The behaviour of semi-stable filters under hydraulic loading normal to the interface
This thesis describes a series of both mathematical and numerical models of the processes that govern the behaviour of semi-stable geotechnical granular filters. Existing modelling of filters, which ascribe probability functions to the motion of material through the filter are examined. These models fail because they do not accurately describe the behaviour of the sand water mixture, and hence the transport of sand through the filter. Here the problem is approached by considering which processes are important to the behaviour of the filter, and the relation of these processes to each other. The starting point is a simplified model of the filter and foundation medium. By considering the demands of continuity of material moving up through the filter and the body of the filter moving down, the relation between the settlement rate and the rate of transport through the material is obtained. This model reveals that two parameters are important the rate of material transport and the proportion of material which remains under compressive stresses within the foundation. In order to describe the transport of material a mathematical model of two the flow of a particle fluid mixture is developed. This model has the advantage over many variable viscosity models in that it includes a particle particle interaction. Although the model is based on considerations of the flow round a typical particle at the micro scale, the final product of the model is a system of macro equations which describe the fluid as a continuum. Analysis of the stability of these equations in the presence of heterogeneity in the density of the solid fraction reveals much about the behaviour of such two phase mixtures. Fluidization of the foundation medium below the filter, can only occur once the material has dilated to achieve a well defined fluidization density. This has important consequences on the processes governing the blocking of pores within the filter. The equations which describe the fluid particle mixture are implemented in a numerical model of the flow of material through the filter. Pathways through the filter are modelled as pipes which vary in diameter in such a way as to simulate the pores between the grains of the filter. The flow of material through these pipes is then modelled numerically by use of a finite difference scheme. In this way the rate of material flow through the filter is calculated and the conditions under which the filter becomes blocked are determined. The final model calculates the form of the stress field under the filter. This effects the settlement rate by influencing both the compliance of the foundation medium and the amount of foundation material available for transport. The model requires that the filter is homogeneous at the macro scale, this allows the loading pattern on the micro scale to be simulated as a small section repeated periodically. The foundation is treated as a continuum, and the stress field is then calculated by solving the static equilibrium equations by the use of Fourier transforms. Various forms for the loading pattern are investigated and the amount of material available for transport from the foundation is estimated. A set of simple filter experiments are described. The purpose of these experiments was to gain information on the transport processes within the filter. This is achieved by constructing the filter in a transparent tube and observing the transport through the walls of the tube. In a second set of experiments by using pyrex glass as the filter medium and oil as the fluid, the filter itself was made transparent. In this way transport deep within the filter could be observed.