Discrete Element Modelling of Critical State Soil Mechanics

Soil is a complex material comprising solid particles and voids. When a soil is sheared with full drainage, for a given stress level, a loose soil contracts and a dense soil dilates to the same ultimate density. For a given density, if the soil is sheared at this constant density, then the same ultimate effective stress condition is reached, no matter what the initial stress conditions are. In fact, if shear stress, mean effective stress (mean total stress minus pore pressure) and the voids ratio (volume of voids/volume of solids) are plotted on three mutually orthogonal axes, then there is a unique CRITICAL STATE LINE in this space, which a soil state, when sheared, will tend towards. The concept of the Critical State has been around for over half a century and forms the basis for all soil mechanics and geotechnical engineering.

The micro mechanical origin of the Critical State Line has never been explored. Tradtionally, the CSL has been accepted as being parallel to the one-dimensional normal compression line - this is the line in voids ratio - log stress space for a sample compressed in a piston with no lateral strain. Recently, McDowell has published a model (McDowell and de Bono, 2013) which shows that the one-dimensional normal compression line is linear in log(voids ratio)-log(stress) space and the slope is a function of the size effect on particle strength as particles break and become statistcally stronger, and a fractal distribution of particle sizes evolves. This was done using the Discrete Element Method (DEM), which can model a soil particle as a ball, a clumped group of balls, or a group of bonded balls (an "agglomerate") which can then fracture. The contact forces between the particles are related to their relative displacements. These forces are used via Newton's 2nd law to calculate accelerations, which are integrated twice to give displacements and hence new contact forces. Until recently, the problem with using agglomerates of bonded balls to represent particles was that the modelled particles were too porous. This meant that the internal voids become external voids when the particles break. This made it difficult to model the compaction of soil properly. In addition, it has been shown that agglomerates need to have at least 500 balls in them to be representative of real particles, and this is too onerous in terms of computational time. McDowell and de Bono (2013) overcame this problem by modelling the compression of soil using non-porous solid particles, which break when the forces distributed around them reach critical values and each broken particle is then replaced by smaller fragments. They replicated the process of one-dimensional normal compression, in three dimensions, for the first time, without using agglomerates. The slope of the predicted normal compression line was correct, as was the resulting particle size distribution which evolved.

The fact that the normal compression of soil can now be modelled correctly by replacing spheres under high stress with smaller fragments, means that it should be possible to model the whole of Critical State Soil Mechanics. A knowledge of the micro mechanics of Critical State Soil Mechanics will enable researchers and practising engineers to develop more accurate constitutive models which incorporate soil particle crushing. The geotechnical industry will benefit in the long term from these improved models in design and analysis, and ultimately will be able to use DEM to analyse boundary value problems. This will, in the long term, lead to better design, improved safety and better and more economic infrastructure. The mining and powder technology industries will also benefit from using this model to simulate processes such as mineral crushing and powder compaction.

The end result of the proposed work will be that those in the soil mechanics, geotechnical engineering, and powder and granular mechanics communities, will, for the first time, have a micro mechanical understanding of Critical State Soil Mechanics, and hence the micro parameters which affect macroscopic behaviour. By understanding the micro mechanical parameters which govern constitutive behaviour, it will be possible to develop better predictive models for soil behaviour and also to model some boundary value problems in DEM directly. This will, in the long term, lead to better design, improved safety and better and more economic infrastructure. This is a fundamental proposal which aims to explain the Critical State Soil Mechanics framework that is central to all of soil mechanics and geotechnical engineering and so the impact is global and of very high significance. Almost every model in geotechnical engineering has Critical State Soil Mechanics at its core, but with no micro mechanical basis. It is anticipated that this proposal will result in a new text book which teaches Critical State Soil Mechanics from a micro mechanical perspective, and thus will be useful to any civil engineering undergraduate, practising engineer and those researching the behaviour of granular materials in civil engineering, mining, powder processing and the pharmaceutical industry.