关于散粒元法物性参数的探讨

一、前言散粒元法(Distinct Element Method,简称DEM)是一九七一年由英国学者Cundall提出而近年来随着计算机的发展受到广泛注目的一种处理不连续体的方法。它将不连续体处理成—个个独立刚体单元的集合。

围压卸载速率对砂岩力学性质影响数值试验研究

【目的】为了排除天然岩石试件离散性与试验过程多种应力路径相互转换对试验结果的叠加影响,进一步探讨围压卸载速率对岩石破坏失稳的影响机理。【方法】利用离散元法开展均质数值试件在恒定轴压与两种固定围压卸载速率条件的数值试验研究,对比与讨论了两种围压卸载速率下的试件宏观与细观力学特性与规律。【结果】结果表明:两种条件下,宏观和细观破裂分布具有一定相似性和规律性,慢速围压卸荷条件较快速条件的试件承载强度更高,快速卸荷条件局部破裂分布密度相对更大。两种卸载速率试验过程出现轴压和围压的“跌落”和“上升”,反映试件经历了多阶段突发式渐进破坏过程,因局部破坏不断累积导致试件向整体失稳方向发展。两种卸载速率条件下的张拉破裂数量显著大于剪切破裂数量,张拉破裂增长速率大于剪切破裂,试件表现为张拉破坏为主,快速卸载条件破裂总数量相对更大。慢速卸载条件相对充分地调动了试件局部承载能力,使试件极限承载能力有所提高。【结论】两种条件下,20次以上声发射事件构成的裂纹分布程度最不均一,随着组成每条裂纹的声发射事件数增加,震级整体逐渐增大,快速卸荷形成裂纹过程总体释放能量相对更高,而慢速卸荷以相对较慢的速率传递应力,使裂纹形成过程释放能量相对更低、平稳且均一。

Virtual rutting test of asphalt mixture using discrete element method

In order to investigate the permanent deformation behavior of asphalt mixtures from discontinuity, the virtual rutting test of asphalt mixtures is developed by the discrete element method （DEM）. A digital specimen generation procedure considering aggregate gradation and irregular shape is developed based on the probability theory and the Monte Carlo method. The virtual rutting test is then conducted based on the generated digital specimen. In addition, on the basis of the time-temperature superposition （TTS） principle, a calculation method is used to reduce the computation time of the virtual rutting test. The simulation results are compared with the laboratory measurements. The results show that the calculation method based on the TFS principle in the discrete element （DE） viscoelastic model can significantly reduce the computation time. The deformation law of asphalt mixtures in the virtual rutting test is similar to the laboratory measurements, and the deformation and the dynamic stability of the virtual rutting test are slightly greater than the laboratory measurements. The two-dimensional virtual rutting test can predict the permanent deformation performance of asphalt mixtures.

Radial mixing and segregation of granular bed bi-dispersed both in particle size and density within horizontal rotating drum

Taking simultaneous variations in both particle volume and density into account, the radial mixing and segregation of binary granular bed in a rotating drum half loaded were investigated by a 3D discrete element method. Then, based on the competition theory of condensation and percolation, radial segregation due to differences in particle volume and/or density was analyzed. The results show that if either percolation effect induced by volume difference or condensation effect induced by density difference dominates in the active layer of moving bed, separation will occur. Controlling the volume ratio or density ratio of the two types of particles can achieve an equilibrium state between percolation and condensation, and then homogenous mixture can be obtained. When the percolation balances with the condensation, the relationship between volume ratioand density ratiopresents nearly a power function. Scaling up a rotating drum will not affect the mixing degree of the granular bed so long as the volume ratio and density ratio are predefined.

Virtual fracture test of asphalt mixture based on discrete element method

In order to study fracture behaviors of asphalt mixtures, virtual tests of the two-dimensional（2D） microstructure based on the discrete element method（ DEM） are designed. The virtual structure of the 2D digital specimen of asphalt mixture is generated based on a particle generation program, in which the gradation and the irregular shapes of aggregates are considered. With the 2D digital specimens, a DEM-based mixture model is established and center-point beam fracture simulation tests are conducted by the DEM. Meanwhile, a series of calibration tests are carried out in laboratory to evaluate the DEM model and validate the methods of virtual fracture tests. The test results indicate that the fracture intensity of asphalt mixtures predicted by the DEM matches very well with the intensity obtained in laboratory. It is concluded that the microstructural virtual tests can be used as a supplemental tool to evaluate fracture properties of asphalt mixtures.

Dynamic response of multi-scale structure in flexible pavement to moving load

In order to study the dynamic responses in the microstructures of the pavement structure, the multi-scale modeling subjected to moving load is analyzed using the discrete element method （DEM）. The macro-scale discrete element model of the flexible pavement structure is established. The stress and strain at the bottom of the asphalt concrete layer under moving load are calculated. The DEM model is validated through comparison between DEM predictions and the results from the classical program. Based on the validated macro-scale DEM model, the distribution and the volumetric fraction of coarse aggregate, mastics and air voids at the bottom of the asphalt layer are modeled, and then the multi-scale model is constructed. The dynamic response in the microstructures of the multi-scale model are calculated and compared with the results from the macro model. The influence of mastic stiffness on the distribution of dynamic response in the microstructures is also analyzed. Results show that the average values and the variation coefficient of the tensile stress at the aggregate-mastic interface are far more than those within the mastics. The dynamic response including stress and strain distributes non-uniformly in both mastics and the interface. An increase in mastic stiffness tends to a uniform distribution of tensile stress in asphalt concrete.

EFFICIENT NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FLEXIBLE ROD HIT BY RIGID BALL

Impact dynamics of flexible solids is important in engineering practice. Obtaining its dynamic response is a challenging task and usually achieved by numerical methods. The objectives of the study are twofold. Firstly, the discrete singular convolution （DSC） is used for the first time to analyze the impact dynamics. Secondly, the efficiency of various numerical methods for dynamic analysis is explored via an example of a flexible rod hit by a rigid ball. Three numerical methods, including the conventional finite element （FE） method, the DSC algorithm, and the spectral finite element （SFE） method, and one proposed modeling strategy, the improved spectral finite element （ISFE） method, are involved. Numerical results are compared with the known analytical solutions to show their efficiency. It is demonstrated that the proposed ISFE modeling strategy with a proper length of con- ventional FE yields the most accurate contact stress among the four investigated models. It is also found that the DSC algorithm is an alternative method for collision problems.

Geo-engineered buffer capacity of two-layered absorbing system under the impact of rock avalanches based on Discrete Element Method

Many rock avalanches were triggered by the Wenchuan earthquake on May 12, 2008 in southwest China. Protection galleries covered with a single soil layer are usually used to protect against rockfall. Since one-layer protection galleries do not have sufficient buffer capacity, a two-layered absorbing system has been designed. This study aims to find whether an expanded poly-styrol （EPS） cushion, which is used in the soil-covered protection galleries for shock absorption, could be positioned under dynamic loadings. The dynamic impacts of the two-layered absorbing system under the conditions of rock avalanches are numerically simulated through a 2D discrete dement method. By selecting reasonable parameters, a series of numerical experiments were conducted to find the best combination for the two- layered absorbing system. The values of the EPS layer area as a percentage of the total area were set as 0% （Sl）, 22~ （S2）, and 70% （$3）. 22~ of the area of the EPS layer was found to be a reasonable value, and experiments were conducted to find the best position of the EPS layer in the two-layered absorbing system. The numerical results yield useful conclusions regarding the interaction between the impacting avalanches and the two-layered absorbing system. The soil layer can absorb the shock energy effectively and S2 （0.4-m thick EPS cushion covered with soil layer） is the most efficient combination, which can reduce the impact force, compared with the other combinations.

Permanent deformation and prediction model of construction and demolition waste under repeated loading

This study aims to reveal the macroscopic permanent deformation(PD)behavior and the internal structural evolution of construction and demolition waste(CDW)under loading.Firstly,the initial matric suction of CDW was measured by the filter paper method.Secondly,the PD of CDW with different humidity and stress states was investigated by repeated load triaxial tests,and a comprehensive prediction model was established.Finally,the discrete element method was performed to analyze the internal structural evolution of CDW during deformation.These results showed that the VAN-GENUCHTEN model could describe the soil-water characteristic curve of CDW well.The PD increases with the increase of the deviator stress and the number of cyclic loading,but the opposite trend was observed when the initial matric suction and confining pressure increased.The proposed model in this study provides a satisfactory prediction of PD.The discrete element method could accurately simulate the macroscopic PD of CDW,and the shear force,interlock force and sliding content increase with the increase of deviator stress during the deformation.The research could provide useful reference for the deformation stability analysis of CDW under cyclic loading.

Discrete Element Modeling of Debris Avalanche Impact on Retaining Walls

In China,gravity retaining walls are widely used as protection structures against rockfalls,debris flows and debris avalanches along the roads in mountainous areas.In this paper,the Discrete Element Method(DEM) has been used to investigate the impact of granular avalanches and debris flows on retaining walls.The debris is modeled as two dimensional circular disks that interact through frictional sliding contacts.The basic equations that control the deformation and motion of the particles are introduced.A series of numerical experiments were conducted on an idealized debris slide impacting a retaining wall.The parametric study has been performed to examine the influences of slope geometry,travel distance of the sliding mass,wall position,and surface friction on the impact force exerted on the wall.Results show that:1) the force achieves its maximum value when slope angle is equal to 60°,as it varies from 30° to 75°;2) an approximate linear relationship between the impact force and the storage area length is determined.

Discrete element approach for mine dump stability analysis

Mine overburden dumps have posed significant safety issues in the operations of various unit operations of open pit min-ing especially the external dumps. The external dumps are composed of a mixture of fragmented rocks and loose soil. Their charac-teristic is comparable to heavily discontinuous solid mass. The conventional approach of limit equilibrium methods provide safety factors for the slope but nothing about the stress-strain characteristics of the large dump mass. The designs of dump location and their respective geometry are integrated for the know-how of the stability characteristics of these dumps. The discrete element method uses a circular disk to represent the granular solid mass and their interactions are described by the Newton’s third law of motion. The displacement is described by the sliding of the circular disk. This work is focused on the modeling efficiency of the discrete element methods to represent the behaviour of mine dump masses with the specified joint plane for the limit equilibrium method. The advantage of the work lies on the ease of information retrieval at any point at the dump mass concerning the stress and strain histories, displacement, failures etc. which when integrated produces a better understanding of the stability of the dump masses.

Unloading responses of pre-flawed rock specimens under different unloading rates

Based on the stress redistribution analysis of rock mass during the deep underground excavation, the unloading process of pre-flawed rock material was simulated by distinct element method (DEM). The effects of unloading rate and flaw inclination angle on unloading strengths and cracking properties of pre-flawed rock specimens are numerically revealed. The results indicate that the unloading failure strength of pre-flawed specimen exhibits a power-function increase trend with the increase of unloading period. Moreover, combined with the stress state analysis on the flaws, it is found that the unloading failure strength increases with the increase of flaw inclination angle. The cracking distribution of pre-flawed specimens under the unloading condition closely depends on the flaw inclination angle, and three typical types of flaw coalescence are observed. Furthermore, at a faster unloading rate, the pre-flawed specimen experiences a sharper and quicker unloading failure process, resulting in more splitting cracks in the specimens.

Continuum and Discrete Element Coupling Approach to Analyzing Seismic Responses of a Slope Covered by Deposits

Numerical analyses of earthquake effects on the deformation, stability, and load transfer of a slope covered by deposits are traditionally based on the assumption that the slope is a continuum. It would be problematic, however, to extend these approaches to the simulation of the slide, collapse and disintegration of the deposits under seismic loading. Contrary to this, a discrete element method （DEM） provides a means to consider large displacement and rotation of the non-continuum. To take the advantages of both methods of continuum and non- continuum analyses, seismic responses of a slope covered by deposits are studied by coupling a twodimensional （a-D） finite difference method and a 2-D DEM, with the bedrock being modelled by the finite difference grids and the deposits being represented by disks. A smooth transition across the boundaries of the continuous/discontinuous domains is obtained by imposing the compatibility condition and equilibrium condition along their interfaces. In the course of computation, the same time-step value is chosen for both continuous and discontinuous domains. The free-field boundaries are adopted for lateral grids of bedrock domain to eliminate the radiation damping effect. When the static equilibrium under gravity load is obtained, dynamic calculation begins under excitation of the seismic wave input from the continuum model bottom. In this way, responses to the earthquake of a slope covered by deposits are analyzed dynamically. Combined with field monitoring data, deformation and stability of the slope are discussed. The effects of the relevant parameters of spectrum characteristic, duration, andpeak acceleration of seismic waves are further investigated and explained from the simulations.

NUMERICAL ANALYSIS OF SOIL PLUG INSIDE SUCTION FOUNDATIONS DURING SUCTION PENETRATION BY DISCRETE ELEMENT METHOD

The phenomenon of the soil plug usually rising inside the suction foundations during suction penetration was quantitatively described and predicted. The formation process of the soil plug was simulated and calculated by DEM （discrete element method） model. The seepage flow, the self-weight of soil, the friction on the chamber wall as well as the suction inside the chamber are considered as the main external forces in the process. The results are compared with a set of laboratory model tests performed by using three soil types （sand, silty clay and clay） in the Bohai Sea area. The heights of soil plug from numerical estimations are lower than those from model test results, mainly because the suction pressure and friction resistance are applied in an ideal way under the numerical simulation.

Mechanical behavior and deformation mechanism of ballast bed with various fouling materials

In order to study the interaction between various fouling particles and ballast,a multi-layer and multi-scale discrete element model(DEM)including the sleeper,ballast bed and the surface layer of subgrade was developed.Two typical fouling particles,the hard particles(sand)and soft ones(coal fines),are considered.A support stiffness test of the ballast bed under various fouling conditions was conducted to calibrate the microscopic parameters of the contact model.With the model,the influence of fouling particles on the mechanical behavior and deformation of the ballast bed was analyzed from macro and micro perspectives.The results show that the increase in the strength of the fouling particles enlarges the stiffness of the ballast bed.Hard particles increase the uniformity coefficient of the contact force bondγof ballast by 50.4%.Fouling particles increase the average stress in the subgrade,soft particles by 2 kPa and hard particles by 1 kPa.Hard particles can reduce the elasticity,plastic deformation and energy dissipation in the track structure.As the fouling particle changes from hard to soft,the proportion of the settlement in ballast bed increases to 40.5%and surface layer of swbgrade settlement decreases to 59.5%.Thus,the influence of fouling particles should be considered carefully in railway design and maintenance.

Effects of confining pressure on deformation failure behavior of jointed rock

For a deeper understanding of the deformation failure behavior of jointed rock, numerical compression simulations are carried out on a rock specimen containing non-persistent joints under confining pressure with the bondedparticle model. The microscopic parameters which can reflect the macroscopic mechanical properties and failure behavior of artificial jointed specimens are firstly calibrated. Then, the influence of joint inclination and confining pressure on stress-strain curves, crack patterns, and contact force distributions of jointed rock are investigated. The simulation results show that both the compressive strength and elastic modulus of the specimens increase with increasing confining pressure, and these two mechanical parameters decrease first and then increase with the increase of joints inclination. The sensitivity of strength and elastic modulus to confining pressure is not the same in different joints inclinations, which has the least impact on specimens with α=90°. Under low confining pressure, the failure modes are controlled by the joint inclination. As the confining pressure increased, the initiation and propagation of tensile crack are gradually inhibited, and the failure mode is transferred from tensile failure to shear-compression failure. Finally, the reinforcement effect of prestressed bolt support on engineering fractured rock mass is discussed.

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.

Discrete element simulation of mechanical characteristic of conditioned sands in earth pressure balance shield tunneling

The discrete element method (DEM) was used to simulate the flow characteristic and strength characteristic of the conditioned sands in the earth pressure balance (EPB) tunneling. In the laboratory the conditioned sands were reproduced and the slump test and the direct shear test of the conditioned sands were implemented. A DEM equivalent model that can simulate the macro mechanical characteristic of the conditioned sands was proposed,and the corresponding numerical models of the slump test and the shear test were established. By selecting proper DEM model parameters,the errors of the slump values between the simulation results and the test results are in the range of 10.3%-14.3%,and the error of the curves between the shear displacement and the shear stress calculated with the DEM simulation is 4.68%-16.5% compared with that of the laboratory direct shear test. This illustrates that the proposed DEM equivalent model can approximately simulate the mechanical characteristics of the conditioned sands,which provides the basis for further simulation of the interaction between the conditioned soil and the chamber pressure system of the EPB machine.

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 method of improved performance of railway ballast bed using elastic sleeper

With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method(DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.