Probability of dike failure due to uplifting and piping

A methodology is presented for determining the probability of dikes failing due to uplifting and piping using directional sampling. The study concerns one dike section in the lower river area of The Netherlands. For this dike section, the three most important random quantities are: the North-Sea water level, the river Rhine discharge, and the critical head in the event of uplifting and piping. Dike failure due to uplifting and piping is defined as the event in which the resistance (the critical head) drops below the stress (the outer water level, a combination of both sea level and river discharge, minus the inner water level). Since the critical head is correlated over the length of a dike, the spatial variation and correlation is modelled using a Markovian dependency structure. Three-dimensional directional sampling on the basis of the polar coordinates of the sea water level, the river discharge, and the critical head is used to determine the failure probability. 2 FAILURE DUE TO UPLIFTING AND PIPING Uplifting occurs when the covering layer of a dike bursts, due to the high water pressure, whereas piping under dikes occurs due to the entrainment of soil particles by the erosive action of seepage flow. The limit-state function of uplifting and piping is given by (see also Figure 1) ) ( b z h up H M H M H Z − + − = (1) and } , max{ p p u u up H M H M H = (2)