Fabric,force and strength anisotropies in granular materials: a micromechanical insight

In micromechanics, the stress–force–fabric (SFF) relationship is referred to as an analytical expression linking the stress state of a granular material with microparameters on contact forces and material fabric. This paper employs the SFF relationship and discrete element modelling to investigate the micromechanics of fabric, force and strength anisotropies in two-dimensional granular materials. The development of the SFF relationship is briefly summarized while more attention is placed on the strength anisotropy and deformation non-coaxiality. Due to the presence of initial anisotropy, a granular material demonstrates a different behaviour when the loading direction relative to the direction of the material fabric varies. Specimens may go through various paths to reach the same critical state at which the fabric and force anisotropies are coaxial with the loading direction. The critical state of anisotropic granular material has been found to be independent of the initial fabric. The fabric anisotropy and the force anisotropy approach their critical magnitudes at the critical state. The particle-scale data obtained from discrete element simulations of anisotropic materials show that in monotonic loading, the principal force direction quickly becomes coaxial with the loading direction (i.e. the strain increment direction as applied). However, material fabric directions differ from the loading direction and they only tend to be coaxial at a very large shear strain. The degree of force anisotropy is in general larger than that of fabric anisotropy. In comparison with the limited variation in the degree of force anisotropy with varying loading directions, the fabric anisotropy adapts in a much slower pace and demonstrates wider disparity in the evolution in the magnitude of fabric anisotropy. The difference in the fabric anisotropy evolution has a more significant contribution to strength anisotropy than that of force anisotropy. There are two key parameters that control the degree of deformation non-coaxiality in granular materials subjected to monotonic shearing: the ratio between the degrees of fabric anisotropy and that of force anisotropy and the angle between the principal fabric direction and the applied loading direction.     

Macroscopic model with anisotropy based on micro–macro information

Physical experiments can characterize the elastic response of granular materials in terms of macroscopic state variables, namely volume (packing) fraction and stress, while the microstructure is not accessible and thus neglected. Here, by means of numerical simulations, we analyze dense, frictionless granular assemblies with the final goal to relate the elastic moduli to the fabric state, i.e., to microstructural averaged contact network features as contact number density and anisotropy. The particle samples are first isotropically compressed and then quasi-statically sheared under constant volume (undrained conditions). From various static, relaxed configurations at different shear strains, infinitesimal strain steps are applied to “measure” the effective elastic response; we quantify the strain needed so that no contact and structure rearrangements, i.e. plasticity, happen. Because of the anisotropy induced by shear, volumetric and deviatoric stresses and strains are cross-coupled via a single anisotropy modulus, which is proportional to the product of deviatoric fabric and bulk modulus (i.e., the isotropic fabric). Interestingly, the shear modulus of the material depends also on the actual deviatoric stress state, along with the contact configuration anisotropy. Finally, a constitutive model based on incremental evolution equations for stress and fabric is introduced. By using the previously measured dependence of the stiffness tensor (elastic moduli) on the microstructure, the theory is able to predict with good agreement the evolution of pressure, shear stress and deviatoric fabric (anisotropy) for an independent undrained cyclic shear test, including the response to reversal of strain.     

Numerical analysis of critical state behaviors of granular soils under different loading conditions

Discrete element method is used to simulate granular assembly behaviors with different initial conditions under three different loading conditions—plain strain, conventional triaxial compression, and direct shear. Different deformation modes of specimens with different conditions are presented. Some important parameters of the critical state theory are investigated. Uniqueness of the critical state line is checked which shows that there is no a unique critical state line for specimens with different initial void ratios under different loading conditions. Frictional angles and dilation angles of specimens with different conditions at critical state are compared. Void ratios and coordination numbers of specimens at critical state are studied. Anisotropies of the particle orientation and normal contact force at initial state, critical state, as well as the evolutions during shearing are analyzed. The anisotropy is shown to have significant effects on the soil behaviors and is related to the non-uniqueness of the critical state line. The developed numerical models can be used to study the micromechanics and microstructure of the specimen subjected to different loading conditions in the future.     

DEM simulation of the undrained shear behavior of sand containing dissociated gas hydrate

A numerical simulation technique is proposed using discrete element method (DEM) to study the undrained shear behavior of sand containing dissociated gas hydrate. Dissociation of gas hydrate in sand samples under undrained conditions is simulated first, followed by undrained bi-axial compression of these samples, which consist of three phases, i.e., sand particles, water, and methane gas. The simulations demonstrate that hydrate dissociation under undrained conditions generates significant excess pore pressure and volumetric dilation, the magnitudes of which are found to be comparable with those predicted by theoretical analysis. During the undrained bi-axial compression, samples with different initial degrees of hydrate saturation exhibit markedly different shear behavior. Complete strain softening behavior, i.e., static liquefaction, is observed for the samples with relatively high initial degrees of hydrate saturation, while other samples reach quasi-steady state followed by strain hardening at large strains. The observed static liquefaction is believed to be a combined result of the looser sand structure induced by hydrate dissociation, and the essentially stiff modulus of fluid under high pore pressure, despite the existence of gas in sand pores. The influence of initial sample porosity and particle shape is also investigated.     

Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.     

3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography

Many experimental studies have demonstrated that mechanical response of granular materials is highly influenced by micro-structural fabric and its evolution. In the current literature, quantification of fabric and its evolution has been developed based on micro-structural observations using Discrete Element Method or 2D experiments with simple particle shapes. The emergence of X-ray computed tomography technique has made quantification of such experimental micro-structural properties possible using 3D high-resolution images. In this paper, synchrotron micro-computed tomography was used to acquire 3D images during in-situ conventional triaxial compression experiments on granular materials with different morphologies. 3D images were processed to quantify fabric and its evolution based on experimental measurements of contact normal vectors between particles. Overall, the directional distribution of contact normals exhibited the highest degree of isotropy at initial state (i.e., zero global axial strain). As compression progressed, contact normals evolved in the direction of loading until reaching a constant fabric when experiments approached the critical state condition. Further assessment of the influence of confining pressure, initial density state, and particle-level morphology on fabric and its evolution was formed. Results show that initial density state and applied confining pressure significantly influence the fabric-induced internal anisotropy of tested specimens at initial states. Relatively, a higher applied confining pressure and a looser initial density state resulted in a higher degree of fabric-induced internal anisotropy. Influence of particle-level morphology was also found to be significant particularly on fabric evolution.     

Evolution of fabric during undrained cyclic loading

Abstract

Undrained cyclic triaxial tests are performed on specimens of Ottawa sand to study the evolution of fabric during undrained cyclic loading. Isotropic consolidation tests and triaxial drained compression or extension tests are conducted before or after cyclic loading to characterize the state of fabric indirectly. The effects of stress path, cyclic stress ratio, cyclic number, and initial fabric on fabric evolution during undrained cyclic loading are investigated.     

Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations

This paper presents the results of numerical simulations using the three-dimensional discrete element method (DEM) on the critical state behaviour of isotropically compressed and rebounded assemblies of granular materials. Drained and undrained (constant volume) numerical simulations were carried out. From these numerical simulations of drained and undrained tests, it has been shown that the steady state is same as the critical state. Critical state for both isotropically compressed and rebounded assemblies form unique curved line that can be approximated by a bilinear line as proposed by Been et al. [Géotechnique 41(3): 365–381, 1991]. Further more, evolution of the internal variables such as average coordination number and induced anisotropy coefficients during shear deformation has been studied.     

Probing into the strain induced anisotropy of Hostun RF loose sand

Several recent linear drained preloading histories with fixed direction were especially designed to study the effects of strain induced anisotropy of loose Hostun RF sand in the compression side of the classical triaxial plane. Nearly identical void ratio and a same initial isotropic stress state prior to the final undrained shearing in compression are the requirements of the experimental program to take into account only the deviatoric strain histories. The effects of previous deviatoric strain histories on the undrained response of loose Hostun RF sand are identified: mainly the progressive transformation of a contractive and unstable behaviour of very loose sand into a dilative and stable behaviour of dense-like sand by previous linear drained history, while remaining in the same state of loose density. Experimental data evidence the directional dependency of the initial gradient of the effective stress paths, independent of the length of the approaching linear stress paths; the large common non linear effective stress response up to the deviatoric stress peak; the progressive appearance of the dilatancy domain and the unexpected evolution of the undrained behaviour of loose and presheared sand. The paper provides new insights into the mechanisms of strain induced anisotropy of loose sand created by simple linear triaxial stress paths from an isotropic stress state.     

Numerical and experimental stiffness characterisations applied to soft textile composites for tensile structures

This paper presents numerical and experimental stiffness characterisation methods for soft composite textile membranes used in fabric roof structures. The studied material is a polyester plain-woven fabric coated with PVC. We present three numerical textile composite micro-structure models. They are integrated in stiffness calculation software programs which are used to identify linear elastic characteristics for a coated fabric sample. The first two models are based on the laminated thin plate theory; the fabric is represented by a stacking of unidirectionally-reinforced layers, or by the ‘Crimp Model’. The third one considers a geometrical approach to the basic cell of the fabric; the elastic characteristics are calculated by assembly of the meshing elements. In addition, an inverse and experimental stiffness identification method, based on biaxial tensile tests conducted (in orthotropic directions), is proposed. Load-controlled tests are conducted on cross-shaped samples with different loading ratios in warp and weft directions: 1/1,1/2,2/1.     

Micro origins for macro behavior in granular media

We report the latest advances in understanding, characterization and modeling of key micro mechanisms and origins underpinning the interesting and complex macroscopic behavior of granular matter. Included in this Topical Collection are novel theories, innovative experimental tools and new numerical approaches, focusing primarily on three subtopics governing important multiscale properties of granular media: (a) the jamming transition from fluid- to solid-like behavior, critical state flow and wave propagation, (b) the signature of fabric and its evolution for granular media under general loading conditions, and (c) mechanisms like rotation, breakage, failure and aggregation. The significance of these contributions and exploratory future directions pertaining to cross-scale understanding of granular matter are discussed.     

Static liquefaction of sandy soil: An experimental investigation into the effects of saturation and initial state

The effects of initial state of the samples and the saturation evaluated in terms of Skempton??s pore pressure B on the behavior of Chlef sand are studied in this article. For this purpose, the results of two series of drained and undrained monotonic triaxial compression tests on medium dense sand are presented. In the first test series, the influence of the specimen??s fabric and confining pressure has been studied. The tests were conducted at initial confining pressure of 50, 100, and 200?kPa. The specimens were prepared by two depositional methods that include dry funnel pluviation and wet deposition. All the samples were subjected to a monotonic loading after a consolidation phase. The results of the tests demonstrate that initial confining pressure and the specimen??s fabric have detectable effects on the behavior of the sand. In the second series of tests, the saturation influence on the resistance to the sand liquefaction has been realized on samples at an effective stress of 100?kPa for Skempton??s pore pressure coefficient varying between 13 and 90%. It was found that the increase in Skempton??s pore pressure coefficient B reduces the soil dilatancy and amplifies the phase of contractancy.     

Experimental study on yielding and failure of an anisotropic clay

The effect of initial and stress-induced anisotropies on yielding and failure of an anisotropic clay has been studied experimentally by loading soil samples along different stress paths under triaxial stress. Five orientations of bedding planes of clay fabric were tested. In all the loading paths, it was observed that the strain increment vectors were not coaxial with the stress vectors. The degree of disassociation depended on initial fabric anisotropy and stress-induced anisotropy. The test results indicated that for the inherently anisotropic material, there is no particular requirement (a) for the yield and plastic potential surfaces to coincide, and (b) for an associated flow rule to hold.     

Coupled damage tensors and weakest link theory for the description of crack induced anisotropy in concrete

Crack induced anisotropy in concrete is modeled within the general framework of damage mechanics. The damage state, formulated by using the effective stresses, is described by two second order tensors for direct and for induced cracks, respectively. These variables are deduced from different causes of deterioration by the generalized weakest link theory. The major contributions of this paper are the development of a failure criterion in multiaxial compression loading, and the definition of a projection method for assessing the effects of an initial oriented damage in any loading direction. The model is applied to the numerical analysis of concrete structures and the results are compared to available experimental data.     

Influence of fabric on liquefaction and densification potential of cohesionless sand

For simple shearing under constant pressure, the effects of fabric on liquefaction and densification potentials of saturated cohensionless granular materials are examined theoretically and experimentally. The fabric is identified with the distribution of the dilatancy angles (the angle between the sliding and the macroscopic shearing directions), and the influence of prestraining on this distribution and hence on the macroscopic sample behavior is studied. It is shown that prestraining with zero residual stress can reduce resistance to liquefaction by one or even two orders of magnitude, although the sample density and other conditions are kept the same. The micromechanical features responsible for this and related behaviors are examined in some detail. Finally, some tentative results on the effect of the inherent anisotropy that is produced during sample preparation are reported, showing that a method which yields samples more resistive in triaxial cyclic tests may provide samples less resistive in cyclic shearing.     

Stress-chain based micromechanics of sand with grain shape effect

The mechanical behaviors of granular media are controlled by grain properties and microstructure. The primary property of granular media is denoted by its grain shape, grain size distribution, stiffness, and interparticle friction. The grain shape itself is of particular importance. Microstructures are formed in the connection paths of contact points between grains. In this paper, the deformation of granular materials with different grain shapes was simulated using two-dimensional DEM under different stress-levels and densities. After analyzing the results, the authors investigated fabric changes. The evolution rule of stress-induced anisotropy and its limitation as well as the existence of a critical state of fabric are revealed.     

Numerical assessment of temperature effects on concrete failure behavior

This work focuses on the evaluation of temperature effects on concrete failure behavior and modes by means of a realistic thermodynamically consistent non-local poroplastic constitutive model, previously developed by the authors, which is modified in this work. In this regard, two original contributions are presented and discussed. Firstly, and based on significant published experimental results related to this very complex aspect such as the effects of temperature in concrete failure, a temperature dependent non-associated flow rule is introduced to the poroplastic constitutive model to more accurately account for the temperature dependent inelastic volumetric behavior of concrete in post-peak regime. This is crucial for improving overall model accuracy, particularly regarding the temperature effects on concrete released energy during degradation processes. Secondly, and more importantly, the explicit solution of the localization condition in terms of the critical hardening modulus is developed regarding the non-local poroplastic constitutive model reformulated in this work, which allows the analysis of localized failure modes in the form of discontinuous bifurcation of quasi-brittle porous materials like concrete under different temperature, hydraulic and stress state scenarios. Also numerical procedures are followed, which also allow the evaluation of temperature effects on the critical directions for localized failure or cracking which is performed in this work for a wide spectrum of stress states and temperatures. Both, undrained and drained hydraulic conditions are evaluated. The results in this work demonstrate the soundness of the proposed constitutive model modifications and of the derived explicit solution for the critical hardening modulus to accurately predict the temperature effects on both, concrete volumetric behavior, and on the failure modes and related critical cracking direction. They also demonstrate that concrete failure mode and critical localization directions are highly sensitive to temperature, particularly in the compressive regime.     

The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials

The effects of rolling resistance on the stress-dilatancy behavior and fabric anisotropy of granular materials were investigated through a three-dimensional discrete element method (DEM). A rolling resistance model was incorporated into the DEM code PFC3D and triaxial DEM simulations under simulated drained and undrained conditions were carried out. The results show that there existed a threshold value of the rolling friction. When the rolling friction was smaller than this value, the mechanical behavior of granular materials under both drained and undrained conditions were substantially influenced by the rolling friction, but the influence diminished when it was larger than the threshold value. A linear relationship has been observed between the dilatancy coefficient and the natural logarithm of the rolling-friction coefficient when it was smaller than the threshold value. An increase in the rolling friction led to an increase in the fabric anisotropy of all strong contacts under both testing conditions until the threshold value was attained. The investigation on the effect of rolling friction on the microstructure of granular materials revealed that the rolling friction enhanced the stability of force chains, which resulted in the difference in the stress-dilatancy behavior. Finally, the relationship between the stress ratio q/p\(^{\prime }\) and the fabric measure at strong contacts \(\hbox {H}_{\mathrm{d}}^{\mathrm{s}} /\hbox {H}_{\mathrm{m}}^{\mathrm{s}}\) was found independent of the inter-particle friction, rolling friction and testing conditions.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.