Design relationship for filters in bed protection

A simple design relationship is derived for the filter ratio of a stable geometrically open filter in a bed protection, the filter ratio here being defined as the ratio between the diameters of two layers, one on top of the other. The relationship is based on the assumption that the largest hydraulic loading in a bed protection is related to the hydraulic loading on the top layer. The stability of the top layer and the underlying layer under hydraulic loading is estimated using a Shields type relationship. The hydraulic gradient in the filter is derived from the time-average hydraulic gradient, taking into account pressure fluctuations which determine the gradient fluctuations. The equation derived is compared with the results of published experimental work. This shows that the smaller the material needed for a stable bed protection, the higher the permissible filter ratio. Application of this result may lead to one or two filter layers less than required with a geometrically tight designed bed protection.