Probabilistic internal erosion analysis in stratified and unstratified foundations of embankment dams using copulas

The internal erosion analysis in the foundation of an embankment dam is affected by various sources of uncertainty such as the random soil properties, their correlations and stratified or unstratified conditions at the foundation, which were addressed together in this paper as a novel probabilistic approach. In this regard, the bivariate probabilistic internal erosion analysis was carried out using two correlated soil properties including the representative soil particle size, d₇₀, and hydraulic conductivity, K. The joint probability distributions were obtained for K–d₇₀ pair values using the elliptical and Archimedean copulas and applied to different embankment geometries with stratified and unstratified foundations. According to the results, Archimedean copulas locally lead to higher dependence structure between random variables than elliptical copulas, but T-Student copula from elliptical family globally outperforms other copulas. A stratified foundation also caused an increase in the probability of internal erosion due to preferred seepage flows along the interfaces of soil layers. Finally, the Kolmogorov Smirnov tests showed that, the internal erosion index can be appropriately modeled by the general extreme value method. A polynomial relationship was also obtained for the probability of internal erosion against the dimensionless base length of the embankment in both stratified and unstratified foundations.