, a lateral resistance field test was carried out by using a custom-made device. The contact force distributions in the different parts of sleeper as well as the interaction between ballast and sleeper were discussed in depth. The results show that fouling of ballast bed evidently reduces the lateral resistance of sleeper and the decreasing degree is also related to the fouled position of ballast bed, in the order of shoulder > bottom > side.Therefore, the effect of fouling, especially the fouling in the ballast shoulder, on the lateral resistance of sleeper, should be taken into account in ballast track maintenance work.

A review of discrete modeling techniques for fracturing processes in discontinuous rock masses

The goal of this review paper is to provide a summary of selected discrete element and hybrid finitediscrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations.

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.

Discrete element method for adhesion properties evaluation of deep-sea sediment from macro and micro perspectives

The adhesion between the mining machine and the deep-sea sediments will significantly affect the driving performance of the mining machine in the deep-sea environment.When the mining machine and the deep-sea sediment interaction simulation was carried out,the accuracy of the particle interaction parameters will directly affect the simulation results.This study proposed a method to systematically calibrate the interaction parameters between deep-sea sediment and grouser through the combination of experiment and simulation.The uniaxial compression test and macro adhesion test and corresponding discrete element numerical simulation were carried out,modifying the contact parameters until the simulation results are close to the experimental results.Then the micro-parameters of the JKR adhesion contact model were back calibrated with the test results,and the contact parameters between soil particle-soil particle and soil particle-metal are calibrated.Besides,the adhesion test shows that the adhesion forces were ranked in the order of 5052<STi80<TA2<TC4 under the same surface roughness,which indicates the aluminum alloy 5052 has the best anti-adhesion performance.The relationship between surface adhesion force and microscopic contact parameters was studied by discrete element numerical simulation,and the result shows that the coefficient of static friction and the coefficient of rolling friction has little effect on adhesion force.While it is mainly affected by the coefficient of restitution and surface energy,the surface adhesion force tends to decrease with the increase of the coefficient of restitution and increase with the growth of surface energy.The obtained parameters of soil particle to soil particle and soil particle to metal affecting the adhesion can contribute to the design optimization for the grouser of mining machines to decrease surface adhesion and enhance its movability and mining efficiency.

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.

Optimized design of a linear vibrating screen based on efficiency maximisation and mesh wear minimisation employing discrete element method

This article investigates the combined effect and the order of influence of feed rate,inclination angle,vibration amplitude,frequency,and angle on the efficiency and mesh wear rate of a linear vibrating screen,as well as the average velocity,and mass of the accumulated particles.The discrete element modeling simulations were conducted using LIGGGHTS open-source code to analyze particles behaviour.The Taguchi method was employed to evaluate the combined effect of the parameters.Finally,the simulation results were analyzed using analysis of variance.The optimal values of the parameters for maximising efficiency and minimising mesh wear were determined using grey relational analysis.The results indicated that the most effective parameters on screening efficiency and average velocity of particles were the inclination angle,vibration angle,frequency,amplitude,and feed rate,respectively.The most influential parameters on screen mesh wear rate were feed rate,inclination angle,vibration angle,frequency,and amplitude,respectively.

Mechanism of cross-level settlements and void accumulation of wide and conventional sleepers in railway ballast

The cross-level and twist irregularities are the most dangerous irregularity types that could cause wheel unloading with the risk of derailments and additional maintenance expenses.However,the mechanism of the irregularities initiation and development is unclear.The motivation of the present study was the previous experimental studies on the application of wide sleepers in the ballasted track.The long-term track geometry measurements with wide sleepers show an enormous reduction of the vertical longitudinal irregularities compared to the conventional track.However,wide sleepers had higher twist and cross-section level irregularities.The present paper aims to explain the phenomenon by discrete element method(DEM)modeling the development process of sleeper inhomogeneous support at cross-level depending on the sleeper form.The DEM simulations show that the maximal settlement intensity is up to 3.5 times lower for a wide sleeper in comparison with the conventional one.Nevertheless,the cross-level differential settlements are almost the same for both sleepers.The particle loading distribution after all loading cycles is concentrated on the smaller area,up to the half sleeper length,with fully unloaded zones under sleeper ends.Ballast flow limitation under the central part of the sleeper could improve the resilience of wide sleepers to the development of cross-level irregularities.The mechanism of initiation of the cross-level irregularity is proposed,which assumes the loss of sleeper support under sleeper ends.The further growth of inhomogeneous settlements along the sleeper is assumed as a result of the interaction of two processes:ballast flow due to dynamic impact during void closing and on the other side high pressure due to the concentration of the pressure under the middle part of the sleeper.The DEM simulation results support the assumption of the mechanism and agree with the experimental studies.

High-temperature Creep Behavior Characterization of Asphalt Mixture based on Micromechanical Modeling and Virtual Test

The high-temperature creep behavior of asphalt mixture was investigated based on micromechanical modeling and virtual test by using three-dimensional discrete element method（DEM）. A user-defined micromechanical model of asphalt mixture was established after analyzing the irregular shape and gradation of coarse aggregates, the viscoelastic property of asphalt mastic, and the random distribution of air voids within the asphalt mixture. Virtual uniaxial static creep test at 60 ℃ was conducted by using Particle Flow Code in three dimensions（PFC3D） and was validated by laboratory test. Based on virtual creep test, the micromechanical characteristics between aggregates, within asphalt mastic, and between aggregate and asphalt mastic were analyzed for the asphalt mixture. It is proved that the virtual test based on the micromechanical model can efficiently predict the creep deformation of asphalt mixture. And the high-temperature behavior of asphalt mixture was characterized from micromechanical perspective.

Evaluation of soil fabric using elastic waves during load-unload

It is essential to assess the evolution of soil fabric as it has an important role in the mechanical responses of soils during complex loading conditions.This contribution carries out the physical experiments using three granular materials in the laboratory.The variations of compression and shear wave velocities(Vp and Vs)are investigated during load-unload cycles under dry and drained conditions.Supplementary discrete element method(DEM)simulations are performed to understand the evolution of soil fabric during the equivalent load-unload cycles using spherical particles.Vp and Vs are not always reversible even though the stress state regains its isotropic condition after unload,indicating that Vp and Vs are governed by not only the stress state but also the fabric change.The variations of Vp/Vs are density-and stress-dependent;a higher level of stress ratio(s01/s03)threshold is observed for denser packings to trigger a significant change in wave velocity ratio(Vp/Vs)for experimental results using spherical glass beads and simulation data using spherical particles.Considering the particle shape,a higher s01/s03 threshold is found for more angular particles than rounded particles.The DEM result reveals that Vp/Vs of spherical particles can be correlated linearly with the evolution of fabric ratio(Fver/Fhor)during loadunload in a pre-peak range under dry and drained conditions.

Experimental and numerical investigation of Weibullian behavior of grain crushing strength

The Weibullian behavior of single grain crushing strength was investigated experimentally and numerically with the aim of enhancing the understanding of rock grain breakage.The morphologies of pebble grains were obtained using white light 3D laser scanning and image processing.A grain shape library was constructed for grain shape analysis with different shape descriptors.The use of the shape library and grain stability analysis is discussed for a suggested procedure to rotate a grain to its most stable configuration.Single grain crushing tests were performed for 30 pebbles to obtain force-displacement curves and fracture patterns.Each grain was compressed diametrically between flat platens.As expected,the values of the stress at bulk fracture follow a Weibull distribution.A procedure for generating crushable agglomerates with realistic particle shapes was demonstrated,which was accomplished in the discrete element modeling(DEM)of the single grain crushing test.The work presented here is novel in that both the heterogeneous micro-structures and randomly distributed flaws are considered.The DEM results demonstrate that the proposed modeling approach and calibrated parameters are reliable and can reflect the crushing behavior of rock pebbles.Finally,three parametric studies were presented evaluating the effects of micro-crack density,micro-crack disorder,and grain morphology on the Weibullian behavior of the crushing strength,none of which has previously been thoroughly considered.These three studies provide a deeper insight into the origin of the Weibullian behavior of single grain crushing strength.

Discrete element method simulation of disc type furrow openers in paddy soil

For granular materials,discrete element modeling is one of the best computer tools to simulate their behavior and interactions.A field experiment was carried out to evaluate the performance of disc furrow openers in paddy soil.Discrete element simulation was done to develop a 3D DEM model for notched,toothed and double disc furrow openers using EDEM software.Hertz Mindlin contact model with bonding was applied for simulation to fulfill the obligations of the soil moisture and bonding between the cohesive particles.Simulated and field experimental data were compared to determine the applicability in the different working conditions.The results of the simulation validated the applicability of the Hertz-Mindlin contact model with bonding to simulate the no till paddy soil using an extremely narrow tillage tool.The calibrated value of normal and shear stiffness was 5×10^(7)N/m,and the calibrated value of bond normal and shear strength was 3×10^(7)Pa.The relative error(-1.7%to 20.6%)for the double disc furrow opener was lower as compared with that notch typed(29.2%to 44.4%)and toothed type(31.5%to 45.9%)furrow openers.

Experimental and Numerical Investigation of Stress Condition in Unstable Soil

In unstable soils, a special erosion process termed suffusion can occur under the effect of relatively low hydraulic gradient. The critical hydraulic gradient of an unstable soil is smaller than in stable soils, which is described by a reduction factor α. According to a theory of Skempton and Brogan (1994) [1], this reduction factor is related to the stress conditions in the soil. In an unstable soil, the average stresses acting in the fine portion are believed to be smaller than the average stresses in the coarse portion. It is assumed that the stress ratio and the reduction factor for the hydraulic gradient are almost equal. In order to prove this theory, laboratory tests and discrete element modelings are carried out. Models of stable and unstable soils are established, and the stresses inside the sample are analysed. It is found that indeed in unstable soils the coarse grains are subject to larger stresses. The stress ratios in stable soils are almost unity, whereas in unstable soils smaller stress ratios, which are dependent on the soil composition and on the relative density of the soil, are obtained. A comparison between the results of erosion tests and numerical modeling shows that the stress ratios and the reduction factors are strongly related, as assumed by Skempton and Brogan (1994) [1].