Search

The shear band issue in frictional granular materials has attracted many concerns and perspectives at the micro- and meso-scale have been involved to analyze this problem. At the microscopic level, the contact sliding is associated with the plastic dissipation; while at the mesoscopic level, force chains and loops will change in geometry and topology as deviatoric loads are applied. This paper concerns the unstable behaviors from these two scales which could be regarded as loss of sustainability of internal structures, and tries to relate the microscopic sliding and the mesostructural evolutions. Firstly the heterogeneity generation is identified for the granular assembly subjected to the biaxial loading using DEM. Then the internal structure evolutions and interrelationships are investigated, leading to these main conclusions: sliding contacts are not within force chain structures but will be strongly influenced by the force chain buckling; exchanges within grain loops appear during the whole loading process and differ for domains inside and outside the shear band; the topological dilations are related to the higher probability of contact sliding. In brief, the microscopic dissipative behavior as the contact sliding plays an important role in the mesostructural organizations. [ABSTRACT FROM AUTHOR]

In 2D granular material, column-like structures, called force-chains (FCs), are formed as force transmission tunnels that carry a major external loading. The movement of FCs is highly correlated to the strength and the volumetric behavior of the granular matter. Since FC stability is ensured by the confining structures surrounding them, these confining structures must be quantitatively characterized to investigate the moving pattern of FCs and significant mechanical behaviors of granular materials. In this paper, the meso-scale, a scale larger than the single contact scale (the micro-scale) and smaller than the macro-scale, is introduced such that in this scale the organization and structure among contacts can be characterized by the topology of the meso-structures (called loops). Then the interaction between the FC and its surrounding meso-structures is investigated. This study investigated two aspects: how the FC affects the geometry of the material fabric on the meso-scale, which is constituted of meso-structures; and, the way the meso-structures affect the FC's behavior. The results show that the material is highly heterogeneous on the meso-scale, depending on the distance to the FC. The FC's surrounding area is observed to have greater dilatability than other areas, because it is better able to generate loose structures on the meso-scale. Hence, the FC's adjacent areas can be seen as the main source of the global dilatancy. In contrast, FC movability, a concept closely related to FC instability, is observed to depend to a large extent on the nature of its surrounding meso-structures. As a result, depending on the initial meso-structures, stress boundary conditions will direct dilatancy or contractancy. Finally, the life cycle of the FCs is presented in relation with their confining meso-structures. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the definition of the stress tensor within a granular assembly, when inertial effects are likely to occur. It is shown that the stress tensor can be expressed as a sum of two terms. A first term corresponds to the standard definition of the stress, according to the Love–Weber formula; this term is related to the contact forces existing within adjoining particles. A second term accounts for dynamic effects related to rotation velocities and accelerations of the particles. These results are checked from discrete numerical simulations in order to examine in which context the contribution of inertial effects should not be omitted. With this aim, the simulation of a granular specimen collapse and then a silo discharge is considered. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a theoretical question as to the definition of instabilities in a granular assembly and its proper formulation at the microscopic level. Recently, this question has taken up much prominence with the emergence of intriguing failure modes such as diffuse failure associated to unstable plasticity of granular materials and microstructural instabilities. An analysis of the second-order work as a general and necessary criterion to detect instabilities is conducted both at the macroscopic and microscopic levels including large deformations. On the basis of a micromechanical analysis of a body consisting of arbitrary interacting particles in a representative element volume (REV), a general formula is derived to quantify the microscopic second-order work involving local variables on the grain scale. The latter emerges as a sum of a configurational term that involves contact forces between neighboring grains, plus a kinetic part consisting of the mechanical unbalance of intergranular forces under dynamics at incipient failure. The present analysis is thought to serve as a clarification of the question of failure in geomaterials typified by a transition from static to a dynamic regime with release of kinetic energy originating from microstructural interactions. [Copyright &y& Elsevier]

Abstract: This paper investigates the issue of failure in rate-independent granular material specimens under a novel line of reasoning. The mechanism of failure is related to an increase in kinetic energy. Based on energy conservation, expressed in an incremental form, kinetic energy is shown to be related to the so-called second-order work and a boundary integral involving the external loading directed to the system. Thus, the existence of an outburst in kinetic energy is related to a competition between the second-order work and this boundary integral. Elementary examples are discussed, providing a clear interpretation of the standard laboratory tests (drained, undrained and proportional strain triaxial paths). These theoretical findings are then confirmed based on numerical simulations using a discrete element method. Finally, this approach is assessed in boundary value problems. [Copyright &y& Elsevier]

Abstract: This paper is an attempt to extend the approach of the second-order work criterion to the analysis of structural system instability. Elastic structural systems with a finite number of freedoms and subjected to a given loading are considered. It is shown that a general equation, relating the second-order time derivative of the kinetic energy to the second-order work, can be derived for kinetic perturbations. The case of constant, nonconservative loadings are then investigated, putting forward the role of the spectral properties of the symmetric part of the tangent stiffness matrix in the occurrence of instability. As an illustration, the case of the generalized Ziegler column is considered and the case of aircraft wings subjected to aeroelastic effects is investigated. In the both cases, the consequences of additional kinematic constraints are discussed. [Copyright &y& Elsevier]

Abstract: The question of divergence instability and diffuse failure, which is a common failure mode for granular materials like soils, is tackled here from an experimental, theoretical and numerical perspective. The necessary condition of instability as given by the loss of definite-positiveness of the elasto-plastic matrix (the so-called “second order work criterion”) is considered to analyze some experimental tests leading to diffuse failure, the link between kinetic energy and second order work is established, a discrete element method is used to simulate these failure conditions and eventually a 3D bifurcation analysis is performed with incrementally piecewise and non-linear elasto-plastic relationships. Essentially in relation with the non-associate character of the plastic strains of granular materials, a whole bifurcation domain in the stress space emerges from these analyses, leading to novel views of failure for non-associative materials. [Copyright &y& Elsevier]

Abstract: Solving boundary value problems requires implementation of sufficiently robust constitutive models. Most models try to incorporate a great deal of phenomenological ingredients, but this refining often leads to overcomplicated formulations, requiring a large number of parameters to be identified. A powerful alternative can be found with micromechanical models, where the medium is described as a distribution of elementary sets of grains. The complexity is not related to the constitutive description, but to the multiplicity of contacts oriented along all the directions of the physical space. This paper proposes an advanced micromechanical model that introduces an intermediate scale (mesoscopic scale): elementary hexagonal patterns of adjoining particles. This is advantageous with respect to current micromechanical models that generally describe the material through a single distribution of contacts. This new approach makes it possible to take many constitutive properties into account in a very natural way, such as the occurrence of diffuse failure modes. These preliminary results are presented in order to give clear insights into the capability of such multiscale approaches. [Copyright &y& Elsevier]

Abstract: Cellular structures are widely used in civil engineering. Their design is based on the understanding of the mechanical behavior of geocells. This paper investigates the response of a single geocell to a uniaxial compression test. The geocells were cubic, either 500mm or 300mm on a side. The fill materials were sand and scrapped tire and sand mixtures in different mass ratios. The envelope of the geocell was made up of a hexagonal wire netting cage and a containment geotextile. The response of the geocell is discussed based on the axial load and displacement measurements as well as the change in geocell volume. The axial load was found to be globally governed by the interaction between the fill material and the envelope, which depends on the shape of the wire mesh and the volumetric behavior of the fill material. [Copyright &y& Elsevier]

Abstract: In this paper, the specific effect of additional constraints on the stability of undamped non-conservative elastic systems is studied. The stability of constrained elastic system is compared to the stability of the unconstrained system, through the incorporation of Lagrange multipliers. It is theoretically shown that the second-order work criterion, dealing with the symmetric part of the stiffness matrix corresponds to an optimization criterion with respect to the kinematics constraints. More specifically, the vanishing of the second-order work criterion corresponds to the critical kinematics constraint, which can be interpreted as an instability direction when the material stability analysis is considered (typically in the field of soil mechanics). The approach is illustrated for a two-degrees-of-freedom generalised Ziegler’s column subjected to different constraints. We show that a particular kinematics constraint can stabilize or destabilize a non-conservative system. However, for all kinematics constraints, there necessarily exists a constraint which destabilizes the non-conservative system. The constraint associated to the lowest critical load is associated with the second-order criterion. Excluding flutter instabilities, the second-order work criterion is not only a lower bound of the stability boundary of the free system, but also the boundary of the stability domain, for all mixed perturbations based on proportional kinematics conditions. [Copyright &y& Elsevier]

Abstract: Sudden collapse mechanisms strictly inside the Mohr–Coulomb plastic limit condition have been observed in granular materials in the laboratory as well as in the field. The purpose of this paper is to show that the theoretical framework of loss of sustainability is convenient to describe such mechanisms. In this context, the notions of both loading and response variables, which characterize the loading path applied to the specimen considered and its response path, are fundamental. Moreover, by investigating the relation between loading and response parameters, it is established that this framework also embeds the notions of loss of constitutive uniqueness and loss of controllability. Therefore, a unified approach is attempted. Finally, by highlighting the basic role played by the loading parameters, the vanishing of the second-order work is shown to be a proper criterion to detect the occurrence of a bifurcation from a quasi-static regime to a dynamic regime leading to the collapse of the material. [Copyright &y& Elsevier]

Abstract: Although phenomenological constitutive models have the ability to exhibit most salient macroscopic features of granular materials, they generally do not provide any convincing interpretation of them: their basic origin remains hidden. It is now well established that the micro-structure of granular materials plays a significant role in their overall constitutive behavior. In the past few years, a great deal of theoretical and experimental research has been devoted to this domain, giving rise to efficient micro-mechanical approaches. First, this paper reviews the micro-directional model, which is a micro-mechanically based constitutive relation. Then an extension is proposed to describe the possible collapse of force chains. This micro-structural adjunction is shown to be sufficient to simulate work-hardening and softening mechanisms. A granular assembly, containing a multitude of frictional contacts whose orientation is generally anisotropically distributed, exhibits various other typical features such as the nonassociated character of plastic strains. The micro-structural origin of this feature is investigated, and further conclusions related to the existence of a regular or a singular flow rule are drawn. [Copyright &y& Elsevier]

Abstract: In this paper, the notion of loss of sustainability of a mechanical state in a granular assembly is investigated. The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation. Then a link is established between the macroscopic second-order work on the specimen scale and a discrete local expression that introduces microscopic variables defined on each contact scale. This relation opens up a micro-mechanical interpretation allowing one to examine which micro-structural features are responsible for the vanishing of the macroscopic second-order work. Finally, it is established that both geometrical and material micro-structural origins may combine to induce the occurrence of bifurcation on a specimen scale. [Copyright &y& Elsevier]

Abstract: Most rate-independent constitutive relations for granular materials are based on the existence of a regular flow rule. This assumption states that once the mechanical state of a material point belongs to the yield surface, then the direction of the plastic strains is independent of the loading direction. In this paper, the notion of a regular flow rule is shown to exist only for two-dimensional and axisymmetric loading conditions. By considering our incrementally nonlinear constitutive model, it is established that this notion disappears as soon as more general loading conditions are applied, as also predicted from discrete element simulations. Moreover, a sound micro-mechanical interpretation of the vanishing of a regular flow rule in three-dimensional loading conditions is given from a multi-scale perspective using the micro-directional model. This model highlights the great influence of the loading history on the shape of the plastic Gudehus response-envelope. [Copyright &y& Elsevier]

Abstract: It is now well established that for non-associated materials such as geomaterials, a broad domain exists, strictly within the plastic limit, where different failure modes can coexist. In particular, material instability as defined by Hill [Hill, R., 1958. A general theory of uniqueness and stability in elastic–plastic solids. J. Mech. Phys. Solids, 6, 236–249], related to the vanishing of the second-order work, can potentially occur. In this paper, we focus on granular materials and establish from theoretical considerations that the macroscopic second-order work on the assembly scale is related to the microscopic second-order work computed on each contact. This question is examined from a multi-scale approach, and the relation between macroscopic and microscopic second-order works is brought to light using a micro-mechanically based model. Finally, these theoretical results are confirmed from numerical simulations based on a discrete element method. [Copyright &y& Elsevier]

Abstract: It is now well established that for non-associated materials such as geomaterials, there exists a wide domain strictly within the plastic limit where different failure modes can coexist. In particular, material instability in the sense given by Hill, related to the vanishing of the second-order work, can potentially occur. In this paper we examine the occurrence of such instabilities from the simulation of drained triaxial paths, followed by the computation of two-dimensional, then fully three-dimensional Gudehus response-envelopes using the micro-directional model. This model can be seen in the continuity of Hill’s multi-slip theory, because it accounts for the association of a large number of elementary elasto-plastic bodies. Each body is linked to a contact direction in physical space and therefore takes into account the behavior of the contacts oriented along that direction. Simulations confirmed that some loading directions led to the vanishing of the second-order work. In line with the research initiated by Mandel, a micro-mechanical analysis of the origin of these potential instabilities revealed that this macro-scale phenomenon could be directly related to the constitutive nature of the local contact model between neighboring particles. Finally, this investigation provides a clear physical understanding of Hill’s material stability condition for frictional materials. [Copyright &y& Elsevier]

Abstract: Reinforced soil structures can be used to protect infrastructures against rockfalls. An innovative way to implement such protection is to construct the front face using a cellular assembly. This paper focuses on the cellular scale, with the cell a complex heterogeneous material, composed of a wire netting box filled with rocky particles. The behaviour of a single cell was modelled using the discrete element method, thus accounting for the interaction between the rocky particles and the interaction between the box and the rocky particles. A constitutive model was developed and calibrated along confined compression loading paths, then preliminary elements of validation were obtained from the simulation of unconfined compression tests. [Copyright &y& Elsevier]

Abstract: It is now well established that the micro-structure of granular materials plays a significant role in their overall constitutive behavior. In the past few years, a great deal of theoretical and experimental research has been devoted to this domain, giving rise to constructive micro-mechanical approaches. However, constitutive models for granular materials based on a micro-mechanical approach remain scarce; solving practical engineering problems most often requires using phenomenological models, which often introduce numerous parameters with no physical meaning. This paper derives a “parameter-free” constitutive behavior of granular materials on the macroscopic level from a microscopic-scale description, taking a statistical description of the fabrics into account. In this approach, the location of each particle is ignored, but the probability of contact in a given direction is investigated. Modelling the creation or the loss of contacts in given directions makes it possible to analyze how the probability density of having contacts in these directions evolves, and thus a directional constitutive model can be developed. Highlighting micro-structural processes responsible for the transmission of local contact forces, the existence of two phases in the granular assembly was accounted for, giving rise to a partition of the stress tensor. The capability of the model is assessed from the simulation of standard tests, leading to satisfying preliminary qualitative results. [Copyright &y& Elsevier]

In many industrial or civil engineering applications, design of structural elements may require analysing the mechanical interaction between a flowing material and an open structure made of a metallic mesh. This paper presents some theoretical results, first in a two-dimensional case and then extended to a three-dimensional context. In particular, we establish that the distribution of forces applied to a wire structure by a flowing material whose behaviour is viscous does not depend upon the viscosity of the material. Further numerical computations provide valuable elements to confirm these results. An application to the case of a snowpack interacting with an avalanche net structure is presented, focusing on the fundamental numerical consequences resulting from the mechanical analysis. [Copyright &y& Elsevier]

The mechanical modelling proposed in Part I has led to the development of computational software allowing easy design of avalanche nets. This tool provides for the evolving forces acting on several parts of the net as a function of the snow situation. Some important numerical aspects are considered here, confirming the relevance of the proposed approach. To exemplify the capability of the software, a complete simulation is presented. [Copyright &y& Elsevier]

The search to improve protective techniques against natural phenomena such as snow avalanches continues to use classic methods to calculate flexible structures. This paper deals with a new method for designing avalanche protection nets, based on a coupled analysis of both the net structure and the snow mantel using a coupled Lagrangian–Discrete approach. As a thorough analysis of the behaviour of a snow cover in interaction with a structure is required, a multiscale approach allowing the overall behaviour of the snowpack to be inferred from the local properties is presented. The constitutive equations are obtained from a statistical description of the mantel, regarded at the micro level as a cohesive granular assembly. [Copyright &y& Elsevier]

The search to improve protective techniques against natural phenomena such as snow avalanches requires thorough analysis of the behaviour of a snow cover in interaction with a structure. This paper deals with a multiscale approach allowing the overall behaviour of the snowpack to be inferred from the local properties. The constitutive equations are obtained from a statistical description of the mantel, regarded at the micro level as a cohesive granular assembly. Further general results are derived on the changes in fabrics as an application, the case of a snow pack in interaction with a flexible structure is discussed. [Copyright &y& Elsevier]

One of the challenge that face the effectiveness of Polyvinyl Chloride geomembranes (PVC GMs) as a hydraulic barrier is the capacity to withstand unexpected mechanical actions, particularly tensile forces, during installation and throughout their lifespan. These forces pose risks of premature failure and impermeability degradation. In this study, the characterization of the short and long-term mechanical response of PVC GMs to uniaxial tensile forces has been investigated. Uniaxial tensile test have been performed for tensile rates spanning several orders of magnitude. Analysis of the true stress-strain curves reveals a significant decrease in tensile modulus, strength, and strain at failure at low strain rates, which are relatively close to those applied in situ. Long-term investigations have been conducted as well, through relaxation tests. Our key results unveil two distinct characteristic times in stress relaxation, with the fast relaxation occurring over the first 4 h. During this phase, the pre-relaxation loading rate affects the relaxation behavior. Beyond this phase, the relaxation behavior becomes independent from the pre-relaxation loading rate. Burger's rheological model is proposed to measure the stress relaxation at different rates. The model's results validate the existence of two characteristic times. • Higher tensile loading rates significantly increase the rigidity modulus of PVC geomembranes, while lower rates lead to reduced strength and strain at failure. • Laboratory tests at standard speeds may not accurately predict field performance, highlighting the need for testing at lower rates to avoid the risk of premature geomembrane failure. • Stress relaxation tests demonstrate two distinct relaxation stages, with initial rate-dependent behavior transitioning to a long-term rate-independent response after approximately 4 h. [ABSTRACT FROM AUTHOR]

An intimate understanding of snow failure, particularly under mixed-mode shear and normal loading, is a key ingredient for numerical modelling of snow avalanche release. Due to its highly porous structure, the failure of snow can result in a volumetric collapse. Despite its importance, snow failure and collapse remain poorly understood, mainly due to the fragile nature of the material, which renders systematic experimental exploration difficult and complicates observation at the microscopic level. A microstructure-based discrete element model of snow has been developed and utilized to study snow failure under mixed-mode loading. Depending on applied normal stress, three distinct failure regimes are identified, characterized by different volumetric responses. Shear-induced macroscopic collapse is observed to develop above a critical level of normal stress. A deeper understanding of the mechanisms leading to this volumetric collapse is investigated on the microscopic scale. Force chain buckling within the snow sample leads to volumetric collapse, while stable force chains result in a localized failure and the absence of a volumetric collapse. The stability of the force chains is shown to be insured by the grain contacts between the force chains and the surrounding material. The ratio of contacts close to failure is identified to control the absence or presence of collapse after failure. [ABSTRACT FROM AUTHOR]

• The maximum capacity of storing elastic energy corresponds to the unstable stress peak observed for a dense specimen. • The ultimate shear band corresponds to an optimal dissipative structure that appears later than the beginning of the critical state regime. • Plastic dissipation localizes inside the shear band domain developing in the dense specimen. No further dissipation processes occur outside the shear band. • The shear band domain concentrates more intense elastic processes than the outside shear band domain does. • The shear band is an optimal dissipative structure, marked by a constant degree of dynamic plastic activity together with a complementary dynamic elastic activity. Granular assemblies are an illustrative example of complex material where unexpected macroscopic properties may emerge when they are subjected to a given loading. The complexity is the consequence of the huge geometrical disorder governed by particle rearrangements, entailing plastic dissipation at contacts. This local dissipation, associated with the global geometric disorder, is probably a key ingredient responsible for various macroscopic features, such as the strain localization in dense granular assemblies leading to the formation of a shear band. Based on a discrete element method (DEM), this manuscript investigates the energy processes at the microscopic scale in granular assemblies along biaxial loading paths for dense and loose assemblies. The localized shear band domain in a dense specimen is inspected. The analysis of elastic processes suggests a maximum capacity for storing elastic energy, giving rise to a phase transition from a homogeneous state to a heterogeneous one. This phase transition is marked by a significant release of elastic energy associated with plastic dissipation. The elastic-to-plastic energy transfer is shown to be a key ingredient to reach the stationary state regime characterized by a unique dynamic equilibrium. It is signaled by the constant ratios of elastic storage and plastic dissipation over the available energy, whatever the initial density of granular assemblies. Finally, the energy processes inside the shear band domain are shown to be largely dominated by intense plastic dissipation. This suggests that the shear band acts as an optimal dissipative structure in dense specimens where elastic mechanisms continue to be active at a much higher level than they are in the outside shear band domain. [ABSTRACT FROM AUTHOR]

Abstract The mechanical behavior of granular materials is widely governed by microstructure reorganizations. This constant evolution of the microscale geometry is often taken into account directly at the macroscale within the plasticity context, and more particularly non-associated plasticity. In this paper we propose to revisit the non-associated plastic behavior of granular materials with respect to material instability assessment in terms of the loss of positiveness of the second-order work. It is shown that large incremental plastic strain is a necessary condition for the existence of mechanical instability. The ability of a material to develop substantial plastic incremental strain is then related to the existence of rattlers, i.e., free particles that get jammed into force chains when existing contact networks fail to adapt to incremental loadings. This link between rattlers, plastic deformation and the vanishing of the second-order work is explicitly derived i) from the micro-formulation of the second-order work and ii) directly from discrete element simulations. Highlights • Material mechanical stability is investigated from a micromechanics perspective. • The stabilizing role played by free particles is highlighted. • The influence of rattlers on the intensity of plastic strain increments is shown. • The link between fabric anisotropy and the non-associate flow rule direction is derived. [ABSTRACT FROM AUTHOR]

This paper investigates the interaction between a falling rock boulder and a granular medium through numerical modelling based on a discrete element method. The boulder is modelled as a single sphere with an incident velocity, and the medium is modelled as an assembly composed of poly-disperse spherical particles. A classical elastic-plastic contact law is implemented with rolling resistance to consider the particle shape effects. The numerical modelling is validated by comparison with results from the literature in terms of impact force, impact duration and the boulder’s penetration depth of the boulder. Then the model is used to investigate the energy propagation within the impacted medium as well as the boulder bouncing. The energy propagation processes are investigated by analysing the space distribution of kinetic energy, elastic strain energy and energy dissipation within the medium over time. The boulder bouncing occurrence is studied, varying the impact conditions in terms of medium thickness and boulder size. Relations between the bouncing of the boulder and the response of the granular medium are finally discussed. [ABSTRACT FROM AUTHOR]

The "incremental shear strain chain" concept (simply called "shear chain") has been proposed recently to quantitatively account for local kinematic features of granular materials. At the microscopic scale, contacts can slide and particles can rotate; while at the macroscopic scale, shear bands appear as a typical localized failure mode. Despite visual spatial distribution features, the direct links from microscopic to macroscopic shear behaviors are still missing. This paper investigates shear characteristics appearing at the micro, meso and macro scales in granular materials, and tries to elucidate how they can be correlated by adopting the shear chain concept. Based on the spatial statistics tools, the shear chain and the shear band orientations are compared by demonstrating that the shear band is influenced by the sample aspect ratio while shear chain orientation only depends on the stress state. Shear chains experience a relative steady and high fabric anisotropy, irrespective to the stress state. Micro contact sliding and particle rotation mainly exist in the shear chain connection positions, which gives possible clues on shear chain forming. In conclusion, the shear band is eventually conjectured to be formed of a collection of crossing shear chains at meso scale, according to detailed analysis and discussion on the correlations of shear behaviors across scales. • Shear behaviors of granular materials at different scales are investigated. • Meso shear chains are different from the macro shear bands in many aspects. • Average fabric anisotropy stays almost steady and higher inside shear chains. • Particle rotations are associated with shear chains of opposite orientations. • Shear chains are conjectured to be included inside the developing shear band. [ABSTRACT FROM AUTHOR]

Granular soils exhibit very complex responses when subjected to cyclic loading. Understanding the cyclic behavior of such materials is not only crucial for engineering applications but also the bottleneck of most of constitutive models. This study employs 3D Discrete Element Method (DEM) simulations to explore the accumulative plastic deformation and the internal fabric evolution within granular soils during cyclic loading. Two novel observations are identified: (1) A distinct and unique linear relationship between post-cyclic loading void ratio e and log (p*/p 0) is found independent of the amplitude of cyclic load and the initial stress state prior to cyclic loading, where p* is the mean pressure incorporating cyclic loading stress and p 0 is the mean pressure prior to cyclic loading; (2) When resuming drained triaxial loadings after cyclic loadings, we observe that both microstructural and macroscopic variables converge to the same values they would have reached for pure monotonic drained triaxial loadings. This intriguing behavior underscores and extends to more general loading paths the influential and attractive power of the critical state. [ABSTRACT FROM AUTHOR]

The current study presents a multiscale approach that investigates material instability and localization phenomena in plastic granular materials and the discrete-continuum duality. A bifurcation and stability analysis in continuum mechanics usually requires the material's tangent (stiffness) operator, the computation of which in a micromechanical approach such as Discrete Element Modeling (DEM) requires specific treatment. To bridge the discrete and continuum worlds, a new computational approach incorporating strain probing is proposed to reconstruct the elastoplastic constitutive tensor and its spectral characteristics from DEM simulations. The probing technique permits the computation of the tangent operator that inherits microstructural information from the discrete world to analyze bifurcation in elastoplasticity at the macro level. An incrementally linear constitutive tensor is computed, distinct for each of the ensemble of probing directions belonging to a particular tensorial zone or sector of incremental stress or strain space, thus making it directionally non-linear. Following such an approach, material instability can be evaluated from the spectral characteristics of the tangent constitutive tensor deduced from DEM probing calculations belonging to an identified tensorial zone. A meso-scale analysis is finally offered to detect shear band localization through the well-known Rice's criterion as a continuum-based concept extended to a micromechanical discrete modeling framework. These new numerical results show that the multiscale proposed approach, which allows access to microstructural information, is consistent with a continuum one such as when predicting the localization angle during shear banding in a granular specimen in DEM. • The elastoplastic tangent operator is reconstructed within a DEM framework. • A tensorial Least Square Method is applied to the DEM probing analysis. • Directional dependency of the constitutive relation is captured via tensorial zones. • Spectral analysis of tangent operator is consistent with DEM instability results. • Rice's strain localization criterion is verified in a meso-scale DEM analysis. [ABSTRACT FROM AUTHOR]

Abstract: The accuracy of rockfall trajectory simulations depends to a large extent on the calculation of the rebound of falling boulders on different parts of a slope where rockfalls could occur. The models commonly used for rebound calculation are based on restitution coefficients, which can only be calibrated subjectively in the field. To come up with a robust and objective procedure for rebound calculation, a stochastic impact model associated with an objective field data collection method was developed and tested in this study. The aims of this work were to assess the adequacy of this approach and to evaluate the minimum amount of field data required to obtain simulation results with a satisfactory level of predictability. To achieve these objectives, the rebound calculation procedure developed was integrated into a three-dimensional rockfall simulation model, and the simulated results were compared with those obtained from field rockfall experiments. For rocky slopes, the simulations satisfactorily predict the experimental results. This approach is advantageous because it combines precise modelling of the mechanisms involved in the rebound and of their related variability with an objective field data collection procedure which basically only requires collecting the mean size of soil rocks. The approach proposed in this study therefore constitutes an excellent basis for the objective probabilistic assessment of rockfall hazard. [Copyright &y& Elsevier]

• An effective micromechanical modeling (MM) framework is proposed. • The entire code of the MM model is programmed in a dynamic coding language Julia. • The computational efficiency and accuracy of the DEM and MM models are compared. Modelling the mechanical behaviour of granular materials using the insight of physics, such as discrete element method (DEM), usually costs a lot of computing resources as a result of the storing and transferring of a large amount of particle and contact information. Unlike DEM, the micro-mechanical (MM) model, based on statistics of directional inter-particle contacts of a representative volume of an element, imposes a much lower computational demand while retaining granular physics. This paper presents such a kinematic hypothesis-based MM modelling framework, programmed by a dynamic coding language, Julia. The directional local law of a recently developed model is selected as an example of the implementation. The entire code of the MM model programmed by Julia is structured into several functions by which multilevel loops are called in an order. Moreover, a global mixed-loading control method is proposed in this study by which the stress control and strain control can be achieved simultaneously. Using this method, conventional triaxial tests and proportional strain tests are simulated to calibrate the model according to experimental data. The same experiments are also simulated by DEM for comparison with the MM model to estimate the computational efficiency and accuracy, which demonstrates a significant advantage of the MM model. This study can be directly used for modelling other materials by changing the directional local law and provides helpful guidance for programming of similar multiscale approaches. [ABSTRACT FROM AUTHOR]

Stress-oftening is one of the significant features experienced by cohesive-frictional granular materials subjected to deviatoric loading. This paper focuses on mesoscopic evolutions of the dense granular assembly during a typical drained biaxial test conducted by DEM, and proposes mesoscopically-based framework to interpret both hardening and softening mechanisms. In this context, force chains play a fundamental role as they form the strong contact phase in granular materials. Their geometrical and mechanical characteristics, as well as the surrounding structures, are defined and analyzed in terms of force chain bending evolution, local dilatancy, rotation and non-coaxiality between the principal stress and the geometrical orientation of force chains. By distinguishing two zones inside and outside shear band, force chain rotations are shown to be of opposite sign, which may contribute to the observed macroscopic softening as one of the origin of the structural softening. [ABSTRACT FROM AUTHOR]

Cohesionless binary mixtures are commonly encountered in nature and frequently used as filling materials in geotechnical engineering. It is known that coarse grains have a reinforcement effect on overfilled binary mixtures in which coarse grains are embedded in the matrix of fine-grains. However, the micromechanical origin of this reinforcement effect remains unknown. Using 2D discrete element method (DEM) simulations, this study aims at highlighting the impact of coarse grains on the geometrical fabric and mechanical state of cohesionless overfilled binary mixtures. We show that coarse grains contribute to the stability of cohesionless overfilled binary mixtures by limiting macroscopic plastic deformation. Coarse grains play the role of attractors of force chains, as they promote more connected contact force networks in overfilled binary mixtures. The results of micromechanical analyses further show that embedded coarse grains in overfilled binary mixtures have a long-range influence in the surrounding fine-grain matrix in the form of a "fine bridge," which enables better stress transmission and improves the bearing capacity of the mixture. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the effect of an adsorbed water layer on the mechanical behavior of fine-grained wet granular materials in the pendular regime with isolated capillary liquid bridges. The adsorbed water forms a thin liquid film tightly bound to a particle's surface equilibrated by a so-called "disjoining pressure". In a stress transmission analysis, this disjoining pressure concept is embedded in the so-called Augmented Young-Laplace equation to account for thin film interfacial interactions. Using a homogenization technique for upscaling the micro-scale physics, an adsorptive-capillary stress tensor is derived whose discrete representation reveals a new interparticle cohesive force. In the presence of adsorbed layers, it is shown that the new liquid bridge profile, as numerically solved from the Young-Laplace equation, leads to a higher cohesive interparticle force and rupture distance. The proposed adsorptive-capillary stress tensor is further implemented within a discrete element modeling framework. As such, the evolutions of microstructure, stress tensors, and shear strength are illustrated during suction-controlled triaxial simulations. Our numerical results demonstrate that adsorbed layers have a notable effect on the mechanical behavior of fine-grained materials, particularly at higher suctions. [ABSTRACT FROM AUTHOR]

• Two different DEM models used to predict the barrier response under various loadings • Analysis of the experimental barrier response under single and successive impacts • The discrete element method is assessed for flexible rockfall barrier modeling This paper addresses the use of discrete element modeling approaches for predicting the impact response of flexible rockfall protection barriers. In this purpose, two different models are considered and their results are compared to detailed results from full-scale impact experiments. The studied barrier is a prototype made from a 4-contacts ring net and having a 270 kJ nominal capacity. The two discrete elements method models, developed by separate entities with different codes (Yade-DEM and GENEROCK), use different models for the ring net, the cables and cable-net connections, while other structural elements are modelled the same way : posts, anchors, energy dissipating devices, and boulder. The models for the structural elements (ring net, energy dissipating devices) are calibrated individually from quasi-static tensile tests results. The barrier model is then created assembling the structural elements, before being impacted. The tests consist in a impacting in its center a 3-module barrier, first, to one high kinetic energy impact and, second, to three consecutive impacts with a lower kinetic energy. The models results are confronted to measurements made during the experiments, considering a large set of parameters. Both models reveal satisfactory in predicting the structure response, on quantitative and qualitative points of view, and considering the boulder displacement, forces in the main cables and forces acting within the various energy dissipating devices. The quality of the prediction by each model compared to the other depends on the considered parameter. Little deviations from the experimental results are attributed to the model calibration procedure and to slight differences between the real structure and the modeled ones. In the end, the DEM approach appears suitable for modelling flexible barriers in complex loading conditions (high velocity and successive impacts). [ABSTRACT FROM AUTHOR]