Finite element study of patterns of shear zones in granular bodies during plane strain compression

Numerical investigations of patterns of shear zones in granular bodies obtained during quasi-static plane strain compression tests were performed. The effect of a spatially correlated stochastic distribution of the initial void ratio and roughness of horizontal plates was analyzed. To describe a mechanical behavior of a cohesionless granular material during a monotonic deformation path in a plane strain compression test, a micro-polar hypoplastic constitutive model was used. FE calculations were carried out with both initially dense and initially loose cohesionless sand. A Latin hypercube method was applied to generate Gaussian truncated random fields of initial void ratio in a granular specimen. A weak correlation of the initial void ratio in both directions and its large standard deviation were assumed for all specimens. The horizontal boundaries were either ideally smooth or very rough. The FE results show similar patterns of shear zones as compared to experiments.     

Effect of grain crushing on shear localization in granular bodies during plane strain compression

This article deals with the effect of grain crushing on shear localization in granular materials during plane strain monotonic compression tests under constant lateral pressure. The grain diameter and the initial void ratio were stochastically distributed using a spatial correlation. To describe the mechanical behavior of cohesionless granular materials during a monotonic deformation path in plane strain compression, we used a micropolar hypoplastic constitutive model that is able to describe the salient properties of granular bodies including shear localization. The model was extended by introducing changes to the grain diameter with varying pressure using formulae from breakage mechanics proposed for crushable granulates. The initial void ratios and grain diameters took the form of correlated random spatial fields described by both symmetric and nonsymmetric random distributions using a homogeneous correlation function. The field realizations were generated with the help of an original conditional rejection method. A few representative samples of the random fields selected from the generated set were taken into account in numerical calculations. Copyright © 2011 John Wiley & Sons, Ltd.     

FE-modeling of shear resistance degradation in granular materials during cyclic shearing under CNS condition

The behaviour of dry and cohesionless granular material during quasi-static cyclic shearing under a constant normal stiffness (CNS) condition is theoretically studied. A particular attention is laid to the volumetric strain change and the degradation of the shear resistance in the course of shearing. Numerical calculations are carried out for several shear cycles under boundary conditions which are relevant to investigate the shear interface behaviour. The global and local evolution of deformation, stress and density within the granular material is investigated with a finite element method on the basis of a hypoplastic constitutive model extended by micro-polar quantities: rotations, curvatures and couple stresses. A mean grain diameter is used as a characteristic length of micro-structure. The constitutive equations for stresses and couple stresses take also into account the effect of the evolution of the void ratio, pressure dependent relative density, direction of rate of deformation and rate of curvature. The numerical results are qualitatively compared with corresponding laboratory tests on direct wall shearing performed by DeJong, Randloph and White. In addition, the results for cyclic shearing of an infinite granular layer between two very rough boundaries under CNS conditions are also enclosed and discussed.     

A new theoretical method for analyzing confined dry granular flows

A granular body may deform in a continuous fashion such that the solid particles remain in close contact. Previous research works have always used the frictional Coulomb-like continuum treatment for analyzing granular bodies. However, this approach is only applicable for quasi-static conditions and cannot capture the complicated granular contact behavior of solid particles inside a failing granular body. This paper applies a revised Savage–Hutter equation to model granular flows moving down a confined, sloping channel. The Coulomb contact friction law is modified to consider the effect of the shear rate inside a granular body. This new method also considers the confinement effect of a sloping channel on granular flow mobility. The derived depth-averaged equations of motion bear a resemblance to nonlinear shallow-water wave equations. Results computed using the derived equations are compared with measurements from flume model tests, and consistency is found between the two.     

Discrete modelling of hexagonal wire meshes with a stochastically distorted contact model

This paper presents an improved discrete element model, which incorporates stochastically distorted contact mechanics, for the simulation of double-twisted hexagonal wire meshes that are commonly used in rockfall protection. First, the characteristics of such meshes are investigated by conducting quasi-static and dynamic experimental tests. Second, the discrete model for the simulation of such meshes is presented. A stochastically distorted contact model is introduced to account for distortions of the wires and hexagons, allowing a more realistic representation of the mechanical response of the mesh from the deformation point of view and the force point of view. Quasi-static tensile tests of a plane net sheet, subjected to a constant strain rate, are used to study the effect of the stochastically distorted contact formulation and to calibrate the numerical model. Finally, the dynamic response of an impacting block on a horizontal mesh sheet is used to compare the numerical predictions against experimental results in order to validate the proposed approach.     

Three dimensional steady-state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

In this paper, steady-state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three-dimensional conditions.     

Predictive potential of Perzyna viscoplastic modelling for granular geomaterials

This paper reappraises Perzyna-type viscoplasticity for the constitutive modelling of granular geomaterials, with emphasis on the simulation of rate/time effects of different magnitude. An existing elasto-plastic model for sands is first recast into a Perzyna viscoplastic formulation and then calibrated/validated against laboratory test results on Hostun sand from the literature. Notable model features include (1) enhanced definition of the viscous nucleus function and (2) void ratio dependence of stiffness and viscous parameters, to model the pycnotropic behaviour of granular materials with a single set of parameters, uniquely identified against standard creep and triaxial test results. The comparison between experimental data and numerical simulations points out the predicative capability of the developed model and the complexity of defining a unique viscous nucleus function to capture sand behaviour under different loading/initial/boundary and drainage conditions. It is concluded that the unified viscoplastic simulation of both drained and undrained response is particularly challenging within Perzyna's framework and opens to future research in the area. The discussion presented is relevant, for instance, to the simulation of multiphase strain localisation phenomena, such as those associated to slope stability problems in variably saturated soils.     

Variational principles and finite element simulations for thermo-elastic consolidation

In this paper, a general variational principle for the initial boundary value problem of quasi-static thermoelastic consolidation is developed by assuming infinitesimal deformation and an incompressible fluid flowing through a linearly elastic solid. By manipulating the coupling operators, an extended form of the variational pronciple is derved. The associated finite element formulation based on this principle is presented and numerical applications for plane strain thermo-elastic consolidation are revealed.     

Modelling strain localization in granular materials using micropolar theory: numerical implementation and verification

Implementation and applications for a constitutive numerical model on F‐75 silica sand, course silica sand and two sizes of glass beads compressed under plane strain conditions are presented in this work. The numerical model is used to predict the stress versus axial strain and volumetric strain versus axial strain relationships of those materials; moreover, comparisons between measured and predicted shear band thickness and inclination angles are discussed and the numerical results compare well with the experimental measurements. The numerical model is found to respond to the changes in confining pressure and the initial relative density of a given granular material. The mean particle size is used as an internal length scale. Increasing the confining pressure and the initial density is found to decrease the shear band thickness and increase the inclination angle. The micropolar or Cosserat theory is found to be effective in capturing strain localization in granular materials. The finite element formulations and the solution method for the boundary value problem in the updated Lagrangian frame (UP) are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling the time‐dependent behaviour of granular material with hypoplasticity

This paper presents a constitutive model for time‐dependent behaviour of granular material. The model consists of 2 parts representing the inviscid and viscous behaviour of granular materials. The inviscid part is a rate‐independent hypoplastic constitutive model. The viscous part is represented by a rheological model, which contains a high‐order term denoting the strain acceleration. The proposed model is validated by simulating some element tests on granular soils. Our model is able to model not only the non‐isotach behaviour but also the 3 creep stages, namely, primary, secondary, and tertiary creep, in a unified way.     

考虑颗粒破碎的粗粒土剪胀性统一本构模型

粗粒土作为无黏性散粒状材料具有状态依赖特性,土体的剪切特性受密度和应力水平影响。易破碎是粗粒土的另一个特点,颗粒破碎影响粗粒土的剪胀、内摩擦角、峰值强度和渗透系数。为了能够准确地描述粗粒土的应力-应变关系,采用初始状态参量描述粗粒土的内部状态,根据三轴试验数据建立考虑颗粒破碎耗能的应力-应变关系,采用相关联流动法则推导考虑颗粒破碎的粗粒土剪胀性“统一本构模型”,并建立初始状态参量与模型参数之间的关系。所建立的统一本构模型既考虑了颗粒破碎对剪胀、内摩擦角的影响,又考虑了剪切特性对土体初始状态的依赖。采用变异粒子群算法拟合试验曲线,确定模型参数。模型计算结果能够很好地拟合试验曲线。采用同一组参数对假定的初始状态进行模拟计算,计算结果表明,模型能够模拟不同初始密度和应力水平下粗粒土变形的一般规律。     

On the weak turbulent motions of an isothermal dry granular dense flow with incompressible grains: part II. Complete closure models and numerical simulations

The complete thermodynamically consistent turbulent closure models of isochoric and isothermal dry granular dense flows with incompressible grains and weak turbulent intensity are established on the basis of a linearized theory with respect to the granular coldness for the dynamic responses of the closure conditions. The models are applied to study a gravity-driven stationary turbulent flow down an inclined moving plane, and the numerical simulations are compared with the experimental outcomes. It shows that while the mean velocity decreases monotonically from its boundary value on the moving plane toward the free surface, the mean porosity and granular coldness display more “exponential-like” increasing/decreasing tendencies. Of particular interest is that the granular coldness evolves from its maximum value on the moving plane toward its minimum value on the free surface, leading to the turbulent dissipation evolving in a similar manner, while the turbulent kinetic energy demonstrate a reverse tendency. The obtained results show good agreements to the experimental outcomes and are similar to the characteristics of conventional Newtonian fluids in turbulent shear flows.     

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。     

Analysis of excavations in jointed rock of infinite extent

The subject of this work is the development of a code to study the behaviour of stratified and jointed rock masses around underground excavations. The rock mass is divided into two types of regions, one which is supposed to exhibit linear elastic behaviour and which may extend to infinity, and the other which will include discontinuities that behave inelastically. The former has been simulated by a symmetric direct, boundary integral, plane strain, quadratic, orthotropic module, and the latter by quadratic plane strain, membrane and inelastic joint elements. The two modules are coupled in one program. Sequences of loading include static point, pressure, body and residual loads, construction and excavation sequences, and quasi-static earthquake load. The programe is interactive, with graphics. A numerical example is presented to illustrate the method.     

A critical state sand plasticity model accounting for fabric evolution

Fabric and its evolution need to be fully considered for effective modeling of the anisotropic behavior of cohesionless granular sand. In this study, a three‐dimensional anisotropic model for granular material is proposed based on the anisotropic critical state theory recently proposed by Li & Dafalias [2012], in which the role of fabric evolution is highlighted. An explicit expression for the yield function is proposed in terms of the invariants and joint invariants of the normalized deviatoric stress ratio tensor and the deviatoric fabric tensor. A void‐based fabric tensor that characterizes the average void size and its orientation of a granular assembly is employed in the model. Upon plastic loading, the material fabric is assumed to evolve continuously with its principal direction tending steadily towards the loading direction. A fabric evolution law is proposed to describe this behavior. With these considerations, a non‐coaxial flow rule is naturally obtained. The model is shown to be capable of characterizing the complex anisotropic behavior of granular materials under monotonic loading conditions and meanwhile retains a relatively simple formulation for numerical implementation. The model predictions of typical behavior of both Toyoura sand and Fraser River sand compare well with experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

Heat extraction through a geothermal reservoir on an oblique fault plane

The heat extraction through a geothermal reservoir on an oblique fault plane in the earth's crust is considered. The fault could be modelled mechanically as a frictional contact interface of two elastic bodies. The heat is recovered by circulating fluid through the reservoir, and then the surface of the reservoir is cooled by the fluid. The analysis is based on the two-dimensional theory of quasi-static thermoelasticity. It is concluded from numerical calculations that a geothermal reservoir can be created on an oblique fault plane, and the opened region, i.e. the fluid-filled region, increases gradually with time during the heat extraction. Also discussed are the effects of the fluid pressure and the coefficient of friction on the behaviour of the reservoir.     

Continuum hydrodynamics of dry granular flows employing multiplicative elastoplasticity

We present a Lagrangian formulation for simulating the continuum hydrodynamics of dry granular flows based on multiplicative elastoplasticity theory for finite deformation calculations. The formulation is implemented within the smoothed particle hydrodynamics (SPH) method along with a variant of the usual dynamic boundary condition. Three benchmark simulations on dry sands are presented to validate the model: (a) a set of plane strain collapse tests, (b) a set of 3D collapse tests, and (c) a plane strain simulation of the impact force generated by granular flow on a rigid wall. Comparison with experimental results suggests that the formulation is sufficiently robust and accurate to model the continuum hydrodynamics of dry granular flows in a laboratory setting. Results of the simulations suggest the potential of the formulation for modeling more complex, field-scale scenarios characterized by more elaborate geometry and multi-physical processes. To the authors’ knowledge, this is the first time the multiplicative plasticity approach has been applied to granular flows in the context of the SPH method.     

A kinematic hardening constitutive model for sands: the multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright © 1999 John Wiley & Sons, Ltd.     

FE-studies on the influence of initial void ratio,pressure level and mean grain diameter on shear localization

The paper is concerned with shear localization in the form of a spontaneous shear zone inside a granular material during a plane strain compression test. The influence of an initial void ratio, pressure and a mean grain diameter on the thickness of a shear zone is investigated. A plane strain compression test with dry sand is numerically modelled with a finite element method taking into account a polar hypoplastic constitutive relation which was laid down within a polar (Cosserat) continuum. The relation was obtained through an extension of a non-polar hypoplastic constitutive law according to Gudehus and Bauer by polar quantities: rotations, curvatures, couple stresses and a characteristic length. It can reproduce the essential features of granular bodies during shear localization. The material constants can be easily calibrated. The FE-calculations demonstrate an increase in the thickness of the shear zone with increasing initial void ratio, pressure level and mean grain diameter. Polar effects manifested by the appearance of grain rotations and couple stresses are only significant in the shear zone. A comparison between numerical calculations and experimental results shows a satisfying agreement. Copyright © 1999 John Wiley & Sons, Ltd.