PROBABILISTIC ANALYSIS OF EXIT GRADIENTS DUE TO STEADY SEEPAGE

The traditional approach for estimating the exit gradient i(c) downstr eam of water retaining structures due to steady seepage is to assume h omogeneous soil properties and proceed deterministically, perhaps usin g flow-net techniques. Once the exit gradient is estimated, a large sa fety factor of at least five or six is applied. The reason for this co nservative approach is twofold. First, the consequence of piping and e rosion brought about by i(c) approaching the critical value i(c),can b e very severe, leading to complete and rapid failure of civil engineer ing structures with little advance warning. Second, the high safety fa ctors reflect the designer's uncertainty in local variations of soil p roperties at the exit points and elsewhere within the how domain. This paper presents an alternative to the safety factor approach by expres sing exit gradient predictions in the context of reliability-based des ign. Random field theory and finite-element techniques are combined wi th Monte-Carlo simulations to study the statistics of exit gradient pr edictions as a function of soil permeability variance and spatial corr elation. Both two- and three-dimensional boundary-value problems are c onsidered. The approach enables conclusions to be drawn about the prob ability of critical conditions being approached and hence failure at a given site. The reliability approach is thought to represent a more r ational methodology for guiding designers in the decisionmaking proces s.