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.     

Disturbed state model for sand–geosynthetic interfaces and application to pull-out tests

Successful numerical simulation of geosynthetic-reinforced earth structures depends on selecting proper constitutive models for soils, geosynthetics and soil–geosynthetic interfaces. Many constitutive models are available for modelling soils and geosynthetics. However, constitutive models for soil–geosynthetic interfaces which can capture most of the important characteristics of interface response are not readily available. In this paper, an elasto-plastic constitutive model based on the disturbed state concept (DSC) for geosynthetic–soil interfaces has been presented. The proposed model is capable of capturing most of the important characteristics of interface response, such as dilation, hardening and softening. The behaviour of interfaces under the direct shear test has been predicted by the model. The present model has been implemented in the finite element procedure in association with the thin-layer element. Five pull-out tests with two different geogrids have been simulated numerically using FEM. For the calibration of the constitutive models used in FEM, the standard laboratory tests used are: (1) triaxial tests for the sand, (2) direct shear tests for the interfaces and (3) axial tension tests for the geogrids. The results of the finite element simulations of pull-out tests agree well with the test data. The proposed model can be used for the stress-deformation study of geosynthetic-reinforced embankments through numerical simulation. Copyright © 1999 John Wiley & Sons, Ltd.     

Performance of geosynthetic-reinforced granular piles in soft clays: Model tests and numerical analysis

The laboratory model tests and numerical analyses have been performed on reinforced granular piles installed in very soft clay. The granular piles were reinforced with geosynthetic in the form of vertical encasement, horizontal strips and combined vertical-horizontal reinforcement. The short term-displacement control model tests were carried out either only a granular pile loaded or with an entire area loaded. The laboratory results in the form of vertical load intensity-settlement behaviour were compared with that obtained from FEM software, PLAXIS 3D. The results indicated significant improvement in ultimate load intensity and stiffness of treated ground due to inclusion of geosynthetic.     

Performance of quasilinear elastic constitutive models in simulation of geosynthetic encased columns

Past numerical simulations of geosynthetic encased columns (GECs) using different versions of the quasilinear elastic hyperbolic model for the encased granular material have, in certain cases, yielded unrealistic results. In this paper the cause of such results is investigated by performing three-dimensional finite element analyses of GECs in soft clay, utilizing three common functional forms of the hyperbolic model for the encased granular material. Results indicate that one form of the hyperbolic model can predict an unrealistic lateral response for GECs during application of load to the column. In addition, the inability of hyperbolic models to properly account for soil behavior near failure compromises their ability to realistically capture the behavior of encased granular soil in GECs. Modeling the behavior of soil near failure is essential for properly simulating the behavior of GECs, as soil shear failure is necessary to mobilize the tensile stresses in the encasement and improve the stress–displacement response of the GEC. Although this type of hyperbolic model behavior was demonstrated for the specific case of encased soil in a GEC, the limitations of the hyperbolic model described herein apply equally to other geotechnical problems in which some portion of the soil mass is at or near failure.     

水压致裂起裂压力的细观离散元模拟及试验研究

水压致裂起裂压力的预测对于油气开采、地应力测量、水工结构物抗裂设计等具有重要的意义。采用颗粒离散元结合域-管道渗流模型的流固耦合非连续数值模拟方法,基于扩展前端法生成的含规则形状钻孔的颗粒体模型,对水压致裂的细观起裂过程和起裂压力大小进行了定量模拟。结果表明,在消除了颗粒体中钻孔形状不规则性的基础上,钻孔壁的接触力链分布与理论解较为一致,拟合的离散元起裂压力公式也与理论解较为接近。进一步地,从颗粒材料受挤压时产生局部张拉力的角度解释了起裂压力拟合公式与理论解之间的差别。最后,设计了含预制钻孔的抗渗砂浆试块制备方法,对不同主应力组合下的起裂压力大小进行了真三轴室内试验,验证了离散元模拟结果的可靠性。     

颗粒材料数值样本的坐标排序生成技术

颗粒材料离散颗粒模型的数值模拟结果与颗粒材料的数值样本密切相关,随着离散单元在颗粒材料数值模拟领域的广泛应用,颗粒材料的数值样本生成技术日益受到重视。基于RSA模型研究如何使随机生成的颗粒材料更密实,对均匀颗粒而言亦即如何在指定区域内生成更多的颗粒,讨论了4类修正方案,并建议了一种基于坐标排序的样本生成技术。研究表明,在传统的颗粒体随机生成技术基础上,通过对随机生成的x坐标序列或y坐标序列进行排序,可使生成的颗粒材料数值样本更密实。     

Numerical Analysis of Multi Layer Geosynthetic-Reinforced Granular Bed over Soft Fill

In this paper, considering the plain strain conditions, a numerical study has been conducted to investigate the behavior of multi layer geosynthetic-reinforced granular bed overlying a soft soil using the Fast Lagrangian Analysis of Continua (FLAC) program. The granular fill, soft soil, and geosynthetic reinforcements are considered as linear elastic materials. The geosynthetic reinforcements are modeled as cable elements fully bonded with the surrounding soil, thus neglecting any slip. The results obtained from the present investigation showed very close agreement when compared with the results of finite element analysis and lumped parameter modeling. The distribution of vertical, lateral and shear stresses in the soil are greatly affected as the number of reinforcement layers is increased. If the tensile stiffness of geosynthetic layers increases and its value is no more than 4,000–5,000 kN/m, the settlement of the reinforced foundation decreases significantly. The reduction in settlement is insignificant when the tensile strength of the geosynthetics exceed the above value.     

Limit Equilibrium Analyses for Internal Design of Geosynthetic Reinforced Slopes: Influence of Potential Failure Surface and Strength Distribution

The paper presents results from a computer code, based on limit equilibrium analyses, able to quantify earth pressure coefficients for the internal design of geosynthetic reinforced soil structures and identify the potential failure surfaces. Failure mechanisms assuming bilinear or logarithmic spiral failure surfaces are considered. The influence of the potential failure surface and geosynthetic strength distribution on the earth pressure coefficient is analysed. Required reinforcement tensile strengths calculated by the developed program are compared with values published in the literature. To further evaluate the capabilities of limit equilibrium analyses, the numerical modelling of a geosynthetic reinforced steep slope, designed at ultimate limit state conditions (FS = 1), is also presented. Good agreement was achieved between the potential failure surfaces predicted by limit equilibrium analyses and those obtained with numerical modelling.     

Multiscale modeling of large deformation in geomechanics

Large deformation soil behavior underpins the operation and performance for a wide range of key geotechnical structures and needs to be properly considered in their modeling, analysis, and design. The material point method (MPM) has gained increasing popularity recently over conventional numerical methods such as finite element method (FEM) in tackling large deformation problems. In this study, we present a novel hierarchical coupling scheme to integrate MPM with discrete element method (DEM) for multiscale modeling of large deformation in geomechanics. The MPM is employed to treat a typical boundary value problem that may experience large deformation, and the DEM is used to derive the nonlinear material response from small strain to finite strain required by MPM for each of its material points. The proposed coupling framework not only inherits the advantages of MPM in tackling large deformation engineering problems over the use of FEM (eg, no need for remeshing to avoid mesh distortion in FEM), but also helps avoid the need for complicated, phenomenological assumptions on constitutive material models for soil exhibiting high nonlinearity at finite strain. The proposed framework lends great convenience for us to relate rich grain-scale information and key micromechanical mechanisms to macroscopic observations of granular soils over all deformation levels, from initial small-strain stage en route to large deformation regime before failure. Several classic geomechanics examples are used to demonstrate the key features the new MPM/DEM framework can offer on large deformation simulations, including biaxial compression test, rigid footing, soil-pipe interaction, and soil column collapse.     

A continuum‐discrete model using Darcy's law: formulation and verification

This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.     

Capturing strain localization in reinforced soils

Lade’s single hardening soil model with Cosserat rotation embodied in the finite element method is employed to investigate the behavior of geosynthetic reinforced soils with special attention to the development of shear banding. The ability of the finite element model to detect shear banding in a reinforced soil is examined against three high quality small-scale laboratory plane strain tests on Toyoura sand with and without reinforcement. These three tests were chosen because of the clear failure surfaces that developed in the soil during loading. The FEM analyses were able to reasonably simulate the plane strain laboratory tests including both unreinforced and reinforced cases. The FEM analyses gave reasonably good agreement with the experimental results in terms of global stress–strain relationships and shear band occurrences. Furthermore, and based on FE analyses of a hypothetical geosynthetic reinforced soil (GRS) retaining wall, it is shown that the geosynthetic reinforcements are very effective in hindering the formation of shear bands in GRS retaining walls when small spacing between the reinforcement layers was used. When used properly, the geosynthetic reinforcements made the soil behave as a truly reinforced mass of considerable stiffness and strength.     

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.     

加筋材料动态松弛有限元模型的建立及应用

为分析加筋材料的抗弯刚度对加筋性能的影响,加筋材料采用梁单元形式。基于动态松弛法,通过定义梁单元的刚度矩阵,求解内力矢量,随后定义虚拟质量密度而建立总质量矩阵,将加筋材料的梁单元有限元模型嵌入到已有的动态松弛法求解程序中。通过对简支梁的简单加载模拟验证了该梁单元模型的准确性能。随后,将该有限元模型与已有的动态松弛法计算程序结合（含砂土本构及弱面单元模型）,对加筋砂土地基室内模型试验进行了数值模拟。将梁单元的模拟结果与杆单元（梁单元的特例）模拟结果进行了比较,并分别探讨了抗拉刚度和抗弯刚度对加筋砂土地基承载性能的影响。结果表明：抗拉刚度对承载能力的影响较小;抗弯刚度对承载力的影响程度与加筋材料的布置形式有关,特别是当加筋砂土中出现剪切带以后,其影响逐渐增大。因此,在分析加筋砂土结构的增强机制时,建议采用梁单元（具有一定的抗弯刚度）对加筋材料进行模拟。     

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。     

基于局部单元劈裂的FEM/DEM自适应分析方法

为了模拟岩体中裂纹的萌生、扩展,Munjiza提出了有限元法/离散元法(FEM/DEM)耦合分析方法。因为裂纹是沿单元边界进行扩展的,亦即裂纹扩展具有网格依赖性,为获得较好的裂纹扩展形态,需要划分密集的初始网格。为解决上述难题,基于FEM/DEM耦合分析方法,提出了基于局部单元动态劈裂的FEM/DEM自适应分析方法,以克服裂纹扩展形态对网格的依赖性。该方法在最初建模时无需划分很密的初始网格,随着荷载的施加,对裂纹尖端附近的局部单元进行动态劈裂,为裂纹的后续扩展提供了更多可能的扩展方向,使得裂纹扩展不必沿着初始网格的单元边界扩展,即可以沿着单元内部进行扩展,裂纹扩展形态更为平滑,与实际情况更为接近。同时相对原FEM/DEM耦合分析方法一开始就划分很密的网格而言,新方法可以划分较为稀疏的初始网格,计算成本降低。最后,通过巴西劈裂算例与原FEM/DEM耦合分析方法对比,分析表明,新方法在一定程度上克服了裂纹扩展形态对初始网格的依赖性。     

Hydro-micromechanical modeling of wave propagation in saturated granular crystals

Biot theory predicts wave velocities in a saturated granular medium using the pore geometry, viscosity, densities, and elastic moduli of the solid skeleton and pore fluid, neglecting the interaction between constituent particles and local flow, which becomes essential as the wavelength decreases. Here, a hydro-micromechanical model, for direct numerical simulations of wave propagation in saturated granular media, is implemented by two-way coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), which resolve the pore-scale hydrodynamics and intergranular behavior, respectively. The coupling scheme is benchmarked with the terminal velocity of a single sphere settling in a fluid. In order to mimic a small amplitude pressure wave entering a saturated granular medium, an oscillating pressure boundary on the fluid is implemented and benchmarked with the one-dimensional wave equation. The effects of input waveforms and frequencies on the dispersion relations in 3D saturated poroelastic media are investigated with granular face-centered-cubic crystals. Finally, the pressure and shear wave velocities predicted by the numerical model at various effective confining pressures are found to be in excellent agreement with Biot analytical solutions, including his prediction for slow compressional waves.     

Numerical study on stress states and fabric anisotropies in soilbags using the DEM

Wrapping granular soils in geosynthetic containers, such as soilbags, results in a considerable increase in the bearing capacity due to the effective restraint on the dilatancy of the soil. This paper numerically investigates the stress states and fabric anisotropies in the wrapped soil using the discrete element method, providing a novel perspective for new insights into the reinforcement mechanisms and the development of constitutive relations for soilbags. The two most anticipated loading conditions, namely, unconfined compression and simple shear, are considered, and numerical predictions are compared to experimental results. During unconfined compression, both global and local p–q stress paths evolve linearly, having the same slope until the global failure of the wrapping geosynthetic. Under simple shear, the global stress path approaches the critical state line first and then turns to the compression line of the wrapped soil. Some local loading–unloading stress paths are observed, which may account for the high damping of soilbags during cyclic shear. The reduced fabric anisotropies of the normal and tangential force chains suggest greater confinement from the lateral sides of the geosynthetic container in either loading course. The performance and mechanisms of the soilbag earth reinforcement method, i.e., confinement and interlocking, can be better understood based on these new findings on the stress states and fabric anisotropies.     

Soil–Structure Interaction of Damped Infinite Beams on Extensible Geosynthetic Reinforced Earth Beds Under Moving Loads

In the present paper, soil-structure interaction analysis of an infinite beam resting on extensible geosynthetic reinforced earth beds has been carried out for an applied load moving with constant velocity. The viscous damping of the soil-foundation system has been given due consideration in the analytical procedure. The infinite beam has been treated as resting on a granular fill layer overlying the naturally occurring weak soil layer. Geosynthetic layer has been provided in the granular fill layer and has been considered as extensible. This extensible nature has been incorporated with the help of no slip and the compatibility conditions at the interface between reinforcing layer and the neighboring soil. These conditions help in eliminating the two interfacial shear stress parameters and in considering the tensile modulus of geosynthetic layer in the analysis. The influence of various parameters, like magnitude and velocity of applied moving load, viscous damping, relative stiffness of granular fill and tensile modulus of geosynthetic layer, on the response of soil-foundation system has been studied. It has been observed that all these parameters affect the response significantly, however, the effect of velocity of moving load and viscous damping has been found to be more significant especially at higher velocities.     

Discrete element modelling of a granular platform supported by piles in soft soil – Validation on a small scale model test and comparison to a numerical analysis in a continuum

This paper focuses on the mechanisms taking place in a granular platform supported by piles in soft soil. Several modelling approaches were explored. A two-dimensional small scale model test using the Taylor–Schneebeli soil analogue was first developed and the experimental results were compared to a discrete element model using the particle code PFC. The validation of this numerical approach allowed the parametric study to be extended numerically. Parametric studies were also performed on continuum model using the finite-difference code FLAC. Comparison of the parametric studies performed on each modelling approach underlined some differences and lead to a consideration on the macro- and micromechanical parameters.     

Numerical analysis of soilbags under compression and cyclic shear

This paper presents a finite element model for analysing the behaviour of granular material wrapped with polyethylene bags under vertical compression and cyclic shearing. The simple Mohr–Coulomb model is used to represent the soil behaviour. The polyethylene bag is represented by a linear-elastic–perfect-plastic model. The soil-bag interface is modelled with contact constraints. The main purpose of the numerical analysis is to validate the anticipated performance of soilbags under various loading conditions and hence the effectiveness of soilbags as a method of ground improvement.