Clastic mechanics and grain crushing: cornflakes, ballotini, and soil
Dr. Malcolm D. Bolton
CUED
As the mean effective stress p' in a virgin element of soil is allowed to increase from zero there is a small non-linear elastic compression, attributable to the elastic deformation of grains with variable contact geometry. As stress continues to increase a new phenomenon arises. Extra, and much larger, volumetric strain increments occur which are not recovered on unloading. Soil mechanicians are taught to plot this data so to reveal how specific volume v varies with p'. Critical State Soil Mechanics, for example, introduces "elastic" and "plastic" compressibilities κ and λ on a plot of v versus log p'.
Closer attention to the data of virgin soils sometimes shows that these increasing volumetric strains plot as a power curve εv proportional to pk where κ is approximately 1. At some point, however, "plastic hardening" sets in along a power curve v proportional to pL where L is of the order of 0.1 for most soils (sands and clays) irrespective of their initial state. For clay muds (and cornflakes) this hardening initiates around 5 kPa, for shelly sands around 5MPa, and for silica sands around 50 MPa. When v drops below about 1.3 (i.e. 23% porosity), which calls for pressures exceeding 100 MPa consistent with tens of kilometres of continental crust, yet a different expression is required to model the final exclusion of all voids.
Whatever the precise expressions selected, however, all these expressions v = f(p') are dimensionally inconsistent. The occasional use by authors of atmospheric pressure to achieve a dimensionless group for stress can safely be dismissed from the standpoint of physics.
The seminar addresses three main questions:
What material parameter should be used to normalise stress prior to the derivation of plastic volume changes in soils?
How have we previously escaped the potentially serious consequences of ignoring dimensional inconsistency?
What opportunities are opened up by getting the physics right?
The discussion revolves around grain crushing, fractals, power curves, and the normalisation of data. Data of the compression and shearing of both uniform and non-uniform soil gradings will be shown together with some computer simulations and a demonstration with cornflakes.
The proposition which emerges is that the whole stress boundary surface for any soil can be normalised by the crushing strength of a characteristic grain, mediated by frequency distributions of size and roughness. "Clastic mechanics" is a term coined by the lecturer to apply to the behaviour of an aggregate of irregular brittle grains. It is anticipated that many apparently separate and complex features of soil behaviour - sensitivity, creep, ageing, cyclic liquefaction, phase transformation, collapse on wetting etc - might be approached in this more fundamental way and seen to be related. Possible applications range from the selection of road bases to the predicted strength of clay backfill over subsea pipelines.
