Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Laboratory study on the performance of recycled concrete aggregates blended with reclaimed asphalt pavement as pavement granular material

Production of recycled concrete aggregates (RCA) from construction and demolition (C&D) waste has become popular all over the world since the availability of land spaces are limited to dispose. Therefore it is important to seek alternative applications for RCA. The use of RCA in base and sub-base layers in granular pavement is a viable solution. In mechanistic pavement design, rutting (permanent deformation) is considered as the major failure mechanisms of the pavement. The rutting is the accumulation of permanent deformation of pavement layers caused by the repetitive vehicle load. In Queensland, Australia, it is accepted to have the maximum of 20% of reclaimed asphalt pavement (RAP) in RCA and therefore, it is important to investigate the effect of RAP on the permanent deformation properties of RCA. In this study, a series of repeated load triaxial (RLT) tests were conducted on RCA blended with different percentage of RAP to investigate the permanent deformation and resilient modulus properties of RCA. The vertical deformation and resilient modulus values were used to determine the response of RCA for the cyclic loading under standard pressure and loading conditions.

Investigation on characteristics and performance of recycled concrete aggregates as granular materials for unbound pavements

This research was a step forward in investigating the characteristics of recycled concrete aggregates to use as an unbound pavement material. The results present the guidelines for successfully application of recycled concrete aggregates in high traffic volume roads. Outcomes of the research create more economical and environmental benefits through reducing the depletion of natural resources and effectively manage the generated concrete waste before disposal as land fill.

Trans-scale granular modelling of cytoskeleton: A mini-review

Living cells are the functional unit of organs that controls reactions to their exterior. However, the mechanics of living cells can be difficult to characterize due to the crypticity of their microscale structures and associated dynamic cellular processes. Fortunately, multiscale modelling provides a powerful simulation tool that can be used to study the mechanical properties of these soft hierarchical, biological systems. This paper reviews recent developments in hierarchical multiscale modeling technique that aimed at understanding cytoskeleton mechanics. Discussions are expanded with respects to cytoskeletal components including: intermediate filaments, microtubules and microfilament networks. The mechanical performance of difference cytoskeleton components are discussed with respect to their structural and material properties. Explicit granular simulation methods are adopted with different coarse-grained strategies for these cytoskeleton components and the simulation details are introduced in this review.

Falling Weight Deflectometer (FWD) tests on granular pavement reinforced with geogrids– Case study

The use of geogrids in granular pavement layers could increase the modulus and the stiffness of granular layer and hence the required layer thickness can be reduced. Though, geogrids are being used in granular pavements to provide lateral restraint, bearing capacity, and membrane tension support, very limited studies have been carried out to investigate the effects of geogrids on modulus and stiffness of granular layer. In this study, two sections of a granular pavement were constructed: one with a geogrid at the bottom of the base layer and the other without a geogrid. Two sections were then tested using Falling Weight Deflectometer (FWD) and FWD results were analysed to determine the effect of geogrid on the overall modulus and stiffness of the granular pavement. The results suggested that the pavement section with geogrid has higher overall modulus and deflection ratio compared to the pavement section without geogrid.

Effects of particle size distribution in the response of model granular materials in multi-ring shear

Rail track undergoes complex loading patterns under moving traffic conditions compared to roads due to its continued and discontinued multi-layered structure, including rail, sleepers, ballast layer, sub-ballast layer, and subgrade. Particle size distributions (PSDs) of ballast, subballast, and subgrade layers can be critical in cyclic plastic deformation of rail track under moving traffic on frequent track degradation of rail tracks, especially at bridge transition zones. Conventional test approaches: static shear and cyclic single-point load tests are however unable to replicate actual loading patterns of moving train. Multi-ring shear apparatus; a new type of torsional simple shear apparatus, which can reproduce moving traffic conditions, was used in this study to investigate influence of particle size distribution of rail track layers on cyclic plastic deformation. Three particle size distributions, using glass beads were examined under different loading patterns: cyclic sin-gle-point load, and cyclic moving wheel load to evaluate cyclic plastic deformation of rail track under different loading methods. The results of these tests suggest that particle size distributions of rail track structural layers have significant impacts on cyclic plastic deformation under moving train load. Further, the limitations in con-ventional test methods used in laboratories to estimate the plastic deformation of rail track materials lead to underestimate the plastic deformation of rail tracks.

The mechanics of disc degeneration from an engineering and computational modelling viewpoint

The anatomy and microstructure of the spine and in particular the intervertebral disc are intimately linked to how they operate in vivo and how they distribute loads to the adjacent musculature and bony anatomy. The degeneration of the intervertebral discs may be characterised by a loss of hydration, loss of disc height, a granular texture and the presence of annular lesions. As such, degeneration of the intervertebral discs compromises the mechanical integrity of their components and results in adaption and modification in the mechanical means by which loads are distributed between adjacent spinal motion segments.

Performance analysis of unified enterprise application security framework

Unified Enterprise application security is a new emerging approach for providing protection against application level attacks. Conventional application security approach that consists of embedding security into each critical application leads towards scattered security mechanism that is not only difficult to manage but also creates security loopholes. According to the CSIIFBI computer crime survey report, almost 80% of the security breaches come from authorized users. In this paper, we have worked on the concept of unified security model, which manages all security aspect from a single security window. The basic idea is to keep business functionality separate from security components of the application. Our main focus was on the designing of frame work for unified layer which supports single point of policy control, centralize logging mechanism, granular, context aware access control, and independent from any underlying authentication technology and authorization policy.