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A three-dimensional discrete element model is used to investigate the effect of grain crushing on the tip resistance measured by cone penetration tests (CPT) in calibration chambers. To do that a discrete analogue of pumice sand, a very crushable microporous granular material, is created. The particles of the discrete model are endowed with size-dependent internal porosity and crushing resistance. A simplified Hertz–Mindlin elasto-frictional model is used for contact interaction. The model has 6 material parameters that are calibrated using one oedometer test and analogies with similar geomaterials. The calibration is validated reproducing other element tests. To fill a calibration chamber capable of containing a realistic sized CPT the discrete analogue is up-scaled by a factor of 25. CPT is then performed at two different densities and three different confinement pressures. Cone tip resistance in the crushable material is practically insensitive to initial density, as had been observed in previous physical experiments. The same CPT series is repeated but now particle crushing is disabled. The ratios of cone tip resistance between the two types of simulation are in good agreement with previous experimental comparisons of hard and crushable soils. Microscale exploration of the models indicates that crushing disrupts the buttressing effect of chamber walls on the cone. 相似文献
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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. 相似文献
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Stress–dilatancy based modelling of granular materials and extensions to soils with crushable grains
Stress–dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics. In this paper, a method to construct thermodynamically consistent (isotropic, three‐invariant) elasto‐plastic models based on a given stress–dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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This article presents a fundamental study on the role of particle breakage on the shear behavior of granular soils using the three‐dimensional (3‐D) discrete element method. The effects of particle breakage on the stress ratio, volumetric strain, plastic deformation, and shear failure behavior of dense crushable specimens undergoing plane strain shearing conditions are thoroughly investigated through a variety of micromechanical analyses and mechanism demonstrations. The simulation of a granular specimen is based on the effective modeling of realistic fracture behavior of single soil particles, which is demonstrated by the qualitative agreement between the results from platen compression simulations and those from physical laboratory tests. The simulation results show that the major effects of particle breakage include the reduction of volumetric dilation and peak stress ratio and more importantly the plastic deformation mechanisms and the shear failure modes vary as a function of soil crushability. Consistent macro‐ and micromechanical evidence demonstrates that shear banding and massive volumetric contraction depict the two end failure modes of a dense specimen, which is dominated by particle rearrangement–induced dilation and particle crushing–induced compression, respectively, with a more general case being the combination and competition of the two failure modes in the medium range of soil crushability and confining stress. However, it is further shown that a highly crushable specimen will eventually develop a shear band at a large strain because of the continuous decay of particle breakage. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials. 相似文献
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For research on granular materials, establishing a method to calculate continuum strain from particle displacements is necessary for understanding the material behaviour at macro-level and developing continuum constitutive models. Existing methods are generally based on constructing a mesh or background grid to calculate strain from particle motions. These methods offer rigorous ways to measure strain for granular materials; however, they suffer from several problems such as mesh distortion and lacking grid-to-particle strain mapping procedure, which hinders their capability of calculating strain accumulation during large deformation processes of granular media. To address this issue, this study proposes a new strain calculation method for discrete element simulations of granular materials. This method describes a particle assembly as an equivalent continuum system of material points, each of which corresponds to a particle centre and represents a continuous region with its initial volume/area presumably equal to the volume/area of Voronoi cells generated in accordance with the particle assembly configuration. Smooth Particle Hydrodynamics (SPH) interpolation functions are then employed to calculate strain for these material points. This SPH-based method does not require any mesh or background grid for computation, leading to advantages in calculating strain accumulation under large deformation. Simulations of granular materials in both uniform and heterogeneous gradations were carried out, and strain results obtained by the proposed method indicate good agreements with analytical and numerical solutions. This demonstrates its potential for strain calculations in discrete element simulations of granular materials involving large deformations and/or large displacements. 相似文献
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Equivalent continuum strain calculations based on 3D particle kinematic measurements of sand 
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下载免费PDF全文 Siavash Amirrahmat Khalid A. Alshibli Maha F. Jarrar Boning Zhang Richard A. Regueiro 《国际地质力学数值与分析法杂志》2018,42(8):999-1015
Constitutive modeling of granular materials has been a subject of extensive research for many years. While the calculation of the Cauchy stress tensor using the discrete element method has been well established in the literature, the formulation and interpretation of the strain tensor are not as well documented. According to Bagi, 1 researchers mostly adopt well‐known continuum or discrete microstructural approaches to calculate strains within granular materials. However, neither of the 2 approaches can fully capture the behavior of granular materials. They are considered complementary to each other where each has its own strengths and limitations in solving granular‐mechanics problems. Zhang and Regueiro 2 proposed an equivalent continuum approach to calculating finite strain measures at the local level in granular materials subjected to large deformations. They used three‐dimensional discrete element method results to compare the proposed strains measures. This paper presents an experimental application of the Zhang and Regueiro 2 approach using three‐dimensional synchrotron microcomputed tomography images of a sheared Ottawa sand specimen. Invariant Eulerian finite strain measures were calculated for representative element volumes within the specimen. The spatial maps of Eulerian octahedral shear and volumetric strain were used to identify zones of intense shearing within the specimen and compared well with maps of incremental particle translation and rotation for the same specimen. The local Eulerian volumetric strain was compared to the global volumetric strains, which also can be considered as an averaging of all local Eulerian volumetric strains. 相似文献
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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. 相似文献
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Revisiting the existence of an effective stress for wet granular soils with micromechanics 下载免费PDF全文
下载免费PDF全文 A possible effective stress variable for wet granular materials is numerically investigated based on an adapted discrete element method (DEM) model for an ideal three‐phase system. The DEM simulations consider granular materials made of nearly monodisperse spherical particles, in the pendular regime with the pore fluid mixture consisting of distinct water menisci bridging particle pairs. The contact force‐related stress contribution to the total stresses is isolated and tested as the effective stress candidate for dense or loose systems. It is first recalled that this contact stress tensor is indeed an adequate effective stress that describes stress limit states of wet samples with the same Mohr‐Coulomb criterion associated with their dry counterparts. As for constitutive relationships, it is demonstrated that the contact stress tensor used in conjunction with dry constitutive relations does describe the strains of wet samples during an initial strain regime but not beyond. Outside this so‐called quasi‐static strain regime, whose extent is much greater for dense than loose materials, dramatic changes in the contact network prevent macroscale contact stress‐strain relationships to apply in the same manner to dry and unsaturated conditions. The presented numerical results also reveal unexpected constitutive bifurcations for the loose material, related to stick‐slip macrobehavior. 相似文献
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This study investigates the influence of the intermediate principle stress on the particle breakage of granular materials. The crushable agglomerate method is applied to model soil particles and numerical true triaxial tests were carried out. The results show that particle breakage increases with increasing b value, the relationship of which follows an exponential function and agrees well with previous experimental results. More importantly, the study found that the relationship between particle breakage and total energy input is independent of the intermediate principle stress, which provides a good basis for the constitutive modeling of granular materials. 相似文献
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砂土的力学响应具有显著的增量非线性特征，这与离散颗粒的微观结构，即组构特性密不可分。采用应变响应包络可以较好地获得材料在不同加载方向上的增量力学响应。在物理试验中无法同时获得同一试样在不同加载方向下的宏、微观响应，故采用离散元方法，对具有不同应力历史、不同应力状态和不同级配的试样在Rendulic平面上的增量力学响应进行了系统研究和分析。离散元模拟结果表明，传统的塑性理论不能很好地描述具有复杂应力历史试样的增量力学响应，而基于颗粒间接触法向的组构增量与剪应变之间在多种不同的工况条件下均具有较强的线性相关性。当砂土的相对密实度相同时，该线性系数主要与围压的大小有关，对颗粒级配、应力历史以及应力比的变化均不敏感。由于组构的大小可以较好地量化砂土的内结构各向异性程度，进而表征应力历史的作用。上述模拟结果为在本构建模中引入组构演化机制，综合反映外荷载和内结构各向异性对砂土增量本构关系的影响提供了较好的微观物理依据。 相似文献
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Ciantia Matteo O. Arroyo Marcos O’Sullivan Catherine Gens Antonio 《Acta Geotechnica》2019,14(5):1337-1356
In granular soils grain crushing reduces dilatancy and stress obliquity enhances crushability. These are well-supported specimen-scale experimental observations. In principle, those observations should reflect some peculiar micromechanism associated with crushing, but which is it? To answer that question the nature of crushing-induced particle-scale interactions is here investigated using an efficient DEM model of crushable soil. Microstructural measures such as the mechanical coordination number and fabric are examined while performing systematic stress probing on the triaxial plane. Numerical techniques such as parallel and the newly introduced sequential probing enable clear separation of the micromechanical mechanisms associated with crushing. Particle crushing is shown to reduce fabric anisotropy during incremental loading and to slow fabric change during continuous shearing. On the other hand, increased fabric anisotropy does take more particles closer to breakage. Shear-enhanced breakage appears then to be a natural consequence of shear-enhanced fabric anisotropy. The particle crushing model employed here makes crushing dependent only on particle and contact properties, without any pre-established influence of particle connectivity. That influence does not emerge, and it is shown how particle connectivity, per se, is not a good indicator of crushing likelihood.
相似文献15.
This study proposed a novel approach for generating crushable agglomerates with realistic particle shapes in discrete element modeling (DEM). The morphologies of sand particles were obtained by X-ray micro-computed tomography scanning and image processing. Based on the particle surface reconstructed by spherical harmonic analysis, the crushable agglomerates with realistic particle shapes can be generated in DEM simulations. The results of single particle crushing tests showed that particle shapes significantly influence the fracture patterns and crushing strengths of sand particles. Furthermore, two one-dimensional compression tests were conducted to investigate the particle shape effect on micro- and macro-mechanical behaviors of crushable sands. 相似文献
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It is well known that the compressibility of crushable granular materials increases with the moisture content,due to the decrease of particle strength in a humid environment.An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work.But how the material humidity can affect this relationship is not clear,and experimental evidence is quite scarce.Based on compression tests on dry and saturated crushable sand recently reported by the present authors,a new non-linear relationship is proposed between the amount of particle breakage and the plastic work.The expression contains two parameters:(1)a material constant dependent on the grain characteristics and(2)a constant depending on the wetting condition(in this study,dry or saturated).A key finding is that the relationship does not depend on the stress path and,for a given wetting condition,only one set of parameters is necessary to reproduce the results of isotropic,oedometric,and triaxial compression tests.The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression.The breakage ratio is introduced into the expression of the elastic stiffness,the critical state line and the hardening compression pressure.Incremental stress-strain computations with the model allow the plastic work to be calculated and,therefore,the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations.Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained. 相似文献
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It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill‐posedness and mesh dependency. Therefore, a non‐local theory with internal length scales is needed to overcome such problems. The micropolar and high‐order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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The critical state is significant to the mechanical behaviors of granular materials and the foundation of the constitutive relations. Using the discrete element method (DEM), the mechanical behaviors of granular materials can be investigated on both the macroscopic and microscopic levels. A series of DEM simulations under true triaxial conditions have been performed to explore the critical state and dilatancy behavior of granular materials, which show the qualitatively similar macroscopic responses as the experimental results. The critical void ratio and stress ratio under different stress paths are presented. A unique critical state line (CSL) is shown to indicate that the intermediate principal stress ratio does not influence the CSL. Within the framework of the unique critical state, the stress–dilatancy relation of DEM simulations is found to fulfill the state-dependent dilatancy equations. As a microscopic parameter to evaluate the static determinacy of the granular system, the redundancy ratio is defined and investigated. The results show that the critical state is very close to the statically determinate state. Other particle-level indexes, including the distribution of the contact forces and the anisotropies, are carefully investigated to analyze the microstructural evolution and the underlying mechanism. The microscopic analysis shows that both the contact orientations and contact forces influence the mechanical behaviors of granular materials. 相似文献
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Acta Geotechnica - An elastic–plastic constitutive model considering particle breakage for simulation of crushable granular soils behavior is proposed. In the model, elastic strain rates are... 相似文献