A continuum‐discrete hydromechanical analysis of granular deposit liquefaction

A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd.     

Granular element method for three‐dimensional discrete element calculations

This paper endows the recently‐proposed granular element method (GEM) with the ability to perform 3D discrete element calculations. By using non‐uniform rational B‐Splines to accurately represent complex grain geometries, we proposed an alternative approach to clustering‐based and polyhedra‐based discrete element methods whereby the need for complicated and ad hoc approaches to construct 3D grain geometries is entirely bypassed. We demonstrate the ability of GEM in capturing arbitrary‐shaped 3D grains with great ease, flexibility, and without excessive geometric information. Furthermore, the applicability of GEM is enhanced by its tight integration with existing non‐uniform rational B‐Splines modeling tools and ability to provide a seamless transition from binary images of real grain shapes (e.g., from 3D X‐ray CT) to modeling and discrete mechanics computations.Copyright © 2013 John Wiley & Sons, Ltd.     

Relating discrete element method parameters to rock properties using classical and micropolar elasticity theories

Micro–macro relations for discrete element method (DEM) media are derived using both classical and micropolar elasticity theories. The DEM media are classified into two main categories: dense packing, and loose packing. For both categories, relations for Young modulus (E), Poisson's ratio (ν) to represent static behaviors, and wave velocities (P‐wave and S‐wave) to represent dynamic behaviors are derived using the internal DEM parameters (k_n, k_s) and compared with values obtained from static and dynamic numerical tests. Whereas the dynamic behaviors for the two categories and the static behaviors for the dense packing match the analytical relations, the static behavior for the loose packing does not. Micropolar elasticity theory is also used to study the behaviors of the DEM media, where it is shown that if element rotation is included, DEM media behave according to linear elasticity theory. However, if element rotation is constrained, asymmetrical stresses arise in the DEM media, and a new expression is derived for the S‐wave, which allows it, under certain conditions, to travel faster than the P‐wave. Copyright © 2011 John Wiley & Sons, Ltd.     

Intersecting dilated convex polyhedra method for modeling complex particles in discrete element method

This paper describes a new method for representing concave polyhedral particles in a discrete element method as unions of convex dilated polyhedra. This method offers an efficient way to simulate systems with a large number of (generally concave) polyhedral particles. The method also allows spheres, capsules, and dilated triangles to be combined with polyhedra using the same approach. The computational efficiency of the method is tested in two different simulation setups using different efficiency metrics for seven particle types: spheres, clusters of three spheres, clusters of four spheres, tetrahedra, cubes, unions of two octahedra (concave), and a model of a computer tomography scan of a lunar simulant GRC‐3 particle. It is shown that the computational efficiency of the simulations degrades much slower than the increase in complexity of the particles in the system. The efficiency of the method is based on the time coherence of the system, and an efficient and robust distance computation method between polyhedra as particles never intersect for dilated particles. © 2014 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

单粒组密砂剪切带的直剪试验离散元数值分析

为分析砂土的剪切力学特性,采用离散元商业软件PFC2D对单粒组密砂在直剪试验中出现的剪切带进行了数值分析。改进传统的分条带观察方式,采用矩形格分割法观察试样内部不同区域的变形特性。对离散元商业软件进行了二次开发,实现了大小主应力及其应力主方向角的可视化,分析了试样内部的应力偏转情况。同时,以纯转动率和颗粒速度等微观变量为中心,观察了试样内部颗粒的运动状态,解析了直剪试验中砂土剪切带形成的微观机制。研究表明,直剪试验中应变局部化区域集中在剪切面附近的一个条带内。通过转动场和速度场的分析可知,剪切带宽度约为10～15倍的砂土平均粒径,带内颗粒转动明显,带边缘出现大的速度和转动变化梯度。对组构和接触力分布的分析可知,剪切过程中粒间接触点和接触力的主轴方向发生了相一致的偏转,偏转后的主轴方向为60°左右。     

A new potential function for the calculation of contact forces in the combined finite–discrete element method

Although the potential contact force proposed by Munjiza overcomes the difficulties inherent in the traditional discrete element methods, the physical meaning of the potential is not clear and the contact force derived from the original potential function is strongly dependent on the mesh configuration. In this study, we redefine a potential function and propose a new contact force calculation method based on a unified standard. Moreover, the new potential function retains all the advantages of the original potential function but has less mesh dependency. Copyright © 2016 John Wiley & Sons, Ltd.     

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter-grains elongation/compression energy from inter-grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model.     

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。     

A discrete element approach to elastic properties of layered geomaterials

Discrete element methods (DEMs) are used for layered geomaterials to investigate the dependency of traditional engineering constants on material properties and loading conditions. Shear deformations and compression tests parallel and perpendicular to layering are conducted on samples of varying kerogen volume fractions, confining pressures, porosities, and layer geometries. The goal of this article is to develop a method to better characterize oil shale (a transversely isotropic layered geomaterial) while eliminating high experimental costs. The DEM simulations conducted in this study demonstrate strong dependencies of Young's modulus, Poisson's ratio, and shear modulus on kerogen volume fraction and porosity. Furthermore, a rule of thumb for layer thickness and particle resolution is proposed for simulation design. Results agree well with robust effective medium theories, solidify the ability of DEM to model the mechanical properties of layered heterogenous materials, and encourage the use of DEM to study more complicated layered media and material failure. Copyright © 2011 John Wiley & Sons, Ltd.     

A numerical model for sedimentation from highly-concentrated multi-sized suspensions

The principal numerical approach to describing sedimentation from multi-component suspensions (Mirza and Richardson, 1979) has been applied only to systems containing two or three particle size populations, but is theoretically applicable to suspensions containing a wider range of particle sizes. In order to adapt this model to the simulation of sedimentation from natural high-density sediment-laden flows, we have conducted computational tests on the sedimentation of suspensions with up to ten particle size populations. The tests run smoothly with binary systems and sometimes ternary systems, but fail with systems containing more than three particle size populations. One cause of the discrepancy between theoretical predictions and computational tests arises from the method used to calculate the changing concentration of particles in each zone of a stratified settling suspension. In quantifying the changing sediment budget for each sedimentation zone, the equation set fails to include the apparent outflow of finer particle populations across the upper boundary of the zone. In the present study, we express the sediment budget of each particle population within each sedimentation zone as the net sediment flux, the algebraic sum of the apparent particle inflow from the zone's lower boundary and the apparent particle outflow across the zone's upper boundary. This revised model successfully predicts the evolution of multi-component suspensions containing up to ten particle size populations over the length of time required for complete sedimentation, up to 8×10⁵ seconds. It can be used to predict the sediment sorting and the vertical textural variation of beds formed by the simulated sedimentation of a multi-component suspension. The model provides the basis for future computer simulation of sedimentation from highly concentrated sediment flows and for the prediction of downslope textural and structural variations of turbidites.     

椭圆形颗粒堆积体模拟颗粒材料力学性能的离散元数值方法

针对离散元中圆形颗粒模拟出的内摩擦角小于真实砂土内摩擦角的缺陷,将已有NS2D离散元程序中的圆形颗粒参量改进为椭圆形颗粒参量,形成改进的NS2D程序。介绍了改进后NS2D程序的基本力学模型,详细推导了程序中椭圆颗粒间以及椭圆颗粒与墙之间接触点的力-位移关系。利用改进后的离散元程序分别模拟了恒定围压下长短轴比例分别为1.1:1、1.4:1,孔隙比均为0.19的椭圆颗粒堆积体的双轴试验,所得的内摩擦角在真实砂土的内摩擦角范围之内,且其应力特征与已有成果吻合良好,证明了改进后的NS2D离散元程序能够模拟分析真实砂土的力学性能     

Discrete element modelling of deep penetration in granular soils

This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil–penetrometer interface friction. A two‐dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K₀ lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil–penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd.     

The influence of the void fraction on the particle migration: A coupled computational fluid dynamics–discrete element method study about drag force correlations

Granular soils subjected to flow through their soil skeleton can show a behaviour in which fine particles migrate through the pore space between coarser particles. This process is called internal instability or suffusion. This contribution deals with the numerical analysis of the migration of fine particles in a soil column subjected to fluid flow with unresolved coupled computational fluid dynamics–discrete element method (CFD–DEM) with special regards to the used drag force correlation. The contribution investigates the influence of the Schiller–Naumann model and its extension with a voidage term on the migration behaviour of fine particles. The voidage term is further varied with a parameter, which controls the impact of the change of the void fraction on the drag force. It could be observed that the Schiller–Naumann model does not yield in a suffusive behaviour while the extended models show significant particle migration. Thereby, increasing the impact of the void fraction on the drag force results in stronger particle migration. These results reveal the need for good validation techniques. They indicate how the drag force correlation can be adapted to depict the correct particle migration behaviour.     

A coupled discrete element model for the simulation of soil and water flow through an orifice

Soil erosion around defective underground pipes can cause ground collapses and sinkholes in urban areas. Most of these soil erosion events are caused by fluidization of the surrounding soil with subsequent washing into defective sewer pipes. In this study, this soil erosion process is simplified as the gradual washout of sand particles mixed with water through an orifice. The discrete element method is used to simulate the large deformation behavior of the sand particles, and the Darcy fluid model is coupled with this approach to simulate fluid flow through porous sand media. A coupled 3D discrete element model is developed and implemented based on this scheme. To simulate previous experiments using this coupled model considering the current computing capacity, we incorporated a ‘supply layer’ to study the continuous erosion process. The coupled model can predict the erosion flow rates of sand and water and the shape of erosion void. Thus, the model can be used as an effective and efficient tool to investigate the soil erosion process around defective pipes. Copyright © 2017 John Wiley & Sons, Ltd.     

A virtual experiment technique on the elementary behaviour of granular materials with discrete element method

Multi‐scale investigations aided by the discrete element method (DEM) play a vital role for current state‐of‐the‐art research on the elementary behaviour of granular materials. Similar to laboratory tests, there are three important aspects to be considered carefully, which are the proper stress/strain definition and measurement, the application of target loading paths and the designed experiment setup, to be addressed in the present paper. Considering the volume sensitive characteristics of granular materials, in the proposed technique, the deformation of the tested specimen is controlled and measured by deformation gradient tensor involving both the undeformed configuration and the current configuration. Definitions of Biot strain and Cauchy stress are adopted. The expressions of them in terms of contact forces and particle displacements, respectively, are derived. The boundary of the tested specimen consists of rigid massless planar units. It is suggested that the representative element uses a convex polyhedral (polygonal) shape to minimize possible boundary arching effects. General loading paths are described by directly specifying the changes in the stress/strain invariants or directions. Loading can be applied in the strain‐controlled mode by specifying the translations and rotations of the boundary units, or in the stress‐controlled mode by using a servo‐control mechanism, or in the combination of the two methods to realize mixed boundary conditions. Taking the simulation results as the natural consequences originated from a complex system, virtual experiments provide particle‐scale information database to conduct multi‐scale investigations for better understanding in granular material behaviours and possible development of the constitutive theories provided the qualitative similarity between the simulation results from virtual experiments and observations on real material behaviour. Copyright © 2011 John Wiley & Sons, Ltd.     

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory,implementation, and application

Although numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F²Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.     

基于弹性张量离散化的脆延转变本构模型研究

外部荷载作用下的裂隙扩展在空间上一般是非均匀的,引起岩石材料的衍生各向异性。将材料离散成大量随机分布的由力键连结的物质点,基于力键的方向性,且将局部弹性张量离散成一定数量的方向张量,理论推导出力键模量与宏观弹性参数之间的关系。通过考虑力键断裂效应,建立了各向异性弹性损伤本构模型。为了模拟中等孔隙率岩石在常规三轴压缩试验中脆性向延性转变的力学行为,在力键断裂效应中引入损伤抑制函数。通过模拟Tennessee大理岩和Indiana石灰岩的常规三轴实验,并与试验数据对比,验证了模型的合理性和有效性。     

A time‐discontinuous Galerkin method for the dynamical analysis of porous media

We present a time‐discontinuous Galerkin method (DGT) for the dynamic analysis of fully saturated porous media. The numerical method consists of a finite element discretization in space and time. The discrete basis functions are continuous in space and discontinuous in time. The continuity across the time interval is weakly enforced by a flux function. Two applications and several numerical investigations confirm the quality of the proposed space–time finite element scheme. Copyright © 2006 John Wiley & Sons, Ltd.