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.

IN-PLANE WAVE MOTION IN FINITE ELEMENT MODEL

The analysis method of lattice dynamics in classical physics is extended to study the properties of in-plane wave motion in the hybrid-mass finite element model in this paper. The dispersion equations of P and SV waves in the discrete model are first obtained by means of separating the characteristic equation of the motion equation, and then used to analyse the properties of P-and SV-homogeneous, inhomogeneous waves and other types of motion in the model. The dispersion characters, cut-off frequencies of P and SV waves, the polarization drift and appendent anisotropic property of wave motion caused by the discretization are finally discussed.

Multiscale Hybrid-Mixed Finite Element Method for Flow Simulation in Fractured Porous Media

The multiscale hybrid-mixed(MHM)method is applied to the numerical approximation of two-dimensional matrix fluid flow in porous media with fractures.The two-dimensional fluid flow in the reservoir and the one-dimensional flow in the discrete fractures are approximated using mixed finite elements.The coupling of the two-dimensional matrix flow with the one-dimensional fracture flow is enforced using the pressure of the one-dimensional flow as a Lagrange multiplier to express the conservation of fluid transfer between the fracture flow and the divergence of the one-dimensional fracture flux.A zero-dimensional pressure(point element)is used to express conservation of mass where fractures intersect.The issuing simulation is then reduced using the MHM method leading to accurate results with a very reduced number of global equations.A general system was developed where fracture geometries and conductivities are specified in an input file and meshes are generated using the public domain mesh generator GMsh.Several test cases illustrate the effectiveness of the proposed approach by comparing the multiscale results with direct simulations.

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.

Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model （DPM）. The comparisons results show that the DPM overestimates the inter-porosity coefficient ）, and the storage factor w. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density.

Fifty years of finite elements——a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.

THE PARTIAL PROJECTION METHOD IN THE FINITE ELEMENT DISCRETIZATION OF THE REISSNER-MINDLIN PLATE MODEL

In the paper a linear combination of both the standard mixed formulation and the displacement one of the Reissner-Mindlin plate theory is used to enhance stability of the former and to remove ''locking'' of the later. For this new stabilized formulation, a unified approach to convergence analysis is presented for a wide spectrum of finite element spaces. As long as the rotation space is appropriately enriched, the formulation is convergent for the finite element spaces of sufficiently high order. Optimal-order error estimates with constants independent of the plate thickness are proved for the various lower order methods of this kind.

土壤—耕作工具相互作用建模分析研究现状

准确模拟土壤—耕作工具之间的相互作用可以实现部分替代田间试验环节,不仅能提高效率降低成本,还能优化耕作工具。从经典力学的分析和数值模型分析(有限元分析、离散元分析、流体动力学分析和耦合算法分析)两个方面对土壤—耕作工具相互作用建模分析的研究现状进行综述。提出目前土壤—耕作工具相互作用的建模中对土壤的模拟不够贴近实际、单一建模方法对土壤的模拟有局限性和多软件耦合算法中通过优化边界穿越等问题。通过对多耦合软件中不同模型边界进行优化,提高模拟土壤与耕作工具相互作用的准确性,使模拟结果更贴近实际。

水平振动式滚磨光整加工残余应力离散元有限元耦合仿真与实验研究

为探究水平振动式滚磨光整加工对零件表面残余应力的影响,提出一种适用于动态零件的离散元有限元(DEM-FEM)耦合仿真方法。分析了振动周期内颗粒运动状态以及颗粒间平均接触力的变化,构建了颗粒与零件间的随机接触模型,开展了不同振动参数下的残余应力仿真,并进行了实验验证。研究结果表明:随着振动强度的增大,容器内颗粒运动更加剧烈,颗粒与零件间有效法向接触力发生概率及均值增大,导致零件表面残余压应力呈增大趋势。残余应力仿真值与实验值对振动参数的响应趋势一致,误差在3.6%~11.3%之间。

基于离散元-有限差分耦合方法的格栅加筋道砟力学性能分析

格栅加筋对有砟道床力学性能的改善机理尚不明确。开展柔性边界条件下的道砟压缩试验,并在此基础上采用离散元-有限差分耦合方法,建立精细化格栅加筋道砟仿真模型;采用室内试验与数值仿真相结合的方式,分析格栅加筋对道砟宏观及细观力学性能的影响。结果表明:格栅加筋能有效提升道砟的承载力和抗竖向变形能力,加筋后试样的应变能量密度增加50.0%;格栅能有效限制其周围道砟颗粒的运动,减少道床横向变形,在相同轴向应力作用下最大横向变形减少16.1%,格栅位置处横向变形减少63.2%;格栅加筋可有效提升道床的抗剪强度,加筋后道床水平承载力提高18.8%;铺设格栅能有效增强其上部道床的密实度,建议在超厚道床或线下基础不稳定区段铺设道砟格栅。

基于DEM-FEM法的碎冰区船舶冰致疲劳损伤分析

极地运输船在碎冰区航行时会不断与海冰发生碰撞,致使内部产生周期性损伤,加剧了船体结构的疲劳问题。为此,本文建立一种基于离散元-有限元(DEM-FEM)的碎冰区航行船舶冰致疲劳损伤评估方法。首先,根据实际海冰分布,构造出一种混合海冰模型和数值碎冰航道。利用离散元法(DEM)计算出船体-碎冰碰撞下的冰载荷时历。将冰载荷时历施加到船体上,利用有限元法(FEM)计算出各疲劳子工况下的热点应力时历。采用改进四峰谷值雨流计数法统计热点应力时历的应力水平,基于线性累积损伤准则的S-N曲线法计算出各热点总的疲劳损伤度。最后,将本方法的计算结果与LR规范算法的结果进行对比分析,验证该方法的适用性。本方法可为碎冰区航行船舶的冰致疲劳损伤评估提供一定参考。

FINITE ELEMENT MODELLING OF COMPLEX 3D STATIC AND DYNAMIC CRACK PROPAGATION BY EMBEDDING COHESIVE ELEMENTS IN ABAQUS

This study proposes an algorithm of embedding cohesive elements in Abaqus and develops the computer code to model 3D complex cragk propagation in quasi-brittle materials in a relatively easy and efficient manner. The cohesive elements with softening traction-separation relations and damage initiation and evolution laws are embedded between solid elements in regions of interest in the initial mesh to model potential cracks. The initial mesh can consist of tetrahedrons, wedges, bricks or a mixture of these elements. Neither remeshing nor objective crack propagation criteria are needed. Four examples of concrete specimens, including a wedgesplitting test, a notched beam under torsion, a pull-out test of an anchored cylinder and a notched beam under impact, were modelled and analysed. The simulated crack propagation processes and load-displacement curves agreed well with test results or other numerical simulations for all the examples using initial meshes with reasonable densities. Making use of Abaqus＇s rich pre/post- processing functionalities and powerful standard/explicit solvers, the developed method offers a practical tool for engineering analysts to model complex 3D fracture problems.

A novel two-way method for dynamically coupling a hydrodynamic model with a discrete element model(DEM)

The effect of floating objects has so far been little considered for hazard risk assessment and structure design, despite being an important factor causing structural damage in flood-prone and coastal areas. In this work, a novel two-way method is proposed to fully couple a shock-capturing hydrodynamic model with a discrete element model （DEM） for simulation of complex debris-enriched flow hydrodynamics. After being validated against an idealized analytical test, the new coupled model is used to reproduce flume experiments of floating debris driven by dam-break waves. The numerical results agree satisfactorily with the experimental measurements, demonstrating the model＇s capability and efficiency in simulating complex fluid-debris interactions induced by violent shallow flows.

Analysis of the damage mechanism of strainbursts by a global-local modeling approach

Strainburst is the most common type of rockbursts.The research of strainburst damage mechanisms is helpful to improve and optimize the rock support design in the burst-prone ground.In this study,an improved global-local modeling approach was first adopted to study strainburst damage mechanisms.The extracted stresses induced by multiple excavations from a three-dimensional(3D)global model established by fast Lagrangian analysis of continua in 3 dimensions(FLAC3D)are used as boundary conditions for a two-dimensional(2D)local model of a deep roadway built by universal distinct element code(UDEC)to simulate realistic stress loading paths and conduct a detailed analysis of rockburst damage from both micro and macro perspectives.The results suggest that the deformation and damage level of the roadway gradually increase with the growth of surrounding rock stress caused by the superposition of mining-or excavation-induced stresses of the panel and nearby roadways.The significant increase of surrounding rock stresses will result in more accumulated strain energy in two sidewalls,providing a necessary condition for the strainburst occurrence in the dynamic stage.The strainburst damage mechanism for the study site combines three types of damage:rock ejection,rock bulking,and rockfall.During the strainburst,initiation,propagation,and development of tensile cracks play a crucial role in controlling macroscopic failure of surrounding rock masses,although the shear crack always accounts for the main proportion of damage levels.The deformation and damage level of the roadway during a strainburst positively correlate with the increasing peak particle velocities(PPVs).The yielding steel arch might not dissipate kinetic energy and mitigate strainburst damage effectively due to the limited energy absorption capacity.The principles to control and mitigate strainburst damage are proposed in this paper.This study presents a systematic framework to investigate strainburst damage mechanisms using the global-local modeling approach.

A New 3D Meso-mechanical Modeling Method of Coral Aggregate Concrete Considering Interface Characteristics

On the basis of the three-dimensional(3D)random aggregate&mortar two-phase mesoscale finite element model,C++programming was used to identify the node position information of the interface between the aggregate and mortar elements.The nodes were discretized at this position and the zero-thickness cohesive elements were inserted.After that,the crack energy release rate fracture criterion based on the fracture mechanics theory was assigned to the failure criterion of the interface transition zone(ITZ)elements.Finally,the three-phase mesomechanical model based on the combined finite discrete element method(FDEM)was constructed.Based on this model,the meso-crack extension and macro-mechanical behaviour of coral aggregate concrete(CAC)under uniaxial compression were successfully simulated.The results demonstrated that the meso-mechanical model based on FDEM has excellent applicability to simulate the compressive properties of CAC.

Fracture development around deep underground excavations: Insights from FDEM modelling

Over the past twenty years, there has been a growing interest in the development of numerical modelsthat can realistically capture the progressive failure of rock masses. In particular, the investigation ofdamage development around underground excavations represents a key issue in several rock engineeringapplications, including tunnelling, mining, drilling, hydroelectric power generation, and the deepgeological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finitediscreteelement method （FDEM） code to simulate the fracturing mechanisms associated with theexcavation of underground openings in brittle rock formations. A brief review of the current state-of-theartmodelling approaches is initially provided, including the description of selecting continuum- anddiscontinuum-based techniques. Then, the influence of a number of factors, including mechanical and insitu stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for threedifferent geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropicrock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy onthe development of an excavation damaged zone （EDZ） around a tunnel excavated in a layered rockformation is considered. Finally, the interaction mechanisms between two large caverns of an undergroundhydroelectric power station are investigated, with particular emphasis on the rock mass responsesensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEMsimulations can provide unique geomechanical insights in cases where an explicit consideration offracture and fragmentation processes is of paramount importance. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

水力压裂分段射孔簇多裂缝空间偏转模拟研究

深部致密油气储层水力压裂工程形成复杂缝网形态是影响油气采收率的关键因素,需要准确评估和优化压裂裂缝扩展行为。水平井多射孔簇分段压裂涉及储层和孔隙−裂隙内流体之间的热扩散、流体流动与岩体基质变形,热扩散效应和多物理场耦合作用是深部致密岩体压裂的典型特征;同时,压裂缝网扩展与裂缝间的扰动作用有关,压裂工艺中的射孔簇间距、起裂顺序等造成平行裂缝发生不同程度的非稳定扩展。理解多物理场耦合、裂缝间扰动等内外因素的影响机制,对有效评估压裂缝网具有重要意义。综合考虑深部储层的热−流−固耦合效应,研究水力压裂缝网三维扩展之间的应力阴影效应和多裂缝扰动偏转行为。研究建立水平井分段压裂的工程尺度三维数值模型,利用典型工况计算分析了压裂裂缝三维扩展的热扩散效应影响、不同射孔簇间距以及不同压裂方案(顺序、同步、交替压裂)下裂缝网络的扩展扰动行为。结果表明:深部致密油气储层压裂裂缝扩展引起的应力扰动区域在多裂缝中存在叠加、覆盖行为,形成应力阴影效应、造成裂缝空间偏转;水平井多射孔簇间距的减小,将增大应力阴影区,加剧裂缝间相互干扰;相比多射孔簇顺序压裂,同步压裂将增大应力阴影区,交替压裂可减小应力阴影区,交替压裂成为缓解压裂缝网三维扩展扰动、优化空间缝网形态的有效方案;深部致密油气储层岩体裂缝内的压裂液与岩体基质进行热交换,各压裂方案下的裂缝扩展面积、体积均有提升,表明热效应对裂缝扩展有促进作用,成为影响压裂裂缝扩展的重要因素。

交叉裂隙岩体裂纹扩展试验及混合有限-离散元数值模拟研究

对预制交叉裂隙岩石试样进行裂纹扩展试验,研究了裂纹萌生、扩展、聚合过程,分析了主裂隙和轴向载荷夹角及主次裂隙夹角对裂纹起裂应力和聚合应力的影响,并用混合有限元-离散元程序,即图形处理器并行化的3D Y-HFDEM代码对试验进行了仿真计算,实现了岩石破坏从连续介质向非连续介质的过渡,对裂纹类及损伤破坏模式进行了识别,捕捉到了试验中难以发现的现象。研究表明:随主裂隙与轴向载荷夹角增加,裂纹聚合区的拉伸裂纹数量增加;裂纹起裂和聚合应力与主裂隙与轴向载荷夹角成正比;主次裂隙夹角增加,岩石的破坏模式由拉伸破坏转为剪切破坏,交叉裂隙加剧岩石破碎程度;主裂隙尖端萌生扩展的拉伸-剪切混合裂缝引起的破坏在岩石破坏中占主导地位,是导致岩体失去承载能力的主控裂纹;混合有限元-离散元仿真软件GPGPU并行化的3D Y-HFDEM IDE在岩石裂纹扩展研究中具有优势,可以捕捉实验室难以发现的损伤断裂类型,可以作为岩石裂纹扩展研究的有力工具。

基于不同颗粒形态模拟方法的道砟三轴试样变形特性对比分析

道砟不规则形态是影响有砟道床变形特性的重要因素,对道砟形状及棱角分布等不同尺度形态特征的刻画与数值重构仍是道砟仿真研究的热点问题。该文采用形态重构方法,生成了符合真实道砟形态指标概率分布的多面体道砟试样,构建了不同围压下道砟三轴加载计算模型,并将该仿真结果与三维扫描生成、非统计随机生成的道砟试样的仿真结果及室内试验结果对比分析。结果表明:围压提高,颗粒形态对道砟力学响应的影响逐渐显著,该文方法重构数值试样的应力-应变结果与试验结果的符合度高于非统计随机生成试样;道砟试样横向变形与堆积结构调整有关,与三维扫描生成的道砟试样相比,非统计随机生成试样的颗粒调整程度与侧向鼓胀范围均偏大;形态统计特征对道砟接触力演化趋势影响不大,但是不同形态特征的道砟最大接触力水平差异近50%。

Productivity analysis of a fractured horizontal well in a shale gas reservoir based on discrete fracture network model

The treatment of horizontal wells with massive hydraulic fracturing technology is important for the economical development of shale gas reservoirs, but sometimes is complex because of the induced fractures during the fracturing process. The studies of the fluid flow characteristics in such formations are rare. In this study, a numerical method based on a finite element method (FEM) is developed for the productivity analysis of a horizontal well in a shale gas reservoir with complex fractures. The proposed method takes into account the adsorbed gas and the complex hydraulic fracture branches. To make the problem more tractable, the dimension of the fracture system is reduced from 2-D to 1-D based on the discrete fracture network (DFN) model. The accuracy of the new method is verified by comparing its results with those obtained by the Saphir commercial software. Finally, the productivity of the fractured horizontal wells in shale gas reservoirs with complex fractures systems is evaluated and analyzed. Results show that if a well is produced with a constant bottomhole pressure, the well productivity is much increased due to the existence of fracture branches that can increase the stimulated reservoir volume (SRV). In addition, the number of hydraulic fractures (Nf) and the fracture halMengths (Lf) have an important influence on the well's productivity. The larger the values of Nf,Lf,the greater the well productivity will be. The existence of adsorbed gas can markedly improve the well productivity, and the greater the Langmuir volume, the greater the productivity will be. The conclusions drawn by this study can provide a guidance for the development of unconventional shale gas reservoirs.