A micro mechanical study of critical state soil mechanics using DEM

One of the greatest breakthroughs in soil mechanics was the development of Critical State Soil Mechanics (CSSM) in the 1950s and 1960s and the derivation of a continuum elasto-plastic constitutive model, namely Cam clay, which was the foundation for other continuum models for clays, and much later for sands. However, as yet there has been no micro mechanical analysis which explains the existence of such continuum models; such a micro perspective must take into account the discontinuous nature of soil. Without such insight, the engineer cannot understand which micro parameters affect soil behaviour. This work uses the discrete element method (DEM) to model a silica sand as a sample of discrete particles, with properties which have been calibrated against experimental data in previous work, to build up a micro mechanical picture of the behaviour of sand under different loading conditions. The simplest of loading conditions is the one dimensional or oedometer test and has been modelled to check whether this agrees with previously published research. The simulated sample has then been subjected to isotropic compression to establish a normal compression line in log voids ratio – log stress space, and which turns out to be parallel to the one-dimensional normal compression line, in agreement with CSSM. The evolution of the isotropic normal compression line is due to local shear stresses within the sample, and the origin of the existence of both lines lies in the evolution of a fractal distribution of particles with a fractal dimension of 2.5. The effect of boundary particles has then been minimised by choosing an appropriate aspect ratio and a smaller number of particles in the sample to give a computational time which is acceptable for subsequent shearing to critical states. Isotropically normally compressed samples have been unloaded to different stress levels and sheared to critical states. A unique critical state line (CSL) exists at high stress levels, which is parallel to the normal compression lines, in agreement with CSSM. At low stress levels, the CSL is not linear and is non-unique; that is to say it is a function of preconsolidation pressure because the fractal distribution of sizes has not fully evolved. Samples sheared on the dense side of critical dilate and have a peak strength whilst loose samples exhibit ductile contraction, in agreement with CSSM. At a critical state, the work shows that crushing continues in the formation of ‘fines’, small particles with smaller than 0.1mm dimensions, which plays no part in the mechanical behaviour, which is reflected in the average mechanical co-ordination number and which means that plastic hardening can be assumed to have ceased at a critical state. For the isotropically overconsolidated samples sheared to critical states, a number of different definitions of yield have been used to establish a yield surface in stress space. The work shows that a previously published yield surface for sand (Yu, 1998; McDowell, 2002) gives a good representation of the behaviour, and it has therefore been shown that the sample of discrete particles has been shown to give rise to observed continuum behaviour. The work is, to the author’s knowledge, the first that has shown a DEM soil to show many of the desirable features of sand, in that the sample qualitatively gives normal compression lines and a CSL of the correct slope, which obeys CSSM and which gives a Cam Clay type yield surface in stress space. The work means that the established model can be used in the study of other micro mechanics problems such as particle shape and time effects and the application of DEM to boundary value problems directly