Stochastic Analysis of Internal Erosion in Soil Structures—Implications for Risk Assessments

Abstract

A new modeling framework for internal erosion in heterogeneous stratified soils is developed by combining existing methods used to study sediment transport in canals, filtration phenomena, and stochastic processes. The framework is used to study the erosion process in sediments caused by a flow of water through a covering filter layer that deviates from geometrical filter rules. By the use of spectral analysis and Laplace transforms, mean value solutions 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 canal retards the propagation of the expected bed degradation. An implication is that the heterogeneity of the riprap in this respect prolongs the expected degradation process and the expected lifespan of the structure. The increased variance and decreased correlation length of the riprap reduces the confidence of the mean value solution. The stochastic analysis is therefore suitable as part of risk analyses of extreme events such as failure of embankment dams, for which empirical observations are rare.