Application des techniques de fiabilite pour l'estimation des incertitudes des resultats de simulations numeriques en hydrodynamique des rivieres

In hydraulic engineering, the physical properties governing the flow are known up to some degree of uncertainties. It is thus important for a safe and optimal design of hydraulic structures to evaluate the uncertainties propagation trough the system from the input to the output data. The Monte Carlo simulation is the simplest and direct method to evaluate the probability of safety or failure; however, for very small probabilities such evaluation can prove very prohibitive. On the other-hand, approximate reliability methods such as FORM rely on the solution of an optimization problem. For fast and robust convergence, gradient-based iterative methods are the methods of choice. In this paper we present a coupling of a quasi-Newton algorithm with the FORM and Importance sampling reliability methods to evaluate small probabilities of failure. These techniques are applied in the cases of a flow in the Aisne river (France) and the Saint Lawrence river, where we consider the friction coefficient, the discharge and the bathymetry parameters as the uncertain variables. The 95% confidence interval for the water elevation and the probability of exceeding the height of a protective dyke are then obtained.