Finite element formulation for poroelastic problem with zero effective stress boundary condition

Zero effective stress boundary condition along with constant fluid flux is commonly encountered in geotechnical applications such as uncased borehole stability, fluid injection and production at an uncased borehole, hydraulic fracturing and sand production. This complex boundary condition introduces high nonlinearity in the numerical simulation. Conventional iterative methods such as Newton–Raphson method are required to solve this nonlinear problem iteratively, which involve huge computing time and also pose numerical difficulties on the convergence. To overcome this numerical difficulty and hence reduce the computing time, a novel numerical technique is proposed in this paper. Its performance is evaluated using a numerical example simulating fluid injection around an uncased borehole. Copyright © 2009 John Wiley & Sons, Ltd.     

A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests

Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress-strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM-DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.     

考虑颗粒棱角影响的直剪试验的离散元模拟

为了研究颗粒棱角对颗粒材料力学行为的影响,建立了具有不同棱角度的对称多面体颗粒,采用了一种简单并适合任意颗粒形状的接触本构模型,对三维离散元开源程序YADE进行了修改,研究了颗粒棱角度在模拟直剪试验中的影响以及接触力各向异性在剪切过程中的演化规律。研究结果表明,颗粒棱角度越小,颗粒间相互咬合自锁的作用越小,颗粒受剪更易转动,致使颗粒体系的剪切强度和剪胀性下降;竖向加载力越大,颗粒棱角度的影响越明显;法向接触力的各向异性在剪切过程中表现为先增后减最后趋向稳定的趋势;法向接触力的各向异性变化程度随颗粒棱角度的增大而增大。     

边界条件对土层粘弹性地震反应的影响

边界条件是土层粘弹性地震反应必须考虑的问题。对于地表面，一般作为自由边界，而对于地下深处基岩面，边界条件有两种处理方法：一是静止边界，二是非静止边界的。首先给出了在时间域内单层地基一维土层粘弹性地震反应封闭解析解，然后从理论上分析边界条件对土层粘弹性地震反应的影响，认为采用静止边界进行土层地震反应计算得到的地震动加速度时程符合天然地震记录形式，而采用非静止边界进行土层地震反应计算得到的地震动加速度时程初始阶段出现较大幅度的振荡现象，随着土层厚度增加，这种振荡现象逐渐减弱直至消失。当土层阻尼较小或剪切波速增长时，振荡现象加剧；当土层阻尼比较大或剪切波速减小时，振荡现象减弱。此外，采用非静止边界进行土层地震反应计算，表现出随着土层厚度的增加，土层对基岩输入地震动的放大作用逐步转化为吸收作用。     

A unified CFD‐DEM approach for modeling of debris flow impacts on flexible barriers

This paper presents a unified modeling framework to investigate the impacts of debris flow on flexible barriers, based on coupled computational fluid dynamics and discrete element method (CFD‐DEM). We consider a debris flow as a mixture of fluid and particles where the fluid and particle phases are modeled by the CFD and the DEM, respectively. The fluid‐particle coupling is considered by the exchange of interaction forces between CFD and DEM calculations. The flexible barrier is simulated by the DEM as a network of bonded particles with remote interactions. The proposed coupled CFD‐DEM approach enables us to conveniently handle the complicated three‐way interactions among the fluid, the particles, and the flexible barrier structure for debris flow impact simulations. The proposed approach is first used to investigate the influences of channel inclination and the volumetric solid fraction in a debris mixture on the impact force, the resultant deformation, and the retained mass in a flexible barrier. The predictions agree well with existing experimental and numerical studies. We further examine the possible failure modes of a flexible barrier under debris flow impact and their underlying mechanisms. The performance of different components in a flexible barrier system, including single wires, double twists and cables, and their load sharing mechanisms, are carefully evaluated. The proposed unified framework offers a novel, promising pathway towards physically based, quantitative analysis and design of flexible barriers for debris flow mitigation.     

边坡模型边界效应及材料孔隙率敏感性研究

通过自制的新型试验装置进行不同边界情况下的边坡模型变形破坏研究。探讨了边坡模型破坏开始时的坡角（破坏角）与边界条件的关系。试验结果表明,该破坏角会与模型厚度成一定的反比关系,但随着模型厚度超过一定值,边界条件造成的影响将趋于弱化,同时,运用数学手段定量地印证了这种关系形式。另外,还通过试验验证了相比于边界条件而言,破坏角的变化幅度会对模型材料的孔隙率更加敏感。基于所得结果,可对试验装置进行改进,并优化试验手段。     

用空气单元法求解渗流场的逸出边界问题

依据空气单元模拟排水孔的思路,在渗流场任意可能逸出边界外布置一层渗透性较强的单元,与其他实体单元一起进行渗流计算,可以实现该边界的自动求解。与现行方法相比,不仅省去了逸出边界迭代计算的麻烦,而且避免了由于逸出点定位不准确而可能引起的渗流计算不合理或收敛困难等缺陷。算例分析表明,空气单元法的计算精度与空气单元的相对渗透系数R有关,与厚度L无关。当选取了合适的R值后,可以较好地逼近现行方法。对于因引入空气单元而造成的强弱透水介质界面处数值拟真性差的现象,还提出了加入接触面薄层单元的改进方法。方法改进后,计算精度可进一步提高。最后,以小湾水电站22#坝段渗流场计算为例,说明该法的实用性和可行性。     

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。     

滑移线场理论中非特征线应力边界条件的解析式

给出了岩土材料滑移线场理论中非特征线应力边界条件的解析表达式，根据它，应用滑移线场的基本理论和应力特征线的基本性质，可以方便地构造滑移线网。     

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.     

下边界条件对多年冻土温度场变化数值模拟的影响

在气候变暖背景下,北半球多年冻土呈现不同程度的退化趋势,冻土升温、活动层增厚、地下冰消融改变了区域工程地质条件、地形地貌,不仅对寒区环境和工程稳定性造成潜在的威胁,还影响着这些地区的气候、水文和生态过程.因此,准确评估和预估多年冻土热状况的变化具有重要科学和实践意义.现有用于模拟多年冻土热状况的各类模式重点考虑了近地表...     

Scaled boundary finite‐element analysis of a non‐homogeneous axisymmetric domain subjected to general loading

The scaled boundary finite‐element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power‐law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half‐space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non‐homogeneous half‐space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd.     

An efficient method for packing polygonal domains with disks for 2D discrete element simulation

The discrete element method (DEM) is frequently used in numerical simulation of the behaviour of discontinuum often encountered in granular flow, soil or rock mechanics or powder compaction. The DEM requires an assemblage of elements that need to fill the domain geometry. Generation of such arrangement of elements, such as disks in 2D DEM simulation is not a trivial task. The available methods to create the arrangements of disks can either take considerable time, have limited control over the final outcome of the disk generation or exhibit difficulty in generating a tight arrangement of disk with varying radii. This paper presents an algorithm employing principles of computational geometry to efficiently generate a tight packing of disks while addressing the common problems of disk generation. The algorithm’s performance is linear with respect to time and scales well. As a demonstration of the algorithm’s capabilities, a DEM model of an ore pass is presented.     

黄河下游河道边界条件影响输沙效率研究述评

如何高效输沙始终是黄河下游河道治理的一个根本问题,其中河道边界条件对泥沙输送具有重要的影响,这源于两者之间存在的耦合作用。对现有河道边界条件影响输沙效率相关研究进展及存在的问题进行了系统的总结与分析。河道边界条件不仅影响河道空间沿程输沙效率,而且河道边界条件的演化还决定了输沙效率的时间调整过程。这种影响在不同输沙计算方法(水文学方法、水动力学方法)中的表现形式有所不同,但反映物理本质相同,彼此之间存在一定的联系。能否反映水沙运动与河床变形之间的相互作用及耦合特性,这是判断输沙模拟有效性的关键所在。河道输沙与河床变形作为泥沙赋存状态同一问题的两个方面,提出了从河床演变学角度研究输沙效率的问题,为相关研究的开展提供思路与参考。     

工程中渗流问题的边界元算法与分析

针对河堤、水坝、高速公路档水墙等存在多孔单元介质中的定常渗流问题,将渗流Laplace方程,通过数学变换转化为边界积分方程,进而离散为线性代数方程组。采用边界元编写FORTRAN程序。计算结果表明:该法与有限元法相比,占用CPU时间短,不需要网格化分,使繁杂问题简单化,同时很好地切近实际。      

基于微观力学的胶结岩土材料破损规律离散元模拟

采用离散元法（DEM）研究胶结岩土材料在不同加载条件下的结构破损规律。首先,基于微观力学理论,考虑胶结岩土材料颗粒间胶结特性,给出表征结构性损伤的破损参数式。该式具有微观物理意义,但不能直接用于建立宏观本构模型。其次,采用二维离散元源程序NS2D模拟等向压缩、等应力比压缩以及双轴压缩试验,分析破损参数在不同加载条件下随宏观力学变量（体积应变和剪应变）的演变规律。最后,根据模拟结果提出破损参数数学表达式,其为大主应变的函数。研究结果表明：胶结强度、应力比以及围压均在一定程度上影响了数值试样的结构破损规律。在等向压缩和等应力比压缩试验中,容易用函数式描述数值试样破损参数随体积应变或偏应变的演变规律;而在双轴压缩条件下,由于数值试样有剪胀特性,破损参数随体积应变的演变规律则不易描述。建议的破损参数数学表达式能够较好地描述数值试样在不同加载条件下结构破损规律。     

A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd.     

共和隧道开裂段页岩蠕变本构试验及离散元数值模拟研究

渝湘高速公路共和隧道地质条件十分复杂,隧道施工遇到很大困难,隧道开挖后初期支护多处出现纵向开裂。开裂段围岩为砂质页岩,现场实际监测资料表明,页岩层理、节理发育,易风化,亲水性较强,有水软化倾向并具有一定蠕变性。页岩的这些性质对隧道初期支护效果及隧道长期稳定性具有重要影响。鉴于此,对共和隧道页岩进行蠕变试验,通过系列试验得到不同应力水平下页岩的应变-时间关系曲线,建立与之适应的蠕变模型,并推导出蠕变公式,计算出公式中相应参数值。在此基础上,应用离散元数值计算方法对隧道开裂段施工全过程进行研究,分析了隧道围岩可能的破坏模式以及隧道锚杆支护结构的受力情况等。研究成果为隧道开裂段初期支护结构新方案的设计提供了重要支撑,成功地解决了隧道初期支护纵向开裂的工程难题。     

Determination of soil properties for plane strain condition from the triaxial tests results

Significant difference in stress–strain behavior of dense cohesionless soil has been observed between plane strain and triaxial test conditions. At present, majority of geotechnical laboratories have no plane strain testing facility. Therefore, geotechnical professionals are more dependent on the conventional triaxial test for soil properties, whereas many geotechnical structures prevail close to plane strain condition. A method has been proposed to determine soil properties for plane strain condition from the conventional triaxial tests. This method can especially be used to determine the internal friction angle and stress–strain relationship for plane strain condition from triaxial tests results. Copyright © 2015 John Wiley & Sons, Ltd.     

A dimensional analysis of scaling viscosity and velocity in DEM of constant strain rate tests on asphalt

This paper presents the results from discrete element modelling (DEM) of an idealised (sand) asphalt mixture under constant strain rate (velocity) compressive loading using the Burgers viscoelastic model. Using dimensional analysis it is shown that the effect of scaling applied velocity is the same as that of scaling both viscosities in the Burgers model by the same factor. This has been shown to be the case for a bonded aggregate, and it also has been shown to be applicable even when bond breakage occurs within the sample. This scaling method will be of great benefit in modelling tests on asphalt under different constant strain rates, simply by scaling both viscosities to minimise computational time.