One of the failure mechanisms of a dike is piping. A water level difference between the two sides of a dike causes a groundwater flow in the sand layer under the (clay)dike. This flow can transport sand from under the dike to the exit point of the groundwater flow. The formula of
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One of the failure mechanisms of a dike is piping. A water level difference between the two sides of a dike causes a groundwater flow in the sand layer under the (clay)dike. This flow can transport sand from under the dike to the exit point of the groundwater flow. The formula of Sellmeijer is derived mathematically from the equation of continuity, Poiseuille flow in the slit and equilibrium of grains on the bed of the channel, modeled with the equation of White. The influence of D70 on the critical gradient is linear in the Sellmeijer formula. However, coarse-grained sands are generally more permeable than fine-grained sands, which generally results in a net influence of the grain size on the critical gradient to be less than linear, but still positive. De Wit did experimental research and found that coarse grained sands have a higher critical gradient than fine grained sands. In the framework of Strength and Solicitation Flood Defences (SBW), experiments with piping were performed. It was found the influence of D70 on the critical gradient is less than is predicted with the Sellmeijer model. 1. Problem definition and objective of the research The objective of this thesis is to research the influence of the grain size and other sand characteristics on the critical head of piping, and to find an explanation for the difference found between SBW results and the Sellmeijer formula. Besides the mean objective of this thesis, a theoretical research to the velocity in the channel according to the current Sellmeijer model has been done. 2. Approach and results of the study of variables A study is performed to variables which are considered to have influence on the critical gradient. A multi variate analysis (MVA) has been performed successfully on SBW. The influence of the D70 is less than is predicted with the Sellmeijer formula. For fine sands, the Sellmeijer formula agreed quite well with the experiments, for coarse sands, it gives an unsafe prediction. Based on the MVA on SBW, an adapted Sellmeijer formula was formulated by Sellmeijer (Sellmeijer 2010a). The MVA was also tried on the dataset of de Wit, but was not successful. The data of de Wit was inserted in the adapted Sellmeijer formula. The outcome did not agree, this may be because the data of de Wit was possibly not corrected for the filter resistance, or because the range of variables in the de Wit dataset is different than the range of variables in the dataset of SBW. 3. Approach and results of research to the erosion mechanism In the Sellmeijer model, the equilibrium of grains is according to the model of White, which assumes individual grain erosion. It is researched if this is correct. A test facility was built to research the erosion process experimentally. It was found the grains are dislodged from the granular matrix as mass erosion, with a layer thickness of roughly 7 grains. The transport of sand in the test facility occurs in the pipe in mass transport, in waves, called slurry flow. It is not sure that the observed erosion of the grains from the sand matrix is normative for determining the critical gradient, as the observed erosion may be the erosion type that is present when the critical gradient has already been exceeded. This is still under discussion. The implication of the found dislodging mechanism is that the Sellmeijer formula may possibly describe the dislodging of grains and the piping process in an improper way, however more research is needed to validate if the observed erosion process is normative for determining the critical gradient.