Modeling the Reliability of New Orleans Levees

Modeling the Reliability of New Orleans Levees

by

Robert C. Patev, M.ASCE, David M. Schaaf, P. E., M.ASCE,

Jerry L. Foster, P. E., M.ASCE and Gregory B. Baecher, Ph. D., M.ASCE

Among the many tasks addressed by the federal Interagency Performance Evaluation Taskforce on Hurricane Katrina (IPET) was an assessment of the hurricane hazard and an analysis of the reliability of the Hurricane Protection System (HPS) in providing protection. Together, the hazard assessment and the reliability analysis constituted the building blocks of a systems risk assessment, the purpose of which was to identify parts of the HPS most vulnerable to flooding and to establish the approximate levels of risk. This risk assessment had four parts: (1) a probabilistic evaluation of potential loadings from future hurricanes, (2) a reliability analysis of the performance of the HPS under specific loadings, (3) an assessment of economic and loss-of-life consequences due to possible failures, and (4) a systematic integration of these factors into an assessment of risk. By examining pre- and post-Katrina risks, the effectiveness of repairs since Katrina could be evaluated.

New Orleans has grown over the past two centuries from a small settlement on the topographically high natural levees of the Mississippi River to a sprawling metropolis spreading over lands that were, until recently, Cypress swamp. Except for the crescent city along the river, the rest of New Orleans is mostly below sea level.

Following Hurricane Betsy in 1965, a 350-mile network of levees, floodwalls, and other structures was planned to protect the city. This system was to provide protection against a Standard Project Hurricane, that was thought at the time to have a return period of 200-300 years, although subsequent understanding suggests a smaller return period.

Systems Risk Assessment

The risk assessment was based on an event tree approach in which possible hurricane loadings and structural response were enumerated in a tree-like structure (Figure 1). The hurricane hazard was approximated using a “total probability” approach in which the range of storm parameters and their probability distribution was specified and a large number numerical calculations performed using the ADCIRC computer model (Westerink, et al., 1994). In all, about 1800 numerical runs were made, each associated with a recurrence probability, and the results aggregated into probability distributions.

The event tree calculations account for aleatory, or “random”, uncertainties associated with variation in time or space. To account for epistemic uncertainties due to limited knowledge, a logic tree was used to pre-assign a set of model, parameter, and other systematic uncertainties prior to generating and calculating the event tree. The two-phased analysis of a logic tree combined with an event tree allowed for aleatory and epistemic uncertainties to be combined in a consistent way. In the final results, frequency distributions are generated which describe aleatory uncertainty from the risk assessment, and distributions of uncertainty on those frequency curves are generated to describe epistemic uncertainty.

Geotechnical Reliability Analysis

From a geotechnical perspective, the principal interest lies in the reliability analysis of the levees and floodwalls. The reliability analysis yields conditional probabilities of the HPS performing as intended when subject to given loads. These conditional probabilities were represented in fragility curves summarizing the probability of failure, however defined, as a function of load (Figure 2). In the IPET studies, the load on the HPS was simplified as surge and wave heights on the levees, floodwalls, and closures constituting the system.

The predicted performance of the hurricane protection system was quantified using second-moment structural and geotechnical reliability models of the sort now common in practice. Characterization of the HPS components were based on design and construction information as published in the original U. S. Army Corps of Engineers (USACE) design memoranda for each project section, and on the results of the work of other IPET teams, specifically the Levee Performance Team which analyzed sections of the HPS that had breached or scoured during Katrina. Factors of safety and other indicators published in the original design memoranda were corrected for systematic biases identified by the Levee Performance Team. Systematic uncertainties include things such as model and parameter uncertainty, and statistical estimation uncertainty.

Each drainage basin perimeter was divided into reaches that were deemed to be internally homogeneous in three respects: structural cross section, elevations in the cross section, and geotechnical profile and properties. In all, about 230 such reaches were identified and separately modeled to obtain fragility curves. These fragility curves were adjusted for total length of reach using observed failure lengths during Katrina, and statistical analyses of the spatial variation of soil properties in the various drainage basins.

Geotechnical Uncertainties

Reliability models were developed and evaluated to determine dominant failure modes for each reach in a drainage basin. The reliability models included uncertainties in geotechnical engineering properties, geological soil profiles, and engineering performance models of levees, floodwalls, and transition points. Uncertainties due to spatial and temporal variation, and due to limited knowledge were tracked separately, to provide a best estimate of the aleatory frequency of failure under given loads, along with a measure of the epistemic uncertainty in that frequency.

Geometric and engineering material properties were identified for each reach and summarized in data tables. Structural cross-sections were identified by review of as-built drawings, aerial photographs, and GIS overlays, and subsequently confirmed by on-site reconnaissance of the entire HPS perimeter. Elevations were assessed in the same reconnaissance, supplemented by LIDAR (an acronym for LIght Detection And Ranging technology used to measure distance and other parameters) and field surveys provided to the Risk Team by other parts of the IPET. Surprisingly, freely-available web-based mapping resources from Google and Microsoft proved to be extremely valuable sources of current information in characterizing the existing geometry of levees and floodwalls.

Geotechnical cross-sections and corresponding soil engineering properties were derived from original USACE General Design Memoranda (GDM) for the respective project areas of each drainage basin, supplemented by site characterization data collected post-Katrina at levee and flood wall failure sites (cone penetrometer and laboratory measurements on undisturbed samples). These data are available at: https://ipet.wes.army.mil. Engineering performance models and calculations were adapted from the GDM’s.

Engineering parameter and model uncertainties were propagated through those calculations to obtain approximate fragility curves as a function of water height. These results were calibrated against the analyses of the Performance Team, which applied more sophisticated analysis techniques to similar structural and geotechnical profiles in the vicinity of failures. Failure modes identified by the Performance Team were incorporated into the reliability analyses as those results became available. Reliability assessments were performed for individual reaches of the HPS for given water elevations. This resulted in fragility curves for each reach by mode of failure.

Reliability assessments for each reach and component of the drainage basin perimeter were combined in the HPS risk model. The risk model used the water elevations from the hurricane hazard and the HPS fragilities to calculate probability of volume and duration of flooding within each drainage basin.

Once the fragility curves for each component failure mode were determined, they were input to the systems risk model. For each sequence in the event tree, a ‘sequence’ fragility curve was determined by evaluating the event tree logic at each successive water elevation level. Once each sequence of events was evaluated, the composite or total fragility for system failure was determined for each system performance state (e.g., no flooding in any area protected by the HPS, or flooding as a result of levee or floodwall failure, or flooding as a result of overtopping) by summing the fragility curves for the sequence of events for the same state. Reliability assessments were performed for individual reaches of approximately homogeneous type.

Conclusions

Geotechnical reliability assessments have become ever more common in recent years. While the IPET study is certainly among the most extensive of recent studies, in principle it builds on existing methodologies and understanding of geotechnical risks. The value of the systems risk assessment of the HPS for New Orleans is that it has allowed a formal way of identifying vulnerable sections of the system, and a way of relating risks to economic factors and reconstruction alternatives.

References

Westerink, J.J., C.A. Blain, R.A. Luettich, Jr. and N.W. Scheffner, 1994, ADCIRC: an advanced three-dimensional circulation model for shelves coasts and estuaries, report 2: users manual for ADCIRC-2DDI, Dredging Research Program Technical Report DRP-92-6, U.S. Army Engineers Waterways Experiment Station, Vicksburg, MS., 156p.

Robert C. Patev is Regional Technical Specialist - Navigation, North Atlantic Division, USACE and Geotechnical Engineer, New England District, Concord, MA. He can be reached at .

David M. Schaaf, P. E, is Regional Technical Specialist, Great Lakes and Ohio River Division, USACE, and Structural Engineer, Louisville District, Louisville, KY. He can be reached at .

Jerry L. Foster, P.E., is President, Foster Engineering Services, Annapolis, MD. He can be reached at .

Gregory B. Baecher, Ph. D., is Glenn L. Martin Institute Professor of Engineering, University of Maryland, College Park, MD. He can be reached at .

Figure 1. Structure of event tree used to model aleatory uncertainties in the combination of loads, response of the hurricane protection system, and consequences.

Figure 2. Schematic fragility curve showing the median estimate of frequency of failure for a levee or floodwall which represents aleatory uncertainty; the uncertainty bounds about the medial estimate represent epistemic uncertainty caused by lack of knowledge or information.