Probabilistic Analysis of Exit Gradients due to Steady Seepage

The traditional approach for estimating the exit gradient i_e downstream of water retaining structures due to steady seepage is to assume homogeneous soil properties and proceed deterministically, perhaps using flow-net techniques. Once the exit gradient is estimated, a large safety factor of at least five or six is applied. The reason for this conservative approach is twofold. First, the consequence of piping and erosion brought about by i_e approaching the critical value i_c can be very severe, leading to complete and rapid failure of civil engineering structures with little advance warning. Second, the high safety factors reflect the designer's uncertainty in local variations of soil properties at the exit points and elsewhere within the flow domain. This paper presents an alternative to the safety factor approach by expressing exit gradient predictions in the context of reliability-based design. Random field theory and finite-element techniques are combined with Monte-Carlo simulations to study the statistics of exit gradient predictions as a function of soil permeability variance and spatial correlation. Both two- and three-dimensional boundary-value problems are considered. The approach enables conclusions to be drawn about the probability of critical conditions being approached and hence failure at a given site. The reliability approach is thought to represent a more rational methodology for guiding designers in the decision-making process.