三维梁-颗粒模型在岩石材料破坏模拟中的应用

用三维梁-颗粒模型BPM3D(beam-particlemodelinthreedimensions)对岩石类非均质脆性材料的力学性质和破坏过程进行了数值模拟。梁-颗粒模型是在离散单元法基础上,结合有限单元法中的网格模型提出的用于模拟岩石类材料损伤破坏过程的数值模型。在模型中,材料在细观层次上被离散为颗粒单元集合体,相邻颗粒单元由有限单元法中的弹脆性梁单元联结。梁单元的力学性质均按韦伯(Weibull)分布随机赋值,以模拟岩石类材料力学参数的空间变异性。材料内部裂纹通过断开梁单元来模拟。通过自动生成的非均质材料模型对岩石类材料的破坏机理进行研究。岩石类非均质脆性材料在单轴压缩状态下破坏过程细观数值模拟结果显示,岩石材料宏观破坏是由于其内部细观裂纹产生、扩展、贯通的结果。通过数值模拟结果之间的对比分析,揭示出岩石试样宏观破坏模式随细观层次上韦伯分布参数的变化而不同。与实际矿柱破坏形态的对比分析表明了模型的适用性。根据数值模拟结果对岩石类非均质材料的破坏机理进行了探讨。     

基于PFC~(2D)的贵阳西二环滑坡破坏过程模拟

正近年来,随着计算机技术的发展,数值模拟方法在滑坡领域得到广泛应用。目前的数值模拟方法中,主要包括确定性分析方法和非确定性分析方法两类,而确定性分析方法又可分为连续介质分析与非连续介质分析方法。其中,连续介质数值分析方法有有限单元法、边界元法、有限差分法等,非连续介质分析方法有块体离散元法、颗粒离散元法、关键块体理论、不连续变形分析(DDA法)等[1]-[2]。颗粒流法(PFC)作为离散单元法的一种,是基于离散元的方法来模拟圆盘或球颗粒介质的运动及其相互作用,可以真实地模拟滑坡的失稳破坏过程。目前已广泛应用于滑坡破坏运动分析之中[3]-[5]。     

砂岩类脆性无序介质连续破坏过程的细观模拟

为了分析砂岩类无序介质在各种荷载作用下的连续破坏过程,本文提出了梁-颗粒细观模型。在此模型中,介质被离散为一系列的颗粒单元,这些颗粒单元均由弹脆性的梁单元联结。颗粒的力学行为由离散单元法和有限单元法确定。当某个梁单元所受应力超过其强度时,就随即将它从计算网络中剔除,以模拟介质的破坏行为。为了验证数值模型的可靠性,分别从破坏模式和荷载-位移曲线两方面与物理模型实验进行了对比,结果表明两者基本一致。此外,探讨了无序性对介质裂纹分布形式的影响,并用分维表述了裂纹分布与荷载强度之间的内在联系。      

基于SEM的可变形块体离散元法研究

针对边坡工程中岩土体连续-非连续渐进破坏的特点,提出一种新的变形体离散元方法（DEM）。与传统有限单元法（FEM）不同,弹簧元法（SEM）通过构建一组广义弹簧系统描述单元的力学行为。弹簧元法中的一个广义弹簧可以具有多个方向的刚度系数,确定广义弹簧系统的构造形式及其各刚度系数表达式是弹簧元法的核心。以三角形单元为例,介绍平面弹簧元的基本理论。对任何二维正交广义弹簧系统,通过定义广义弹簧变形与单元应变之间的关系,直接对比单元的应变能与弹簧系统的弹性势能即可得到广义弹簧刚度系数的表达形式。定义泊松刚度系数和纯剪刚度系数两个系统参数,描述正交广义弹簧之间的联系。对任意泊松比的材料,该方法都可准确地描述泊松效应的影响,计算结果与传统有限元法一致。该方法不需要求得有限元单元刚度矩阵的具体形式,具有直接方便、物理意义明确的优点,应用该方法给出任意4节点单元弹簧系统的构造形式及其各刚度系数的表达式。基于SEM的可变形块体离散元法,用弹簧元中的广义弹簧求解块体变形,用离散元中的接触弹簧计算块体间作用力,在单元节点的控制方程中实现弹簧元-离散元耦合计算,通过接触弹簧的状态实现材料由连续到非连续的破坏过程。在基于连续介质离散元法（CDEM）程序的基础上实现弹簧元-离散元耦合程序,应用耦合程序计算均质土坡在重力作用下的弹塑性变形和基覆边坡在重力作用下的破坏,初步证明该方法用于边坡变形渐进破坏分析的可行性。     

一种有限元转化为颗粒离散元的方法及其应用研究

为了充分发挥有限元与颗粒离散元各自的优势,提出了一种由有限元转化为颗粒流的方法。数值模型首先用较粗的有限元网格进行离散,并在单元上引入连续介质本构模型。力学计算开始后,实时跟踪各单元的应力状态。一旦某单元的应力满足Mohr-Coulomb准则或最大拉应力准则,删除该单元,同时创建具有一定数目、随机分布且微嵌入的颗粒簇。其后,该单元所在区域的非连续变形及失稳断裂由颗粒簇演化获得。各颗粒的质量、材料参数、速度、位移、接触力等信息根据插值从有限元单元中继承。为了实现有限元与颗粒流接触面的耦合计算,引入了点-棱（二维）及点-面（三维）接触模型,通过法向及切向弹簧实现接触力的计算。颗粒球与有限元板的碰撞分析、单轴压缩、岩石切割等案例展示了上述方法的精确性及合理性。     

准脆性材料断裂模拟方法研究

针对岩石、混凝土类准脆性材料的断裂过程模拟,发展了基于黏聚裂纹模型的虚节点扩展有限元法,并给出了该法的数值原理和控制方程。通过三点弯曲梁拉伸断裂、单边缺口试件Ⅰ-Ⅱ复合型断裂和Nooru-Mohammed试验多裂纹断裂等典型算例,并与已有解或试验结果对比,表明该法适合于模拟准脆性材料由张开型裂纹支配的断裂过程。相对于节点分离有限元法,该法无需预设开裂路径;相对于塑性损伤有限元法,该法能够可靠模拟多裂纹曲线扩展;相对于标准扩展有限元法,该法无需引入裂尖单元,避免了应力强度因子的计算;相对于高阶富集扩展有限元法,该法具有良好的适用性,便于得到收敛的计算结果。此外,基于单元的位移场描述使其更易于嵌入常用有限元软件,从而利用后者良好的非线性计算功能求解复杂问题。     

基于Forrestal侵彻试验的数值模拟研究

在弹丸侵彻混凝土的数值模拟过程中,材料模型及其相关参数的选取是一项关键且复杂的工作,其原因在于混凝土动力学材料模型参数众多,一般都在几十个以上,而且大多数参数无法通过试验直接获得,有些甚至没有明确的物理意义。通常的办法是通过试验确定少量参数,然后通过数值模拟计算结果反推其他模型参数。鉴于这种情况,非线性动力分析软件LS–DYNA增加了自动生成参数的功能,该成果是由Schwer等在损伤混凝土材料模型的基础上通过大量总结得到的,该特性很大程度上方便了用户在混凝土侵彻数值模拟方面的工作。利用LS–DYNA的该项功能,模拟了Forrestal的部分侵彻试验,并将计算结果同试验数据、经验公式计算结果做了对比分析。结果表明,自动生成参数功能是一种研究弹丸侵彻混凝土问题的简单而有效的办法。     

颗粒接触无网格法及其在边坡成灾范围模拟中的应用

提出了一种基于颗粒接触的无网格方法（PCMM）,并编制了相应的C++程序,解决了有限元等网格类方法在模拟边坡失稳滑动过程中的网格畸变问题。该方法利用颗粒离散元中的接触拓扑创建连续介质单元,通过颗粒的运动演化实现连续介质单元的自动删除及重建,通过在连续介质单元中引入考虑应变软化效应的Mohr-Coulomb模型及最大拉应力模型,实现边坡的弹塑性分析及失稳滑移过程的模拟。利用PCMM分析了均质边坡的弹塑性场、沙堆的形成过程及土质边坡的失稳过程。计算结果表明,PCMM在小变形下具有足够的精度,且在模拟材料大变形方面具有明显优势,是一种模拟边坡成灾范围的有效方法。     

基于MatDEM的砂土侧限压缩试验离散元模拟研究

离散元法基于非连续介质力学理论,尤其适用于砂土等离散介质体的数值模拟研究。利用岩土体离散元模拟软件MatDEM的二次开发功能,研发了砂土侧限压缩试验三维离散元模拟器。对三个不同级配砂土试样进行了侧限压缩试验,并且进行了与之相对应的数值模拟,通过分析对比试验结果与数值模拟结果验证了所开发模拟器的有效性。模拟结果表明:离散元法可以很好地反应砂土压缩过程中的配位数变化;每个模拟样品中,粒径较小的单元受到较大的平均压力,导致平均位移较大;数值计算结果的主要误差是由离散元颗粒自身的泊松比引起的。研究突破了常规土力学研究方法的局限性,为今后岩土工程离散元模拟研究提供了参考。      

一种模拟堆石料颗粒破碎的离散元-比例边界有限元结合法

试验研究和数值模拟都表明,颗粒破碎对颗粒岩土材料的宏观力学响应具有重要的影响。结合离散元与比例边界有限元法,提出一种用于研究堆石料颗粒破碎行为的新的数值计算方法,可以将两种方法各自的优势同时发挥出来。离散单元法将被用于求解颗粒的运动以及相互作用。在每一个时间步尾,采用比例边界有限单元法计算颗粒内部的应力分布。比例边界有限单元法可以仅用一个任意边数的多边形来描述一个颗粒,大大节约应力计算的成本。当应力状态确定之后,Hoek-Brown准则将被引入用于确定颗粒内部的破坏点,当破坏点达到一定的比例时,即视为这个颗粒将破坏。为简化起见,假设破坏路径为直线,如果破坏发生,则该颗粒一分为二,各个新的颗粒将直接参与离散元和比例边界有限元的计算。该方法无需预定义任何子颗粒或网格重划分。最后以一个简单的双轴试验的模拟展现方法的可行性。     

DEM–FEM analysis of soil failure process via the separate edge coupling method

The concurrent multiscale method, which couples the discrete element method (DEM) for predicting the local micro‐scale evolution of the soil particle skeleton with the finite element method (FEM) for estimating the remaining macro‐scale continuum deformation, is a versatile tool for modeling the failure process of soil masses. This paper presents the separate edge coupling method, which is degenerated from the generalized bridging domain method and is good at eliminating spurious reflections that are induced by coupling models of different scales, to capture the granular behavior in the domain of interest and to coarsen the mesh to save computational cost in the remaining domain. Cundall non‐viscous damping was used as numerical damping to dissipate the kinetic energy for simulating static failure problems. The proposed coupled DEM–FEM scheme was adopted to model the wave propagation in a 1D steel bar, a soil slope because of the effect of a shallow foundation and a plane‐strain cone penetration test (CPT). The numerical results show that the separate edge coupling method is effective when it is adopted for a problem with Cundall non‐viscous damping; it qualitatively reproduces the failure process of the soil masses and is consistent with the full micro‐scale discrete element model. Stress discontinuity is found in the coupling domain. Copyright © 2017 John Wiley & Sons, Ltd.     

On the linear elastic responses of the 2D bonded discrete element model

The bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solids in various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM which influence Poisson's ratio and Young's modulus, and accuracy when solving elastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticity analysis, and the distinct lattice spring model (DLSM) are compared in the investigation. It is shown that a shear interaction (local) factor and a geometric (global) factor are two essential elements for the 2D bonded DEM to reproduce a full range of Poisson's ratios. It is also found that the 2D bonded DEM might be unable to reproduce the correct displacements for elastic boundary value problems when the represented Poisson's ratio is close to 0.5 or the long-range interaction is considered. In addition, an analytical relationship between the shear stiffness ratio and the Poisson's ratio, derived from a hyper elasticity analysis and applicable to discontinuum-based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shown that the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.     

Micromechanical analysis of the failure process of brittle rock

The failure process of brittle rock submitted to a compression state of stress with different confining pressures is investigated in this paper based on discrete element method (DEM) simulations. In the DEM model, the rock sample is represented by bonding rigid particles at their contact points. The numerical model is first calibrated by comparing the macroscopic response with the macroscopic response of Beishan granite obtained from laboratory tests. After the validation of numerical model in terms of macroscopic responses, the failure process of the DEM model under unconfined and confined compression is studied in micro‐scale in detail. The contact force network and its relation to the development of micro‐cracks and evolution of major fractures are studied. Confining pressure will prohibit the development of tensile cracks and hence alter the failure patterns. An in‐depth analysis of micro‐scale response is carried out, including the orientation distribution and probability density of stress acting on parallel bonds, the effect of particle size heterogeneity on bond breakage and the evolution of fabric tensor and coordination number of parallel bond. The proposed micromechanical analysis will allow us to extract innovative features emerged from the stresses and crack evolution in brittle rock failure process. Copyright © 2014 John Wiley & Sons, Ltd.     

弹丸侵彻高强度混凝土的高速摄影试验研究

采用高速摄影仪,拍摄轻气炮中弹丸对侵彻面不同侵角的高强度混凝土靶体的侵彻过程,分析靶体侵角、弹丸着靶速度对弹丸侵彻靶体的运动特征。研究结果表明,弹丸以200 m/s左右的低速侵彻靶体时,弹丸在侵彻角度为0°的靶体中作水平运动,靶体侵角大于0°时,弹丸均在着靶后150～200 μs发生偏转;弹丸在靶体中的水平侵彻速度、偏转角度与其侵彻时间有很好的相关性,靶体侵角一定时,弹丸着靶速度越小,弹丸水平侵彻时所需时间越短,靶体飞溅物的速度越小;靶体侵彻面角度对靶体飞溅物速度和弹丸水平侵彻时间的影响作用相对比弹丸着靶速度的大,说明靶体侵角的大小是安全防护工事中不可忽视的重要问题。     

Hierarchical multiscale numerical modelling of internal erosion with discrete and finite elements

This paper presents a coupled finite and discrete-element model (FEM and DEM) to simulate internal erosion. The model is based on ICY, an interface between COMSOL, an FEM engine, and YADE, a DEM code. With this model, smaller DEM subdomains are generated to simulate particle displacements at the grain scale. Particles in these small subdomains are subjected to buoyancy, gravity, drag and contact forces for short time steps (0.1 s). The DEM subdomains provide the macroscale (continuum) model with a particle flux distribution. Through a mass conservation equation, the flux distribution allows changes in porosity, hydraulic conductivity and hydraulic gradient to be evaluated for the same time steps at a larger, continuum scale. The updated hydraulic gradients from the continuum model provide the DEM subdomains with updated hydrodynamic forces based on a coarse-grid method. The number of particles in the DEM subdomains is also updated based on the new porosity distribution. The hierarchical multiscale model (HMM) was validated with the simulation of suffusion. Results for the proposed HMM algorithm are consistent with results based on a DEM model incorporating the full sample and simulation duration. The proposed HMM algorithm could enable the modelling of internal erosion for soil volumes that are too large to be modelled with a single DEM subdomain.