Micro‐inertia origin of instabilities in granular materials

Within the framework of the second‐order work theory, the onset of instabilities is explored numerically in loose granular materials through three‐dimensional DEM simulations. Stress controlled directional analysis are performed in Rendulic's plane, and a particular attention is paid to transient evolutions at the microscale. Thanks to a micromechanical analysis, the onset and development of transient mechanical instabilities is explored. It is shown that these instabilities result from the unjamming and bending of a few force chains associated with a local burst of kinetic energy. This burst of kinetic energy propagates to the whole sample and provokes a generalized unjamming of force chains. As force chains buckle, a phase transition from a quasi‐static to an inertial regime is observed. At the macroscopic scale, this results in a transient softening and a loss of controllability. After the collapse of existing force chains, the development of plastic strain is eventually stopped as new stable force chains are built.     

Diffuse failure in geomaterials: Experiments,theory and modelling

This paper presents a synthesis of the works performed by various teams from France, Italy and Canada around the question of second‐order work criterion. Because of the non‐associative character of geomaterials plastic strains, it is now recognized that a whole bifurcation domain exists in the stress space with various possible modes of failure. In a first part these failure modes are observed in lab experimental tests and in discrete element modelling. Then a theoretical study of second‐order work allows to establish a link with the kinetic energy, giving a basis to explain the transition from a prefailure (quasi)static regime to a postfailure dynamic regime. Eventually the main features of geomaterials failure are obtained by applying second‐order work criterion to five different constitutive rate‐independent models—three being phenomenological and two micromechanical. As a whole this paper tries to gather together all the elements for a proper understanding and use of second‐order work criterion in geomechanics. Copyright © 2010 John Wiley & Sons, Ltd.     

Second‐order work analysis for granular materials using a multiscale approach

It has been established that the second‐order work criterion is a general necessary condition for all instabilities by divergence in rate‐independent granular materials. The relation between the values of discrete second‐order work at the intergranular contact point level and its global macroscopic value is recalled at the beginning of this paper. Then, the basic purpose of the paper is tackled by an analysis of the main features of second‐order work criterion in relation with the granular microstructure. For that, it is considered a novel micromechanical model (the so‐called ‘H‐microdirectional model’), which has the property to involve three scales: grain scale, mesoscale with a specific granular configuration and continuum mechanics macroscale. Eventually, these exhibited features (a bifurcation stress domain and some instability cones) are qualitatively compared with the ones provided by direct numerical simulations issued from a discrete element model. The ultimate goal is to analyse what happens at the granular scale, when the macrosecond‐order work is vanishing at the macrolevel. Copyright © 2013 John Wiley & Sons, Ltd.     

Micromechanics of vortices in granular media: connection to shear bands and implications for continuum modelling of failure in geomaterials

Recent analysis of data from triaxial tests on sand and discrete element simulations indicate the final pattern of failure is encoded in grain motions during the nascent stages of loading. We study vortices that are evident from grain displacements at the start of loading and bear a direct mathematical connection to boundary conditions, uniform continuum strain and shear bands. Motions of three grains in mutual contact, that is, 3‐cycles, manifest vortices. In the initial stages of loading, 3‐cycles initiate a rotation around a region Ω^* where the shear band ultimately develops. This bias sets a course in 3‐cycle evolution, determining where they will more likely collapse. A multiscale spatial analysis of 3‐cycle temporal evolution provides quantitative evidence that the most stable, persistent 3‐cycles degrade preferentially in Ω^*, until essentially depleted when the shear band is fully formed. The transition towards a clustered distribution of persistent 3‐cycles occurs early in the loading history—and coincides with the persistent localisation of vortices in Ω^*. In 3D samples, no evidence of spatial clustering in persistent 3‐cycle deaths is found in samples undergoing diffuse failure, while early clustering manifests in a sample that ultimately failed by strain localisation. This study not only delivered insights into the possible structural origins of vortices in dense granular systems but also a tool for the early detection of the mode of failure—localised versus diffuse—a sample will ultimately undergo. Copyright © 2014 John Wiley & Sons, Ltd.     

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

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

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

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

Spoil pile instabilities with reference to a strip coal mine in Turkey: mechanisms and assessment of deformations

With the increasing adoption of the surface mining of coal, problems associated with spoil pile instability, which affects resource recovery, mining cost, and safety and presents environmental hazards, have become a matter of prime concern to mine planners and operators. The study of geotechnical aspects is thus very important in the rational planning for the disposal, reclamation, treatment and utilization of spoil material. A strip coal mine, one of the largest open pit mines in Turkey, is located in Central Anatolia and provides coal to a thermal power station. Coal production is carried out in two adjacent open pits, the Central Pit and South Pit. A large-scale spoil pile instability over an area of 0.3 km² occurred within the dumping area of the Central pit. In addition, small-scale movement occurred in the outside dumping area. This paper outlines the results of field and laboratory investigations to describe the mechanisms of the spoil pile instabilities and to assess deformations monitored over a long period following the failure. Shear test results indicate that the interface between the floor and spoil material dumped by dragline has a negligible cohesion and is the most critical plane of weakness for spoil pile instability. Back analyses based on the method of limit equilibrium and the numerical modelling technique, and observations in the pit revealed that failure occurred along a combined sliding surface consisting of a circular surface through the spoil material itself and a planar surface passing along the interface between the spoil piles and floor. The analyses also indicated that pore water pressure ratios of about 0.25 satisfy limiting equilibrium condition and that rainfall about one month before the failure may be a contributing factor to the instability. Movement monitoring data obtained following the failure over a 1.5-year period suggested that the ongoing deformations were mainly due to compaction of the spoil material. Based on the monitoring data and the results of the analyses, the failure mode of the local instability occurring at the outside dumping area was considerably similar to that of the large instability.