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。     

颗粒沉降问题的高解析度CFD-DEM-IBM流固耦合数值模拟方法

为实现颗粒沉降问题的精确数值模拟,探索稠密颗粒两相流中流体与颗粒间的影响机制,基于浸入边界法（IBM）,建立了高解析度CFD-DEM-IBM流固耦合数值模拟方法。分别通过流体动力学方法（CFD）及离散单元法（DEM）描述连续流体及非连续颗粒,引入浸入边界法处理颗粒移动边界,并在Navier-Stokes动量方程中附加体力项以体现流固相互作用,采用交错迭代算法在同一时间步内多次迭代求解直至收敛以实现流固间的强耦合。通过单、双、群颗粒的沉降行为模拟,结果表明:与传统CFD-DEM方法相比,该方法能够准确考虑颗粒间及流固两相间的相互作用,获得高解析度的流场信息。模拟结果与前人数值计算结果吻合,验证了该方法的准确性与有效性及其对稠密颗粒两相流问题的适用性与优越性。     

PFC滑坡模拟二、三维建模方法研究

滑坡运动过程模拟避免了试验尺度与监测手段的限制,可以详细观察破坏过程,是定量评估滑坡灾变风险的重要研究手段。开展滑坡运动过程模拟的首要工作是建立滑坡模型。颗粒流程序（PFC) 虽然是滑坡运动过程模拟应用最广泛的程序之一,但在建立滑坡模型的前处理方面较弱,使得其在滑坡运动过程模拟中的推广应用受到限制。对此,本文指出了Ball-Ball和Ball-Wall两种建模方法的适用性、优缺点及滑体滑床边界确定方法,并以2014年地震触发的红石岩滑坡为例,以Brick填充法为基础,从获取地形数据、确定滑体和滑床区域、建立滑体和滑床几何模型、生成颗粒模型4个步骤出发,提出了基于数字等高线地形图建立PFC二、三维复杂滑坡模型的前处理方法,弥补了PFC软件前处理的不足,从而为今后基于PFC的滑坡运动过程模拟提供有益的帮助。     

颗粒离散单元法动力人工边界设置方法

采用颗粒离散单元法进行动力计算时,人工截断边界上需设置吸收边界条件,以防止波的反射。鉴于颗粒离散单元数值计算模型的人工边界上颗粒单元半径大小不一、边界面凸凹不平,在连续介质的黏性、黏弹性、自由场边界条件方程基础之上,推导出适用于离散介质的等效方程。在离散介质的黏性边界条件等效方程中引入微调系数,提出比值迭代法以快速确定其最优值,以实现对波的最佳吸收。采用二维颗粒离散单元计算软件PFC2D,分别建立黏性、黏弹性、自由场边界条件相关数值分析模型,探讨颗粒分布模式对黏性边界上颗粒单元半径、速度分布及比值迭代过程的影响;采用外源波动算例及经典Lamb问题算例验证黏弹性边界设置方法的正确性;通过隧洞算例检验提出的自由场边界条件设置方法的正确性。     

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。     

三维离散元单轴试验模拟甲烷水合物宏观三轴强度特性

填充型水合物的砂性能源土试样可视为特殊的散粒体材料,即砂粒和水合物颗粒混合物,具有明显的非连续特征。为研究填充型水合物的能源土力学特性,初步探索了甲烷水合物在不同温度、反压条件下加荷模式的离散元模拟方法。离散元模拟中,将水合物块体视为由大量颗粒通过强胶结作用凝聚而成的整体,室内试验中的内部孔隙水压作用转化为水合物颗粒间的胶结力,故需要合理确定颗粒间胶结模型参数来实现反压的影响作用。通过参数反演建立了宏观强度、刚度参数与平行胶结模型的微观胶结参数间的宏、微观关系,基于已有室内甲烷水合物三轴试验资料,确定了给定温度和反压条件下的微观胶结参数取值,随后进行离散元单轴压缩试验。离散元单轴压缩试验模拟获得的水合物强度特性,与室内三轴试验结果符合较好;通过建立的宏、微观参数间的关系,实现了不同温度、反压下的水合物加荷模式的模拟。为进一步提出深海能源土离散元数值试验成样方法--孔隙填充水合物生成技术,形成含填充型水合物的能源土试样,研究其力学和变形特性奠定基础。     

河冰数值模拟中不规则边界处理技术探讨

数值模拟是河冰问题研究的重要手段之一, 但受限于天然河道的复杂地形条件, 研究工作开展中往往面临不规则边界的处理问题.基于河冰数值模拟工作现状, 总结和阐述了贴体网格技术对其的应用.针对二维数值模拟提出了采用滑动边界法和势流理论式相结合的方法来进一步提高边界处网格的正交性; 三维网格生成则宜采用σ竖向坐标变换法; 河冰模拟中水面位置确定通常采用标高函数法; 对于非稳态河冰数值模拟, 动边界处理技术可考虑改进并应用干湿法.     

基于四叉树网格和多边形比例边界有限元方法的岩土工程非线性静动力分析

有限单元法(FEM)作为强大的数值分析技术广泛应用于岩土工程结构数值模拟。由于传统有限元的单元形状局限性以及岩土工程模型的复杂性(分层施工模拟、复杂材料分区等),较难编制通用的高质量网格剖分算法,使得模型网格生成消耗整个分析过程的大部分时间,阻碍快速自动化分析进程。采用四叉树网格剖分技术,联合非线性多边形比例边界有限元(PSBFEM)方法,发展了一种可用于岩土工程结构的快速建模和数值分析方法。对某心墙坝进行了静动力数值模拟,并与传统有限元结果对比验证了其正确性。研究表明,文中方法具有使用简便、网格灵活、生成速度快、质量高等特点,可以大幅降低累赘繁琐的人工干涉,为工程结构快速设计–优化提供有力的技术手段。该方法扩展至三维结构将具有更大的研究价值和工程意义。     

用Monte Carlo方法模拟砂土的自然堆积过程

用MonteCarlo随机模拟方法模拟砂土颗粒在重力作用下,在圆柱与长方体容器中的自然堆积过程。首先用参考网格法生成一个砂土颗粒的松散结构,松散结构中粒子与粒子、粒子与边界间不存在任何接触;然后启动MonteCarlo随机模拟算法,即给处于松散结构中的每个粒子施加随机位移,得到新构形,如果新构形中粒子间或粒子与边界间发生重叠,则放弃这个构形;如果没有重叠存在,则判别粒子体系的势能变化,运用Metropolis准则来判别这个构形是否被接受,重复这个过程可以得到砂土的密集堆积结构。采用Schinner建议的接触发现算法判别粒子间是否存在重叠,同时详细介绍了粒子与边界间的接触发现算法。模拟结果表明,用MonteCarlo方法模拟砂土的自然堆积结构是非常有效的,可以为砂土的流动、压实等的数值模拟工作提供初始构形。     

基于单、双重渗透介质降雨边界处理的改进

在降雨入渗模拟中,现有研究无法准确实现复杂降雨条件下降雨边界在流量与压力两类边界之间的双向动态转换。基于饱和?非饱和渗流理论,将降雨补给流量与实际入渗流量的差值作为两类边界动态转换的判别条件,改进了单重渗透介质降雨边界动态转换控制方程,并进一步提出了双重渗透介质降雨边界处理方法及控制方程,在此基础上进行了数值试验及工程实例验证。结果表明：改进的降雨边界动态转换控制方程克服了传统降雨边界只能实现流量到压力边界单向转换的局限性,可准确实现流量边界与压力边界的双向动态实时转换;案例边坡的降雨入渗模拟结果说明了改进后降雨边界的正确性和工程适用性。     

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。     

A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

A coupled 3‐dimensional bonded discrete element and lattice Boltzmann method for fluid‐solid coupling in cohesive geomaterials

This paper presents a 3D bonded discrete element and lattice Boltzmann method for resolving the fluid‐solid interaction involving complicated fluid‐particle coupling in geomaterials. In the coupled technique, the solid material is treated as an assembly of bonded and/or granular particles. A bond model accounting for strain softening in normal contact is incorporated into the discrete element method to simulate the mechanical behaviour of geomaterials, whilst the fluid flow is solved by the lattice Boltzmann method based on kinetic theory and statistical mechanics. To provide a bridge between theory and application, a 3D algorithm of immersed moving boundary scheme was proposed for resolving fluid‐particle interaction. To demonstrate the applicability and accuracy of this coupled method, a benchmark called quicksand, in which particles become fluidised under the driving of upward fluid flow, is first carried out. The critical hydraulic gradient obtained from the numerical results matches the theoretical value. Then, numerical investigation of the performance of granular filters generated according to the well‐acknowledged design criteria is given. It is found that the proposed 3D technique is promising, and the instantaneous migration of the protected soils can be readily observed. Numerical results prove that the filters which comply with the design criteria can effectively alleviate or eliminate the appearance of particle erosion in dams.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

A generic approach to modelling flexible confined boundary conditions in SPH and its application

In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free-surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto-plastic computations of geomaterials, a robust numerical procedure to implement Mohr-Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr-Coulomb model. The proposed approach was first validated against two-dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three-dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.     

Coupled bonded particle and lattice Boltzmann method for modelling fluid–solid interaction

This paper presents a two‐dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid–solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter‐particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid–solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid–solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd.     

颗粒形态对离散介质剪切强度的影响

自然条件下,颗粒介质大多以非规则单元形态存在。非规则几何形态对颗粒介质的宏观力学性能有很大影响。针对颗粒单元的不同几何形态,采用团颗粒单元对离散介质的直剪试验过程进行了离散元数值计算,详细地讨论了颗粒形态对离散介质剪切强度的影响。该非规则颗粒由不同形态、不同数目、镶嵌尺寸、组合方位和颗粒大小的球形颗粒进行随机构造,其在局部与整体坐标之间的转动、力矩和方位关系通过4元素方法进行确定,基本球体颗粒之间的作用力采用具有Mohr-Coulomb摩擦定侓的Hertz-Mindlin非线性接触模型,并考虑了非线性法向粘滞力的影响。通过构造7种具有相同的质量概率分布的不同形态的团颗粒,在不同法向应力下,对团颗粒的直剪试验进行了离散元模拟,分析了不同形态颗粒的剪切强度。通过对不同形态颗粒介质剪切强度的数值分析,进一步揭示了非规则颗粒间的咬合互锁效应,为分析非规则颗粒的宏观动力特性提供了依据。     

透射边界-地基-风电结构地震响应与破坏模式

近海风力发电结构是由无限域地基、基础及上部结构组成的体系,有限域透射人工边界和地震动输入模式直接影响结构体系的动力响应。首先,建立透射人工边界-地基-基础-塔筒结构和固定边界-地基-基础-塔筒结构的有限元模型;然后,简要澄清了透射边界地震动输入之所以采用外力而不采取地震动物理量（加速度、速度和位移）的原因所在;最后,对给出的3种作用模式：（1）固定边界地震动输入,（2）只考虑外源输入波作用,（3）同时考虑外源输入波和内源振动的散射波作用,分别进行计算分析和比较。通过数值计算并结合理论分析,（1）澄清了对透射边界采用外力进行地震激励输入的方法的原因,这种输入方法合理可靠,符合实际情况;（2）在地震波等效荷载的生成中,针对圆形横截面地基提出了一种阻尼力、刚度力的便捷性生成方法,大大减小了工作量;（3）从自身振动特点及阻尼设置角度,解释了地震作用下采用透射边界比采用固定边界时风电结构响应减小的原因;（4）指出了地震作用下透射边界地基模型在结构动力响应与倒塌计算中内源振动反射的不容忽视性。