Stochastic analysis of internal erosion in soil structures - Implications for risk assessments

A new modeling framework for internal erosion in heterogeneous stratified s oils is developed by combining existing methods used to study sediment tran sport in canals, filtration phenomena, and stochastic processes. The framew ork is used to study the erosion process in sediments caused by a flow of w ater through a covering filter layer that deviates from geometrical filter rules. By the use of spectral analysis and Laplace transforms, mean value s olutions to the transport rate and the variance about the mean are derived for a transport constraint at the upstream boundary and a constant initial transport. Increasing the heterogeneity of a defective filter layer in a ca nal retards the propagation of the expected bed degradation. An implication is that the heterogeneity of the riprap, in this respect prolongs the expe cted degradation process and the expected lifespan of the structure. The in creased variance and decreased correlation length of the riprap reduces the confidence of the mean value solution. The stochastic analysis is therefor e suitable as part of risk analyses of extreme events such as failure of em bankment dams, for which empirical observations are rare.