L.W. Saperstein

Doctor of Philosophy, Queen's College, Oxford University, Trinity Term 1967

The Dynamics of Granular Solids

Summary

A theoretical and experimental examination into the dynamics of granular solids has been completed which covers aspects of flow and failure within this material. The investigation is divided into three natural sections; each section being devoted to a different type of failure. As indicated by the title, the subject of the study was cohesionless soil, and thus the basic tenets of soil mechanics and the failure of granular media are applicable.

The first section deals with gravity flow of non-cohesive granular material in both axial and rectangular geometry. Traditional plasticity theory is used to establish characteristics of stress and strain, also stress sliplines within a wedge. From these, two relationships between the angle of internal friction and the bound to a radial flow field are established. A minimum energy theory of flow is discussed and then used to determine mass flow rates. From this theory a velocity profile is deduced an by use of either the entire profile or the vertical ray or the extreme angular ray three relationships between the bound tot he radial flow field and the mass flow rate are established.

The limits to piping in axial symmetry are defined. It is shown that gravity flow in rectangular geometry must always result in pipes.

Experiments were devised to substantiate these findings and they show that, dependent upon the assumptions that were made, the devised relationships bracket, within reasonable limits, the radial bound and the mass flow rate. Work of two other investigators is compared wit the presented experimental results. The definitions of pipe are shown to have validity.

Section Two was the result of an attempt to measure a parameter that was relevant to the investigation in Section Three. The possibility of the passive rather than the active lateral earth pressure acting upon a shifting retaining wall was discovered while attempting the measurement of the coefficient of friction of sand on mild steel.

The third section is concerned with an investigation into the factors that affect the forces on a horizontally propelled model that is immersed in sand. The parameters of depth, speed, projected model area, and other model characteristics were varied, and experimental relationships between the force and these parameters determined. Also, pressure measurements were made within the sand as the model passed to determine the extent of the failure region. Several other experiments, such as the effect of false walls on the force level, were made in order to determine the limits of validity of the main experiment.

It was found that the force on the model varied as the 2.3 power of the depth, linearly with the projected model area, and not at all with model surface, model length, or speed in the range 0-15 feet per minute. The pressure measurements and false-walls studies showed that failure occurred within the sand and not at the walls of the tank; also that failure took the form of successive shear dislocation of pyramidally shaped wedges of sand.

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