模拟岩石破裂过程的块体单元离散弹簧模型

在变形体离散元的基础上建立块体单元离散弹簧模型,并应用于岩石破裂过程的数值模拟研究。该模型以连续介质力学理论为基础,将块体单元离散为具有明确物理意义的弹簧系统,通过对弹簧系统的能量泛函求变分获得各弹簧的刚度系数,进而可以直接利用弹簧刚度求解单元的变形和应力,提高计算效率。以重力作用下的岩质边坡计算为例,通过与传统的有限元进行对比,验证该模型弹性计算结果的正确性。在该基础上,引入Mohr-Coulomb与最大拉应力的复合破坏准则,判断单元的破坏状态及破裂方向。当单元的内部破坏面确定后,则通过块体切割的方式实现单元破坏,并建立单元边界和单元内部的双重破裂机制,实现块体由连续到非连续的破裂过程,进而显示的模拟裂纹的形成和扩展。最后,以巴西圆盘劈裂、单轴压缩破裂以及三点弯曲梁等典型算例验证该方法,结果表明该方法可以较好地模拟拉伸、压剪等应力状态下裂纹的形成和扩展,从而可模拟岩石介质由连续到非连续的破裂过程。     

可变形圆化多边形离散单元法

将基于圆化多边形离散单元法与有限元方法结合,提出一种可变形圆化多边形离散单元法。此法对块体离散元进行圆化处理,可较好地表征不规则块体外形,又保留了颗粒离散元计算高效的优势。在求解接触力时,消除了角点处法向奇异等问题,同时增强计算的稳定性和简化接触判断。同时对切向接触力计算模型进行修正,使得接触力计算效率得到提高。此法突破了圆化多边形刚体假设的限制,可以精确计算任意形状不规则离散单元之间的相互作用,对单元的运动和变形进行模拟。通过超静定梁冲击试验、不规则块体单轴压缩试验和料斗流动“卡阻”试验3个数值模拟算例,论证此法可以有效地捕捉单元的碰撞、分离和变形等空间运动和自身特性以及其细观力学表征。     

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。     

土的三维破坏准则在颗粒流模型中的应用

Savage-Hutter(S-H)颗粒流模型用一个只与材料参数相关的土压力系数来描述颗粒流内部的应力状态,不能很好地反映颗粒体在运动时的本构关系。通过引入颗粒体应力与速度梯度之间的关系,得到了一个能够反映颗粒流本构模型的崩塌动力学模型。另外,为解除S-H模型中对横向应力大小的假定,通过引入Von Mises、Drucker-Prager、Mohr-Coulomb和Matsuoka-Nakai等土的三维破坏准则,得到了广义摩擦系数的4种表达形式。该模型的主要优势是通过引入颗粒流的本构关系,能较好地体现颗粒流体在运动中的内在机制,并且材料强度参数简单易知。分析了由Drucker-Prager准则和Mohr-Coulomb准则所得到的材料强度参数,并探讨了广义摩擦系数与应力洛德角等物理量之间的关系。用所建议的模型来模拟颗粒流的运动过程,并将数值计算与试验结果进行对比,发现两者能够较好吻合。     

冻结砂土力学性质的离散元模拟

基于离散单元法颗粒流理论,土体颗粒单元间采用接触黏结模型中来考虑冻土中冰的胶结作用,建立了冻结砂土的颗粒流模型。通过改变计算模型中颗粒单元的参数,模拟了在不同冻结温度以及不同围压下冻结砂土的宏观力学性质,并与冻结砂土的室内试验结果进行了比较,结果表明：颗粒流方法可以较好地模拟冻结砂土的应力-应变关系以及剪切带的发展变化过程,颗粒流细观参数对温度具有显著的依赖性。研究结果对离散单元法在特殊土中的应用具有一定的理论和应用价值。     

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。      

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。     

颗粒流强度折减法和重力增加法的边坡安全系数研究

将强度折减法和重力增加法的思路引入离散单元法,对土坡安全系数的评价作尝试性研究。运用颗粒流软件,采用强度折减法和重力增加法对边坡进行稳定分析。结果表明颗粒流计算得到的结果与有限元和条分法计算结果比较接近,为计算边坡稳定开辟了一条新的途径。采用颗粒流求解边坡的安全系数不需要条分,也即不需要对条间力做假定,同时不需要假定滑移面的位置和形状,颗粒根据所受到的接触力调整其位置,最终从抗剪强度最弱面发生剪切破坏。最后对强度折减法的不等比例折减提出了不同观点,为今后的研究提供思路。     

一种模拟堆石料的二维多边形离散单元法及程序

在考虑堆石料真实颗粒形状的基础上,将每个颗粒用一个多边形离散单元表示,基于一种线性搜索算法对多边形-多边形之间的接触详情进行检索计算,引入基于势能原理的法向多边形-多边形接触模型及切向库仑摩擦模型,形成了一种多边形离散元计算方法,并开发了相应的PDEM程序。可以从颗粒尺度层面展示颗粒之间的相互作用以及每个颗粒的位移和转动,帮助进一步揭示颗粒的细观特性(形状、大小、材料特性等)对堆石料的宏观强度和变形的影响。最后采用PDEM程序对某粗粒料的二维模型试验进行了数值模拟,得到了与室内试验一致的应力变形规律,展现了其方法和程序用于研究堆石料的有效性。     

使用颗粒流方法研究单轴压缩条件下石灰岩中的荷载传递机理

研究荷载在岩石中的传递机理对岩石工程性质研究具有重要意义。本文以石灰岩试样为例,使用颗粒流方法来研究这一传递机理。研究试样大小为50 mm× 50 mm,岩石成分使用圆盘颗粒集合体来表征,颗粒间的接触模型采用平行连接模型,岩石的弹性模量、峰值应力和泊松比分别为44.24 GPa、101.05 MPa和0.267;将大于平均接触力的力链作为强力链,得到了外部荷载下试样中的强力链分布情况,研究了试样局部孔隙率、配位数等细观参数对接触力大小的影响,探讨了颗粒摩擦系数不同时外荷达到峰值应力后颗粒的接触力分布情况。结果表明,在全部颗粒接触点中,只有19.8%接触点的接触力大于平均接触力,但这些接触点应变能却占总应变能的75%;当法向接触力与切向接触力比值大于3.5时,试样峰后应力主要由法向接触力控制;与样品破坏前相比,破坏后样品中的局部孔隙率变化不大,只减少了0.002。     

粗粒料多边形表征及二维FEM/DEM分析

考虑到颗粒形状对粗粒料的力学特性有重大影响,提出了一种新的表征颗粒形状的方法,即在椭圆上随机选取一系列点连接成多边形颗粒,表征狭长扁平的颗粒。新方法较圆上取点的方法能代表更多类型的颗粒形状,适用范围更广。提出了一种新的粗粒料投放算法,即先缩小颗粒,然采用随机算法将缩小的颗粒投放至给定区域,对颗粒划分好网格后,将颗粒放大到原来的大小,然后采用有限元-离散元(FEM/DEM)方法计算稳定后即生成了相应的试样。通过将上述颗粒生成及投放算法与FEM/DEM结合,应用于粗粒料的数值模拟。分析表明,FEM/DEM是研究粗粒料力学性质的较好方法,对复杂的颗粒形状也可简单建模,且因在颗粒内部划分了有限元网格,复杂的接触判断及接触力计算转化为标准统一的三角形和三角形之间的接触判断及接触力计算,所有的计算均可标准化、统一化。同时因为颗粒是可以变形的,依然保留了连续介质力学中应力和应变的概念,无须像PFC那样需通过测量圆来间接表示某点的应力、应变。最后,通过粗粒料的侧限压缩试验的数值模拟,展现了文中提出的一整套解决方案在模拟粗粒料方面的巨大潜力。     

基于B-DEM的颗粒聚合体应力计算和破碎路径模拟

结合边界元法和离散元法,提出一种可以进行计算颗粒内部应力和破碎路径的方法。该方法利用离散元法求解颗粒的相互作用和每个颗粒上的荷载。然后利用边界元法计算颗粒的应力分布,为了实现动态平衡,将颗粒的加速度视为恒定大小的体力。但体力导致边界积分方程中出现域积分,故采用直线积分法将域积分转化为边界积分,以保证边界元法降维的优势。为了提高边界元的计算效率,对于几何形状相似的颗粒,以其中一个颗粒作为模板颗粒,只需要计算模板颗粒在局部坐标系中的系数矩阵,其他相似颗粒可以通过局部和全局坐标系之间的映射获得。在得到应力后,基于Hoek-Brown准则来判断颗粒是否破碎。此外,将破坏路径简化为直线,并采用最小二乘法拟合得到破坏路径。     

3D analysis of kinematic behavior of granular materials in triaxial testing using DEM with flexible membrane boundary

This paper describes the constitutive behavior and particle-scale kinematics of granular materials in three-dimensional (3D) axisymmetric triaxial testing using discrete element method (DEM). PFC3D code was used to run the DEM simulations using a flexible membrane boundary model consisting of spherical particles linked through flexible contact bonds. The overall deformation behavior of the specimen was then compared with the specimen with rigid boundary and experimental measurements. Computed tomography was used to track the evolution of particle translation and rotation within a laboratory triaxial specimen in 3D. The DEM model of the flexible membrane specimen successfully predicted the stress–strain behavior when compared with laboratory experiment results at different confining pressures. The DEM results showed that the rigid specimen applies a uniform deformation and leads to non-uniformities in the confining stress along the particle-boundary interface in the lateral direction. In contrast, the flexible specimen better replicates the uniformly applied confining stress of a laboratory triaxial experiment. The 3D DEM simulations of the specimen with flexible membrane overpredicted particle translation and rotation in all directions when compared to a laboratory triaxial specimen. The difference between the particle translation and rotation distributions of DEM specimens with rigid and flexible membrane is almost negligible. The DEM specimen with flexible membrane produces a better prediction of the macroscopic stress–strain behavior and deformation characteristics of granular materials in 3D DEM simulations when compared to a specimen with rigid membrane. Comparing macroscale response and particle-scale kinematics between triaxial simulation results of rigid versus flexible membrane demonstrated the significant influence of boundary effects on the constitutive behavior of granular materials.     

Study on the particle breakage of ballast based on a GPU accelerated discrete element method

Breakage of particles will have greatly influence on mechanical behavior of granular material(GM)under external loads,such as ballast,rockfill and sand.The discrete element method(DEM)is one of the most popular methods for simulating GM as each particle is represented on its own.To study breakage mechanism of particle breakage,a cohesive contact mode is developed based on the GPU accelerated DEM code-Blaze-DEM.A database of the 3D geometry model of rock blocks is established based on the 3D scanning method.And an agglomerate describing the rock block with a series of non-overlapping spherical particles is used to build the DEM numerical model of a railway ballast sample,which is used to the DEM oedometric test to study the particles’breakage characteristics of the sample under external load.Furthermore,to obtain the meso-mechanical parameters used in DEM,a black-analysis method is used based on the laboratory tests of the rock sample.Based on the DEM numerical tests,the particle breakage process and mechanisms of the railway ballast are studied.All results show that the developed code can better used for large scale simulation of the particle breakage analysis of granular material.     

Validation of discrete element method by simulating a 2D assembly of randomly packed elliptical rods

This paper aims at establishing the predictive capability of the discrete element method (DEM) by validating the simulated responses of granular systems against experimental observations at both the macroscale and the microscale. A previously published biaxial shearing test on a 2D assembly of randomly packed elliptical rods was chosen as the benchmark test. In carrying out the corresponding DEM simulations herein, the contact model was derived and then validated using finite element analysis; the associated parameters were calibrated experimentally. The flexible (membrane) boundary was modeled by a bonded-particle string with experimentally calibrated parameters. An iteration procedure was implemented to replicate the initial packing and also to satisfy the boundary conditions in the experiment. Overall, the DEM simulation is found effective in reproducing the stress–strain–volumetric response, the statistical observation on the fabric anisotropy and the strain localization. Furthermore, the closer the numerical packing is to the experimental one, the closer the response is reproduced, demonstrating the significance of the initial packing reconstruction. Still, there are some minor differences between the experiment and simulation, reflecting the limitations associated with the particle number and the measurement resolution used in the experiment when reproducing the initial packing.     

Simulations of realistic granular soils in oedometer tests using physics engine

Discrete element method (DEM) has become a preeminent numerical tool for investigating the mechanical behavior of granular soils. However, traditional DEM uses sphere clusters to approximate realistic particles, which is computationally demanding when simulating many particles. This paper demonstrates the potential of using a physics engine technique to simulate realistic particles. The physics engines are originally developed for video games for simulating physical and mechanical processes that occur in the real world to produce realistic game experiences. The simulation accuracy and efficiency of physics engines have been significantly improved in the last two decades allowing them to be used as a scientific tool in many disciplines. This paper introduces modeling methodologies of physics engine including realistic particle representation and the contact model. Then, oedometer tests are simulated using realistic particles scanned by X-ray computed tomography (X-ray CT). The simulation results agree well with experimental results. This paper demonstrates that physics engines can output contact parameters for geotechnical analysis and force chains for visualization.     

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。     

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.

     

DEM modeling of aging or creep in sand based on the effects of microfracturing of asperities and evolution of microstructural anisotropy during triaxial creep

Aging- or creep-related phenomena in sand have been widely studied, and the discrete element method (DEM) has been frequently used to model the associated soil behavior and then to explore the associated underlying mechanisms. However, several difficulties involved in modeling still remain unsolved. To resolve these difficulties, a new approach based on the effect of the microfracturing of asperities is proposed in this study for the DEM modeling of the sand aging or creep process through several aging cycles of associated reduction in the mobilized friction resistance at particle contacts and subsequent particle rearrangement to reach a new equilibrium state. This approach can be easily incorporated into different contact models and DEM simulations of the loading, unloading, and/or reloading processes, in either drained or undrained conditions, before and/or after aging. This new approach is proven effective because the DEM simulations incorporated with this new approach can satisfactorily reproduce the experimental observations in the triaxial creep process, drained and undrained recompression after aging, and 1D secondary compression and rebound. The simulation results also indicate that, based on the stress–force–fabric relationship, the contribution from the contact normal anisotropy to the deviatoric stress q gradually increases, whereas the contribution from the tangential force anisotropy becomes less during triaxial creep under a constant q. Moreover, the contacts between particles are gradually away from the state where the frictional resistance is fully mobilized, and then become more stable. During the subsequent triaxial recompression after creep, the aged samples exhibit enhanced soil stiffness, which is also found to be associated with the evolution of the invariants of the anisotropy tensors. It is worthwhile noting that the aging or creep effects on the microstructural changes, e.g., the invariants of the anisotropy tensors, can be gradually erased upon further recompression. This explains why the stress–strain responses of the aged samples during recompression gradually rejoin the original stress–strain response obtained from the sample without being subjected to aging or creep.