Levee System Reliability Along a Confluence Reach

The random stage in the main river and a flood of random stage height in the tributary determine the water level along the levee reach; a nonuniform steady flow equation is used in discretized form to compute backwater curves for each pair of values. Roughness coefficients in the bed and the flood plain are determined by a model calibration procedure. Using this information, the probability of failure in one levee cross section is computed. Another method is developed to calculate the probability of failure of the whole levee system in which a linear regression model yields discretized values of water stage in each levee subreach. Hydrologic, sample, and model uncertainties are examined. The effect of sample uncertainty is shown to increase the probability of failure of the levee. A practical example is used throughout to illustrate the methodology, which may be applied as is to other problems of this type whenever the joint probability distribution can be fitted to a normal or lognormal density function.