Cavity expansion analyses of crushable granular materials with state‐dependent dilatancy

Crushability is one of the important behaviors of granular materials particularly under high stress states, and affects both the deformability and strength of the materials that are in essence associated with state‐dependent dilatancy. In this presentation, first, a new critical state model is proposed to take into account the three different modes of compressive deformation of crushable granular materials, i.e. particle rearrangement, particle crushing and pseudo‐elastic deformation. Second, the governing equations for cavity expansion in crushable granulates are introduced, in which the state‐dependent dilatancy as well as the bounding surface plasticity model are used. Then, the procedure to obtain semi‐analytical solutions to cavity expansion in the material is described in detail, in which a commercial differential equation solver is employed. Finally, cavity expansion analyses are carried out on Toyoura sand, a well‐documented granular material, to demonstrate the effects of crushability and state‐dependent dilatancy. The study shows that particle crushing does occur at both high stress and critical states and affects the stress fields and the deformation behavior of the material surrounding the cavity in association with state‐dependent dilatancy. This leads to conclusion that particle crushing and state‐dependent dilatancy have to be taken into account when cavity expansion theory is used to interpret cone penetration tests and pressuremeter tests. Copyright © 2011 John Wiley & Sons, Ltd.     

颗粒材料剪胀性的微观力学分析

剪胀性是颗粒材料在加载过程中表现出来的重要变形特性。以孔隙胞元描述颗粒材料内部结构的最小单元,通过对单个孔隙胞元进行剪切受力分析,探讨了剪切过程中颗粒材料体积的改变对应力比和单个孔隙胞元形状的依赖关系,解释了排列密实的颗粒材料在剪切过程中先压缩后剪胀的微观机制。用离散元数值模拟得到了在双轴剪切过程中单个孔隙胞元形状以及孔隙胞元体积变形的演化过程。离散元数值结果表明,加载过程中孔隙胞元形状由初始各向同性到沿大主应力方向变大变长、体积变形先压缩后膨胀,并且体积变形在加载过程中存在局部化现象,体积变化大的孔隙胞元在较大变形时,排列成倾斜的窄带。综合孔隙胞元的受力分析和离散元数值结果表明,致密排列颗粒材料的剪胀性与微观尺度上孔隙胞元的几何结构及其内部的力链传递方式密切相关。     

易破碎粒状材料本构研究

粒状材料被广泛地应用到土木工程的各个领域。大部分粒状材料在外力作用下较容易产生颗粒破碎,颗粒破碎对材料的力学性能有很大的影响。为了更好地描述易破碎粒状材料的力学特性,基于弹塑性力学和临界状态土力学开发了一种能够考虑颗粒破碎效应的本构模型。此本构模型能够考虑在剪应力和压应力作用下引起的颗粒破碎对粒状材料力学性能的影响。为了考虑颗粒破碎的影响,基于对Cambria 砂的高压试验,得出了临界状态线位置与消耗塑性功之间的关系,并称之为“破碎方程”。此本构模型拥有双屈服面,分别考虑剪切和等向压缩产生的塑性变形。通过试验结果与数值计算结果的对比得出,新的本构模型能较好地描述易破碎粒状材料的力学特性     

A numerical investigation of the incremental behavior of crushable granular soils

The mechanical behavior of granular materials is characterized by strong nonlinearity and irreversibility. These properties have been differently described by a variety of constitutive models. To test any constitutive model, experimental data relative to the nature of the incremental stress–strain response of the material is desirable. However, this type of laboratory data is scarce because of being expensive and difficult to obtain. The discrete element method has been used several times as an alternative to obtain incremental responses of granular materials. Crushable grains add one extra source of irreversibility to granular materials. Crushability has been variously incorporated into different constitutive models. Again, it will be helpful to obtain incremental responses of crushable granular materials to test these models, but the experimental difficulties are increased. Making use of a recently introduced crushing model for discrete element simulation, this paper presents a new procedure to obtain incremental responses in discrete analogs of granular crushable materials. The parallel probe approach, previously used for uncrushable discrete analogs, is here extended to account for the presence of crushable grains. The contribution of grain crushing to the incremental irreversible strain is identified and separately measured. Robustness of the proposed method is examined in detail, paying particular attention to aspects such as dynamic instability or crushing localization. The proposed procedure is later applied to map incremental responses of a discrete analog of Fontainebleau sand on the triaxial plane. The effect of stress ratio and granular state on plastic flow characteristics is highlighted. Copyright © 2016 John Wiley & Sons, Ltd.     

Stress–dilatancy behavior for sand under loading and unloading conditions

Experimental results have shown very different stress–dilatancy behavior for sand under loading and unloading conditions. Experimental results have also shown significant effects of inherent anisotropy. In this article, a micromechanics‐based method is presented, by which the stress–dilatancy relation is obtained through the consideration of slips at the interparticle contacts in all orientations. The method also accounts for the effect of inherent anisotropy in sand. Experimental results on Toyoura sand and Hostun sand are used for illustration of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

Breakage and deformation mechanisms of crushable granular materials

Biaxial compressional tests with two types of stress paths were carried out on an assembly of round bars, which can be crushed to investigate the breakage and deformation mechanisms of granular materials at the mesoscale. The following was found experimentally: (1) upon loading, the crushable rods slide, rotate and break, and finally the breakage band forms for the two types of stress paths and different stress states; and (2) for the axial loading stress path, the round rods mainly fail in the vertically split mode and laterally crushed mode. However, for the lateral unloading stress path, the round rods fail with the combination mode of locally crushed and vertically split.     

Gradient plasticity modelling of strain localization in granular materials

The flow stress in the yield surface of plastic constitutive equation is modified with a higher order gradient term of the effective plastic strain to model the effect of inhomogeneous deformation in granular materials. The gradient constitutive model has been incorporated into the finite element code ABAQUS and used to simulate biaxial shear tests on dry sand. It is shown that the shape of the post-peak segment of the load displacement curve predicted by the numerical analysis is dependent on the mesh size when gradient term is not used. Use of an appropriate gradient coefficient is shown to correct this and predict a unique shape of the load displacement curve regardless of the mesh size. The gradient coefficient required turns out to be approximately inversely proportional to the mesh elemental area. Use of the strain gradient term is found to diffuse the concentration of plastic strains within shear band resulting in its consistent width. The coefficient of the higher gradient term appears as a function of the grain size, the mean confining stress, and the plastic softening modulus. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Evolution of induced fabric in a strain space multiple mechanism model for granular materials

The strain space multiple mechanism model idealizes the behavior of granular materials based on a multitude of virtual simple shear mechanisms oriented in arbitrary directions. Within this modeling framework, the virtual simple shear stress is defined as a quantity that depends on the contact distribution function as well as the normal and tangential components of inter‐particle contact forces, which evolve independently during the loading process. In other terms, the virtual simple shear stress is an intermediate quantity in the upscaling process from the microscopic level (characterized by the contact distribution and inter‐particle contact forces). The stress space fabric (i.e. the orientation distribution of the virtual simple shear stress) produces macroscopic stress through the tensorial average. Thus, the stress space fabric characterizes the fundamental and higher modes of anisotropy induced in granular materials. Comparing an induced fabric associated with the biaxial shear of plane granular assemblies obtained via a simulation using Discrete Element Method to the strain space multiple mechanism model suggests that the strain space multiple mechanism model has the capability to capture the essential features in the evolution of an induced fabric in granular materials. Copyright © 2012 John Wiley & Sons, Ltd.     

A constitutive model for granular materials with grain crushing and its application to a pyroclastic soil

A constitutive model for granular materials is developed within the framework of strain–hardening elastoplasticity, aiming at describing some of the macroscopic effects of the degradation processes associated with grain crushing. The central assumption of the paper is that, upon loading, the frictional properties of the material are modified as a consequence of the changes in grain size distribution. The effects of these irreversible microscopic processes are described macroscopically as accumulated plastic strain. Plastic strain drives the evolution of internal variables which model phenomenologically the changes of mechanical properties induced by grain crushing by controlling the geometry of the yield locus and the direction of plastic flow. An application of the model to Pozzolana Nera is presented. The stress–dilatancy relationship observed for this material is used as a guidance for the formulation of hardening laws. One of the salient features of the proposed model is its capability of reproducing the stress–dilatancy behaviour observed in Pozzolana Nera, for which the minimum value of dilatancy always follows the maximum stress ratio experienced by the material. Copyright © 2002 John Wiley & Sons, Ltd.     

Dominant grains network and behavior of sand–silt mixtures: stress–strain modeling

Stress–strain modeling of sand–silt mixtures is important in the analysis and design of earth structures. In this paper, we develop a stress–strain model that can predict the behavior of sand–silt mixtures with any amount of fines content. This model is based on a micromechanics approach, which involves mean‐field assumptions. For the mixtures with low amount of fines, the mechanical behavior is dominated by sand grains network. On the other hand, for the mixtures with high amount of fines, the mechanical behavior is dominated by silt grains network. Using this concept of dominant grains network, the behavior of mixtures with any amount of fines can be predicted from knowing the behavior of sand and silt, alone. We also modeled the critical state friction angle, critical state void ratio, and elastic stiffness for the mixtures as a function of fines content. The applicability of this developed stress–strain model is shown by comparing the simulated and measured results for two different types of sand–silt mixtures with full range of fines content. Copyright © 2012 John Wiley & Sons, Ltd.     

A visco‐plastic constitutive model for granular soils modified according to non‐local and gradient approaches

An already available non‐associated elastic–viscoplastic constitutive model with anisotropic strain hardening is modified in order to describe both the constitutive parameter dependency on relative density and the spatio‐temporal evolution of strain localization. To achieve this latter goal, two distinct but similar approaches are introduced: one inspired by the gradient theory and one by the non‐local theory. A one‐dimensional case concerning a simple shear test for a non‐homogeneous infinitely long dense sand specimen is numerically discussed and a finite difference scheme is employed for this purpose. The results obtained by following the two different approaches are critically analysed and compared. Copyright © 2001 John Wiley & Sons, Ltd.     

Kinematic models for non‐coaxial granular materials. Part I: theory

The purpose of this paper is to present a physically based plasticity model for non‐coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR² model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro‐analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro‐pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro–micro mechanical analysis shows that the APR is a non‐linear function of, among other quantities, the macro‐rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double‐sliding free‐rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR² model the APR tensor and the spin tensor are directly linked with non‐coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR² model for a class of dilatant materials, and analyse its material stability. Copyright © 2005 John Wiley & Sons, Ltd.     

基于CLoE与Gudehus-Bauer亚塑性模型的颗粒材料应变局部化对比研究

基于CLoE与Gudehus-Bauer亚塑性模型数值模拟了平面应变条件下Hostun砂的应变局部化现象。从侧向压力和初始缺陷两个方面对比研究了两种模型所预测应变局部化的产生及演化模式。结果表明：（1）两种模型均能反映Hostun砂刚度随着侧向压力提高而增大的现象。（2）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得出的应变局部化形态与试验结果更加一致。（3）CLoE亚塑性模型能够反映随着荷载增加,砂的体积先膨胀后缩小的特点。（4）相比Gudehus-Bauer亚塑性模型,CLoE亚塑性模型所得到的应变-应力曲线能够更明显地反映应变局部化带中单元的软化现象。（5）CLoE亚塑性模型能够更好地模拟由初始缺陷导致的不均匀应变。总的来说,所得的数值结果表明,CLoE亚塑性模型能够较好地模拟侧向压力和初始缺陷对应变局部化的影响,在模拟应变局部化现象方面较Gudehus-Bauer更有优势。然而,现有CLoE亚塑性模型无法考虑孔隙比,也未包含颗粒材料内尺度变量,有待进一步完善。     

堆石料的临界状态与考虑颗粒破碎的本构模型

高应力水平时堆石料的颗粒破碎对其强度和变形机制有重要影响。临界状态土力学理论对重塑土的应力-应变关系的描述较为成功,但目前颗粒破碎对堆石料的临界状态的影响及其数学描述鲜有研究。对堆石料进行了固结应力从0.4 MPa到4 MPa的18组固结排水和固结不排水常规三轴压缩试验,以及6组等向压缩试验。试验结果表明：在排水条件和不排水条件下,不同的固结应力试样都趋于临界状态;堆石料的临界状态在q-p′平面和e-lgp′平面均为非线性变化。基于此试验结果,通过引入状态参数,在广义塑性力学的理论框架下,建立了考虑颗粒破碎的堆石料本构模型,并给出了模型参数的确定方法。与长河坝料的试验进行了对比,结果表明所建议的本构模型可以较好地模拟堆石料从低围压0.4 MPa到高围压 3.5 MPa下的应力-应变特性     

Solid–fluid transition modelling in geomaterials and application to a mudflow interacting with an obstacle

Given the contrasting behaviour observed for geomaterials, for example, during landslides of the flow type, this contribution proposes an original constitutive model, which associates both an elasto‐plastic relation and a Bingham viscous law linked by a mechanical transition criterion. This last is defined as the second‐order work sign for each material point, which is a general criterion for divergence instabilities. Finite element method with Lagrangian integration points is chosen as a framework for implementing the new model because of its well‐known ability to deal with both solid and fluid behaviours in large deformation processes. A first boundary model considering a sample of initially stable soil, a slope and an obstacle is performed. The results show the power of the constitutive model because the consistent evolution of initiation, propagation and arrest of the mudflow is described. A parametric study is led on various plastic and viscous parameters to determine their influence on the flow development and arrest. Finally, forces against the obstacle are compared with good agreement with those of other authors for the same geometry and a pure viscous behaviour. Copyright © 2014 John Wiley & Sons, Ltd.     

Generalized plasticity state parameter‐based model for saturated and unsaturated soils. Part II: Unsaturated soil modeling

The aim of this paper is to extend the generalized plasticity state parameter‐based model presented in part 1 to reproduce the hydro‐mechanical behavior of unsaturated soils. The proposed model is based on two pairs of stress–strain variables and a suitable hardening law taking into account the bonding—debonding effect of suction and degree of saturation. A generalized state parameter for unsaturated state is proposed to reproduce soil behavior using a single set of material parameters. Generalized plasticity gives a suitable framework to reproduce not only monotonic stress path but also cyclic behavior. The hydraulic hysteresis during a drying—wetting cycle and the void ratio effect on the hydraulic behavior is introduced. Comparison between model simulations and a series of experimental data available, both cohesive and granular, are given to illustrate the accuracy of the enhanced generalized plasticity equation. Copyright © 2010 John Wiley & Sons, Ltd.     

Mechanical properties of granular materials: A variational approach to grain‐scale simulations

The mechanical properties of cohesionless granular materials are evaluated from grain‐scale simulations. A three‐dimensional pack of spherical grains is loaded by incremental displacements of its boundaries. The deformation is described as a sequence of equilibrium configurations. Each configuration is characterized by a minimum of the total potential energy. This minimum is computed using a modification of the conjugate gradient algorithm. Our simulations capture the nonlinear, path‐dependent behavior of granular materials observed in experiments. Micromechanical analysis provides valuable insight into phenomena such as hysteresis, strain hardening and stress‐induced anisotropy. Estimates of the effective bulk modulus, obtained with no adjustment of material parameters, are in agreement with published experimental data. The model is applied to evaluate the effects of hydrate dissociation in marine sediments. Weakening of the sediment is quantified as a reduction in the effective elastic moduli. Copyright © 2008 John Wiley & Sons, Ltd.