Currently there is no consistent, widely accepted procedure for discretizing levee systems subjected to seismic load for probabilistic analysis. Further, statistical independence of performance between levee sections is often assumed without verification. This stems from the difficulty in: quantifying the spatial autocorrelation structure of random variables used to predict performance and, implementing autocorrelation structure into probabilistic levee analysis. In this research we use First Order Reliability Method (FORM), Second Order Reliability Method (SORM), Sequential Important Conditional Sampling (SCIS) and Directional Important Sampling (DIRS) in an attempt to define a robust methodology for discretizing a levee system for probabilistic analysis and to show that assuming independence of performance between individual levee sections is not valid.

We chose to use the levee that protects Sherman Island, CA as our case study. Sherman Island is located in the California Bay Delta, which is the terminus of the Sacramento and San Joaquin rivers and a strategically vital hub of infrastructure for the region and the State of California. To use the reliability tools we have selected it was necessary for us to define compatible levee performance models. Compatible models must be continuous functions of random variables that are differentiable and the random variables must be continuous and described by a joint probability distribution. Rather than develop our own models we adopted levee performance models developed in the Delta Risk Management Strategy (DRMS) Phase 1 Report (URS 2009). This report was a comprehensive risk analysis of the California Bay Delta. The seismic performance models developed within were not fully compatible with or reliability tools. Therefore we made appropriate and technically sound adjustments to the models.

To ensure that our seismic levee performance models were producing reasonable results we used them to calculate point estimates of failure probability at Sherman Island for past seismic events: M≈7.9 1906 Great San Francisco Event, M=5.8 1980 Livermore Event, M=6.19 1984 Morgan Hill Event and M=6.9 1989 Loma Prieta Event. There were no documented seismic failure for the three most recent events and our failure probability estimates agree well with this.

As mentioned above, quantifying the spatial autocorrelation structure of random variables used to predict levee performance is a non-trivial task. As part of this study we investigated the spatial autocorrelation structure of ground motion intensity measures. Specifically we characterized the spatial autocorrelation structure of single-station intra-event residuals and site terms. We did this for three different sets of ground motion data: a Californian dataset (Chiou et al., 2010), a Taiwanese dataset (Lin et al., 2011) and a Japanese dataset (Rodriguez-Marek et al., 2011). Single-station intra-event residuals come from single-station sigma ground motion prediction equations, which are models that have removed repeatable site effects from the standard deviation. We show that the spatial autocorrelation structure of single-station intra-event residuals and site terms are region dependent and sensitive to the period of pseudo spectral acceleration. Further we show that single-station intra-event residuals stay autocorrelated for greater distances than intra-event residuals. We implemented our characterization of ground motion autocorrelation into our levee reliability analysis.

There was not sufficient data for us to quantify the spatial autocorrelation structure of the random variables that describe material properties of the levee. There are studies on spatial autocorrelation of material properties in the literature however; none of studies are at an applicable scale for our analysis. Additionally, there is little guidance on whether or not model error terms are autocorrelated. We test a range of assumptions on the spatial autocorrelation of the material properties and model error terms in our analysis.

The results of our analysis suggest that: A robust methodology for discretization of levee systems under seismic load is dependent on the scale of the potential failure mechanisms and, the assumption of statistical independence of performance between levee sections is not appropriate. Though we were unable to develop a specific methodology for the discretization of a levee system we provide a relationship for adjusting failure probability estimates of a levee based on its length and assumptions about the scale of potential failure mechanisms and the amount of autocorrelation present in random variables used for prediction.