Micro mechanics of the critical state line at high stresses

A critical state line is presented for a crushable numerical soil, which is parallel to the isotropic normal compression line. A previous theory for the normal compression line, which correctly predicts the slope as a function of the size-effect on particle strength is extended to justify the slope of the critical state line. The micro mechanics behind critical states are examined, leading to a theory for a relationship between the volume of smallest particles and mean effective stress. A unique relationship exists for crushed states, leading to a two-dimensional interpretation of the state boundary surface for soils looser than critical

An insight into the yielding and normal compression of sand with irregularly-shaped particles using DEM

The micro mechanics of one-dimensional and isotropic normal compression of granular soil have recently been revealed using the discrete element method. By modelling soil grains as spheres and implementing a new crushing model, the authors have previously investigated the influence of fracture mechanism, particle strengths (and distributions), and the size-hardening law on both the normal compression line and resultant particle size distribution; this resulted in a new compression law. In this work, irregular particle shape is introduced, using ‘clumps’ (groups of spherical particles), allowing different relative densities of the same material to be subjected to normal compression. An investigation into the mechanics of yielding is presented, in which the onset of crushing is related to the average particle octahedral shear stress and ‘yield’ is seen to be a function of the available void space. Beyond yield, the normal compression lines for the clumps at different initial densities are examined and compared to that for spheres. The effect of coordination number and particle shape on the normal compression are studied, and in particular the micro mechanics behind the evolution of a fractal particle size distribution are revealed

The fractal micro mechanics of normal compression

The fundamental fractal micro mechanics of normal compression of granular materials is studied using DEM. This paper examines the emergence of a finite fractal bounded by two particle sizes as stress increases, and the evolution of various definitions of the ‘smallest particles’. It is revealed that if particles are categorised according to their coordination number, then the volume of all particles with 4 contacts or fewer is directly proportional to the void space. These particles are called ‘critical particles’ and are shown, for the first time, to explain quantitatively the voids reduction with increasing vertical stress

Micro mechanics of critical states for isotropically overconsolidated sand

The discrete element method has been used to investigate the micro mechanics of shearing to a critical state on the loose and dense sides of critical. Isotropic compression has previously been modelled in 3D using a large number of particles and without the use of agglomerates. The same procedure is used here. Particle fracture is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Isotropic compression of a silica sand has been simulated to 20 MPa and followed by unloading to a range of stresses before shearing to a critical state, using micro parameters which relate to the silica sand particle strengths. The samples at the lowest stress levels exhibit peak strength and dilation. The sample at the highest stress exhibits contraction and ductile yielding to a critical state. A critical state line is established, which appears to become parallel to the isotropic line in log e-log p space at high stress levels. This paper shows that it is the evolving fractal particle size distribution during isotropic normal compression which governs the behaviour on unloading to different overconsolidation ratios. The micro mechanics of the critical state line are shown to be in the evolving particle size distribution during normal compression, and how such an aggregate behaves when it is unloaded

Investigating the effects of particle shape on normal compression and overconsolidation using DEM

Discrete element modelling of normal compression has been simulated on a sample of breakable two-ball clumps and compared to that of spheres. In both cases the size effect on strength is assumed to be that of real silica sand. The slopes of the normal compression lines are compared and found to be consistent with the proposed equation of the normal compression line. The values of the coefficient of earth pressure at rest K0,nc are also compared and related to the critical state fiction angles for the two materials. The breakable samples have then been unloaded to establish the stress ratios on unloading. At low overconsolidation ratios the values of K0 follow a well-established empirical relationship and realistic Poisson ratios are observed. On progressive unloading both samples head towards passive failure, and the values of the critical state lines in extension in q–p' space are found to be consistent with the critical state angles deduced from the values of K0 during normal compression. The paper highlights the important role of particle shape in governing the stress ratio during both normal compression and subsequent overconsolidation

Migration and Sustainable Livelihoods: A Critical Review of the Literature

This paper focuses on the links between migration and sustainable livelihoods, looking in particular at the institutional factors that connect the two. It argues that much of the development literature makes the false assumption that sedentary patterns in society are the norm, instead making the case that migration is often the rule, rather than the exception. It concludes that migration should be seen as just one of the livelihood strategies open to households, that it is often combined with other strategies, and that it is frequently a two-way process in which migrants maintain close links with their areas of origin over a much longer period than is frequently assumed. Pointing out the range of different types of migration, ranging from voluntary to forced, the paper highlights the complex institutional factors involved in determining who is able to migrate, and who benefits most from it

On the micro mechanics of one-dimensional normal compression

Discrete-element modelling has been used to investigate the micro mechanics of one-dimensional compression. One-dimensional compression is modelled in three dimensions using an oedometer and a large number of particles, and without the use of agglomerates. The fracture of a particle is governed by the octahedral shear stress within the particle due to the multiple contacts and a Weibull distribution of strengths. Different fracture mechanisms are considered, and the influence of the distribution of fragments produced for each fracture on the global particle size distribution and the slope of the normal compression line is investigated. Using the discrete-element method, compression is related to the evolution of a fractal distribution of particles. The compression index is found to be solely a function of the strengths of the particles as a function of size

Micro mechanics of drained and undrained shearing of compacted and overconsolidated crushable sand

A numerical crushable soil sample has been created using the previously published McDowell and de Bono (2013) model and subjected to a range of stress paths. Compacted sand simulations are performed using conventional triaxial stress paths, constant mean stress and constant volume conditions and a critical state line established. Overconsolidated samples have been created by crushing the soil down the isotropic normal compression line, unloading, and shearing at constant radial stress, constant mean stress or constant volume and a critical state line is again established. The critical state line is unique at high stresses for the simulated compacted and overconsolidated sands and is parallel to the isotropic normal compression line, in agreement with available data and a previously published theory. The critical state line at low stress levels is non-unique and a function of the particle size distribution, in agreement with available data. Constant volume tests exhibit the well-known phenomena of phase transformation points and peak strengths are observed for ‘drained’ soils on the dense side of critical. The numerical soil produces a state boundary surface that compares well to available data

On the packing and crushing of granular materials

This paper is a study of the dependence of the volume of voids in a granular material on the particle size distribution. It has previously been proposed that the volume of voids is proportional to the volume of the smallest particles. In a particle size distribution which is progressively becoming wider (e.g. as occurs due to crushing during the compression of sand), the smallest size of particle decreases, yet there are only ever a few of these particles out of many thousands or millions. This paper attempts to identify which particles govern the overall density of a granular material, and a new definition of the ‘smallest particles’ is proposed. These particles are shown to govern the void space in a range of simulations of spherical and non-spherical crushable particles. The theory also applies to idealised Apollonian sphere packings

DEM of triaxial tests on crushable cemented sand

Using the discrete element method, triaxial simulations of cemented sand consisting of crushable particles are presented. The triaxial model used features a flexible membrane, allowing realistic deformation to occur, and cementation is modelled using inter-particle bonds. The effects of particle crushing are explored, as is the influence of cementation on the behaviour of the soil. An insight to the effects that cementation has on the degree of crushing is presented