Mathematical modelling of granular filters and constriction-based filter design criteria

In geotechnical engineering, a filter is designed to protect soils, called base, within or behind a structure from erosion due to seepage. As water flows through the soil, fine particles can be washed out, leading to internal erosion and eventually, the failure of the structure. A correctly designed filter retains loose soil particles, thus preventing erosion. In contrast, it allows unobstructed seepage, preventing build-up of detrimental pore pressure. A filter is commonly a natural or manufactured sand and gravel. Filters are used in dams, agricultural drainage, road pavements, retaining walls, canal linings, coastal protection, landfills and so on. First time in early 1920s, Terzaghi suggested two filter design criteria through laboratory investigations on uniform sands. These criteria involved ratios of some specific sizes of filter and base materials. Most subsequent studies ended up either merely investigating validity of or extending these criteria to other soil types. Current professional guidelines are still empirical and based on particle sizes. However, within filters, it is pores (i.e. constrictions) that govern filtration. Consequently, these particle-based guidelines exhibit some serious limitations. In this thesis, limitations of current professional guidelines are comprehensively discussed. A detailed mathematical procedure is developed to determine constriction sizes, and subsequently, constriction-based criteria are proposed to describe filter effectiveness in various types of soils. The proposed criteria are verified using several large-scale tests carried out at the University of Wollongong including several test data available in the literature. Finally, an enhanced filter design guideline is suggested for the professional practice.