System reliability of flood control levees

Systems of levees are present in many locations world-wide to provide flood protection for urban, industrial, and agricultural resources. In risk assessment of levee systems, the probability of demand (e.g., high water events, earthquakes, waves) exceeding capacity (e.g., freeboard, erodibility, liquefaction susceptibility) is evaluated across the system. We describe and compare two levee system reliability analysis frameworks for cases of seismic and high-water demand types. The first approach considers spatial correlations and distributions of demand and capacity between “segments” (i.e., elemental levee lengths, nominally 50 m in scale) through Monte-Carlo simulation. The capacity correlation model considered in this approach is empirically derived from seismic case histories in Japan. The seismic demand correlation model is also empirical and based on global ground motion data, whereas the high-water correlation is taken as unity. The second approach, which was developed and previously applied in the Netherlands, examines the distribution and correlation of capacities and demands between physics-based “reaches” (i.e., length of levee having uniform statistical distributions of capacity and demand, potentially hundreds of m in length). Statistics and spatial correlation of the limit state function, defined as capacity minus demand, are computed using a first-order reliability method (FORM) procedure based on the distribution functions and spatial correlation functions for capacity and demand. Having computed the distribution function and spatial correlation function for the limit state, the probability of failure of the reach is then computed using level-crossing statistics. We identify a hurdle in the implementation of the level-crossing statistics approach that is related to Markov-type correlation functions for levee capacity – this is overcome by developing a similar-performing Gaussian correlation function. We compute system failure probabilities from reach statistics by assuming statistical independence among reaches. We illustrate application of both methods for an example levee system subjected to realistic demand and capacity distributions. Our results show that characteristic lengths (defined as lengths of levee that can be considered as statistically independent) are comparable for high-water and seismic demands; our interpretation is that this result is driven by the use of similar capacity correlation models, whereas the differences in demand correlation models for the two hazards are not impactful.