Failure In Granular Materials Research Articles

Revisiting strain localization analysis for elastoplastic constitutive models in geomechanics

AbstractThe localization of deformations plays a crucial role in the failure of granular materials. Concerning classical continuum constitutive models, the localization of deformations is considered to be connected to the loss of ellipticity of the governing rate equilibrium equations, and entails mesh sensitivity in finite element simulations. While previous studies are often limited to strain localization analyses of individual tests, the focus of the present contribution lies on studying the localization properties in general constitutive states. For this purpose, a staggered optimization algorithm for determining the loss of ellipticity, considering both extreme values, minimum and maximum, of the determinant of the acoustic tensor, is proposed. Part of this algorithm representing a novel application of spherical Fibonacci lattices for discretizing the feasible domain of the associated optimization problem. In the presented localization study of the widely recognized modified Cam‐clay model, special attention is paid to determining the influence of the individual model parameters. Specifically, three factors favoring strain localization are found, namely (i) a low value of the ratio of the primary compression index and the recompression index, (ii) a large value of the critical state frictional constant, as well as (iii) a large value of Poisson's ratio. Moreover, a structural finite element study is performed, confirming the results of localization analyses at the constitutive level.

Fluctuations and failure in granular materials: theory and numerical simulations

We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model.Graphical Statistical representation of the aggregate: conditional average.

Strain localization in the standard triaxial tests of granular materials: Insights into meso‐ and macro‐scale behaviours

AbstractThe standard triaxial tests cease to be valid as material tests since the homogeneity of the granular mass is lost when localized failures such as shear bands occur requiring a different approach to interpreting and analyzing material responses at the meso scale from the macro behaviour. This study sheds light on the above issue by analyzing the standard triaxial tests of the granular specimens undergoing localized failure at different scales using DEM. For the first time, the behaviour of material inside and outside of the shear band as well as the entire sample are quantitatively quantified through DEM simulations. The results enable confirmation of various theoretical hypotheses and experimental observations on the localized failure in granular materials. For example, by quantifying the inter‐particle contact forces of materials inside and outside the shear band zone, it is confirmed that the material outside the localization band undergoes inelastic unloading beyond the bifurcation point, while those inside the localization band experience inelastic shearing to reach the critical state. Moreover, the analysis in this study suggests that if the volume of the localization zone can be precisely measured from the experiment, the mesoscale constitutive responses that truly represent the inelastic behaviour can be quantified. This gives rise to a more appropriate method to obtain inelastic constitutive responses of granular materials from specimens undergoing localized failure in triaxial tests.

Failure in granular materials based on acoustic tensor: a numerical analysis

We investigate localization in granular material with the support of numerical simulations based upon DEM (Distinct Element Method). Localization is associated with a discontinuity in a component of the incremental strain over a plane surface through the condition of the determinant of the acoustic tensor to be zero. DEM simulations are carried out on an aggregate of elastic frictional spheres, initially isotropically compressed and then sheared at constant pressure p0. The components of the stiffness tensor are evaluated numerically in stressed states along the triaxial test and employed to evaluate the acoustic tensor in order to predict localization. This occurs in the pre-peak region, where the aggregate hardens under the circumstance to be incrementally frictionless: it is a regime in which the tangential force does not change as the deformation proceedes and, consequently, the deviatoric stress varies only with the normal component of the contact force.

A multiscale approach for investigating the effect of microstructural instability on global failure in granular materials

SummaryThis paper aims to develop a multiscale approach that has the ability to characterise the influence of microstructural instabilities on global failures in granular materials. For this purpose, the Chang‐Hicher multiscale constitutive relation has been implemented into a finite element code, and the expression of the second‐order work, as an indicator of the material instability, has been computed at the interparticle contact scale, at the representative element volume scale, and at the boundary value problem scale. At the global scale, the second‐order work can be obtained through the integration of that obtained at interparticle contacts. Hence, it becomes possible to analyse the range of instability from the microstructure to the macrostructure. Drained and undrained triaxial tests were numerically simulated. With this method, it was demonstrated that the grain‐scale origin of the specimen instability was well captured. Additionally, biaxial tests were conducted and the onsets of localised and diffuse failure in granular assemblies were successfully predicted. The transition from diffuse to localised failure was demonstrated at different scales, whereby the coincidence between the direction of local instabilities and the direction of the shear band became evident. The influence of the boundary conditions and of the heterogeneity of the initial porosity on the failure mode of granular materials was also analysed. All these examples demonstrate that the developed multiscale approach can characterise in a satisfactory manner the influence of instability at the inter‐grain contacts upon the global failure of granular assemblies.

Theoretical Model to Adhesion Failure in Granular Materials

Two disjoint particles joined by adhesion materials are here considered when dead load operating over it. We will to perform a theoretical characterization of this micro-system through a behavior specific approach. This last is located within the hypo-elasticity framework since granular material behavior can be in according whit it. Again we expand the framework joining some further aspects which the deformation field. Over this, we focus peculiar response of the extreme elastic deformation through energetic approach. The model will be able to simulate asphalt mixture behavior in the damage evolution for bond adhesion break.

Spatiotemporal analysis of strain localization in dense granular materials

Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain localization have been studied using laboratory experiments and particle-based numerical simulations, and their findings have been preliminarily implemented into continuum constitutive models. In this study, we revisit strain localization in granular materials using the spatiotemporal data analysis technique, which has been extensively employed in data mining science and social science for the sake of different applications. A dense packing of granular material subjected to biaxial compression was simulated using the combined finite and discrete element method. The large amount of particle-level kinematical data, including the translational and rotational particle motion, fluctuating velocity, granular temperature, and local strain, are collected for subsequent spatiotemporal data analysis. The spatiotemporal data analysis provides a new perspective on the strain localization in dense granular materials and a rich body of new insights are presented for the first time. The spatial autocorrelation analysis results in Moran’s I values close to 1, and positive Z scores and statistically significant p values, which indicate that a dense granular system features clustered patterns during shearing. This finding proves yet again that dense granular materials have an inherent short range order. Eventually, correspondence between localized modes with different particle kinematics and spatial distributions of local Moran statistics and quadrant location map are investigated. By assuming shearing of dense granular materials is a first-order Markov chain process, the convergence and time homogeneity of this process are analyzed. Both the maximum likelihood and Pearson test statistics clearly demonstrate that shearing of dense granular materials is a time-homogenous Markov chain process.

A softening hyperelastic model and simulation of the failure of granular materials

The softening hyperelastic model based on the strain energy limitation is of clear concepts and simple forms to describe the failure of materials. In this study, a linear and a nonlinear softening hyperelastic model are proposed to characterize the deformation and the failure in granular materials by introducing a softening function into the shear part of the strain energy. A method to determine material parameters introduced in the models is suggested. Based on the proposed models the numerical examples focus on bearing capacity and strain localization of granular materials. Compared with Volokh softening hyperelasticity and classical Mohr-Coulomb plasticity, our proposed models are able to capture the typical characters of granular materials such as the strain softening and the critical state. In addition, the issue of mesh dependency of the proposed models is investigated.

Some micromechanical aspects of failure in granular materials based on second-order work

This paper discusses the notion of failure in a granular assembly by examining the key microstructural mechanisms which are most likely to trigger the nucleation and propagation of instabilities within a granular material. For this purpose, the key variable to predict the occurrence of failure, known as second-order work, is expressed from variables on the grain scale. The local behaviour incidents (where contacts may open or slide), compared to the global response of the assembly, are analysed by two approaches. First, numerical computations made by a discrete element model confirm the microscopic definition of the second-order work. Secondly, a micromechanical model, based on a homogenization procedure, relating the macroscopic behaviour to microscopic ingredients, namely contact planes, points to a close link between the occurrence of failure on the macroscopic scale as well as on the contact planes.

A biaxial apparatus for the study of heterogeneous and intermittent strains in granular materials

We present an experimental apparatus specifically designed to investigate the precursors of failure in granular materials. A sample of granular material is placed between a latex membrane and a glass plate. A confining effective pressure is applied by applying vacuum to the sample. Displacement-controlled compression is applied in the vertical direction, while the specimen deforms in plane strain. A diffusing wave spectroscopy visualization setup gives access to the measurement of deformations near the glass plate. After describing the different parts of this experimental setup, we present a demonstration experiment where extremely small (of order \(10^{-5}\)) heterogeneous strains are measured during the loading process.

A micromechanics-based model for estimating localized failure with effects of fabric anisotropy

This paper presents a micromechanics-based approach to investigate the effects of fabric anisotropy on the behavior of localized failure in granular materials. Based on a micromechanical analysis, the origin of deviatoric stress is decomposed into two components: contact force anisotropy and fabric anisotropy. Using a micro–macro approach, the back stress is interpreted as an contribution to the change of the fabric’s principal direction. The evolution of the back stress is deduced from the stress–fabric relationship and determined with reference to the deviation of the principal directions between the rate of the reduced stress tensor and the actual reduced stress tensor. With this micro–macro framework, a mixed (isotropic–kinematic) hardening model is developed based on the classical isotropic hardening theory. A laboratory simple shear test is first analyzed to validate the proposed model and illustrate the kinematic-hardening mechanism which is usually displayed under non-proportional loading. The analysis further focuses on the anisotropic aspect of localized failure. It has been discovered that the fabric anisotropy can play an important role in the occurrence of shear banding. An increasing degree of fabric anisotropy tends to delay the initiation of the strain localization and result in higher failure strength. The effects of fabric anisotropy have also been illustrated by comparing the theoretical predictions and measured results on the shear band inclination angle, shear strain level and dilatancy at bifurcation.

The dilatancy and numerical simulation of failure behavior of granular materials based on Cosserat model

The dilatancy of granular materials has significant influence on its mechanical behaviors. The dilation angle is taken as a constant in conventional associated or non-associated flow rules based on Drucker-Prager yields theory. However, various experimental results show the dilatancy changes during progressive failure of granular materials. A non-associated flow rule with evolution of dilation angle is adopted in this study, and Cosserat continuum theory is used to describe the behaviors of granular materials for considering to some extent the its internal structure. Numerical examples focus on the bearing capacity and localization of granular materials, and results illustrate the capability and performance of the presented model in modeling the effect on failure behavior of granular materials.

Second-order work, kinetic energy and diffuse failure in granular materials

Failure in soils and the yielding mechanisms involved are essential to many civil engineering issues such as slope stability. Sudden collapse affecting slopes can be observed after rainfalls, sometimes leading to the devastating flow of a soil–water mixture. Although the notion of failure in soils was long described as a perfect plastic limit, the scientific community now recognizes that failure can occur well before the Mohr–Coulomb criterion is met. This paper considers the collapse of granular soils in relation to a sudden burst of kinetic energy. First, a correlation between the bursts of kinetic energy (leading to sudden avalanches) and the vanishing of the second-order work is clearly obtained from discrete element simulations. Then the link between the vanishing of the second-order work and the increase in kinetic energy is established from a theoretical approach. Finally, these results are confirmed based on laboratory experimental tests where the sudden collapse of soil specimens was obtained.

Micro-mechanics of fabric and failure in granular materials

The paper addresses the underlying source of two forms of induced anisotropy in granular materials: contact orientation anisotropy and contact force anisotropy. A rational, mathematical structure is reviewed for the manner in which fabric anisotropy emerges and evolves during loading. Fabric is expressed as an orientation density, and transport phenomena such as convection, contact generation, and diffusion control the rate of fabric evolution during loading. The paper proposes specific measurable forms for all terms, based upon the micro-mechanics of particle interactions. Discrete element (DEM) simulations are used to verify and quantify these terms, so that the theory can be applied to general loading conditions. The DEM simulations are of densely packed durable spheres, and the emphasis is on soil behavior at large strains, specifically on fabric and strength at the critical state. Once the theory has been developed and quantified, it is applied to predict the effect of the intermediate principal stress on strength.

Failure of granular materials at different scales ‐ microscale approach

AbstractIn recent years there has been an increase of interest in packed granular and discontinuous media. Due to the properties of such materials, a simple continuum approach is not appropriate to describe the material behavior. Breaking and forming of new contacts between grains, distinguishing for granular media, cannot be captured. We apply a computational homogenization method [6] which is based on a two scale concept to complete the task of modeling packed granular materials. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastic/plastic models for soils and sands

Some recent advances in the constitutive modelling of soils, sands and other granular materials are reviewed. These new ideas are based on the use of the concepts of the modern theory of the thermomechanics of continua. Most existing engineering theories of soil behaviour are in the nature of “recipes”, providing rules by which yield loci, flow and hardening rules and failure lines may be constructed to provide models which predict the response and failure of granular materials in a limited set of laboratory experiments. These models rarely have any firm physical basis. The thermomechanical approach, on the other hand, enables us to construct models, which both satisfy the fundamental laws of thermodynamics and have definite physical interpretations in terms of energy storage and dissipation. Of particular importance is the distinction between the rate of plastic work and plastic dissipation, the intimate connection between dissipation and the yield loci and flow rule, and between plastic dilation and induced anisotropy. These ideas lead naturally to the concepts of critical state soil mechanics. In addition the thermomechanical approach offers the real possibility of relating the observed and simulated behaviour of granular materials on the micro- and meso-scales, to the observed behaviour at the continuum level. Some initial steps in this direction are outlined at the end of this paper.

On the Failure of Granular Materials with Fabric Effects

ABSTRACT Anisotropic failure criteria for granular materials are formulated, based on micromechanical analysis. The shear resistance is assumed to consist of two components related to fabric anisotropy and interparticle frictional forces. By considering the directional contribution of contact normals, the failure criteria are developed via two approaches : one employs the invariants of stress and fabric tensors; and the other considers the relation between the traction components acting on the critical plane. In the stress invariant approach, however, some microscopic features of granular materials may not be captured due to the utilization of stress invariants. Numerical examples, examining the variation of shear strength of granular materials with different orientations of bedding plane and the degree of anisotropy, compare the proposed approaches with other models in the literature.

Evolution of Shear-Zone Structure in Undrained Ring-Shear Tests

Undrained monotonic torque-controlled tests were conducted on fine-grained silica sand to study the shear-deformation process in granular materials by using a ring-shear apparatus. Shear-zone structures at various stages in the undrained shear tests were observed during a series of tests in which the experiments were terminated at different shear displacement. For “undisturbed” samples, the shear zone was only developed during the post-failure stage and its thickness increased with progressed shearing. First the shear surfaces had undulating and asymmetric structures; later they gradually became smooth and parallel to the shearing direction. During this process, pore water pressure was generated, and the effective friction angle decreased correspondingly. Generally, the shear zone could be divided into three parts: the compacted core, the adjacent zone above the core, and the adjacent zone below the core. Grain-size analysis on the sample from the shear zone revealed that grain crushing occurred during each stage and the extent of grain crushing differed for different shear stages. An interesting phenomenon occurred during the steady-state deformation where the coarse and fine particles within the shear zone segregated during motions and a parallel orientation structure developed. These results are helpful for understanding the mechanism of progressive failure in granular material as well as the rapid landslide with long runout study.

Instability, shear banding, and failure in granular materials

Two modes of decrease in load bearing capacity of granular materials are discussed in view of experimental results. Both relate to the fact that frictional materials exhibit nonassociated plastic flow and they undergo considerable volume changes, either contraction or dilation. One mode consists of the instability that may occur in certain regions of stress space and potentially result in liquefaction of the granular material. It is the fact that loading of contracting soil (resulting in large plastic strains) can occur under decreasing stresses that may lead to unstable behavior under undrained conditions. As long as the soil remains drained, it will remain stable in the region of potential instability. The other mode is initiated by localization of plastic strains and subsequent development of shear bands, which in granular materials is followed by a decrease in load bearing capacity. These two modes are mutually exclusive and they occur for different loading and material conditions as discussed here on the basis of experimental observations.

Micromechanical investigation of the influence of couple stresses on failure in granular materials : Bardet, J P; Huang, Q; Proubet, J Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P609–617. Publ Rotterdam: A A Balkema, 1992

Micromechanical investigation of the influence of couple stresses on failure in granular materials : Bardet, J P; Huang, Q; Proubet, J Proc 33rd US Symposium on Rock Mechanics, Santa Fe, 3–5 June 1992P609–617. Publ Rotterdam: A A Balkema, 1992