An analysis of flood levee reliability

Abstract

In most studies of flood levee reliability the probability of failure is taken to be equal to the probability that the flood peak discharge will exceed the capacity of the channel‐levee system. Such an analysis assumes that levees fail only by overtopping, whereas in many cases, levees fail at discharges much below the channel capacity. In the present paper the discharge at which levees fail is assumed to be a random variable with a particular distribution. The results on the flood frequency curve are presented for two conditions: one for the failure discharge having a uniform probability density function and the other for failure discharges having a quadratic distribution. In a similar manner the effects on the net benefits from levee construction were also analyzed and results are given.

Separating natural and epistemic uncertainty in flood frequency analysis

“…The descriptive distribution represents the variability of the process while the predictive distribution describes the probability that the random variable will be exceeded in a given time interval, taking into account that the parameters of the descriptive distribution are estimated from limited data. This approach allows the integration of natural variability and sampling uncertainty in a single risk estimation (Davis et al, 1976;Wood, 1977;Tang, 1980;Tung and Mays, 1981a;Booy and Lye, 1989). Other Bayesian approaches have incorporated the uncertainty due to the distribution function (Wood and Rodriguez-Iturbe, 1975;Bobo and Unny, 1976;Tang, 1980;Krzysztofowicz and Yakowitz, 1980;Tung and Mays, 1981a;Chbab et al, 2000).…”

“…(1) and (4) are combined by the total probability theorem given in (3). AFP is an expected exceedance probability for q C with the expectation taken over all feasible values of q (Wood, 1977;Kuczera, 1999). For normally distributed variables Booy and Lye (1989) have derived the mean and variance of the predictive distribution.…”

Levee Decisions and Sustainability for the Sacramento-San Joaquin Delta

“…Assessing the probability of structural failure for a levee or dike is a complicated geotechnical endeavor, depending on several other stochastic variables such as storm events, underlying soils, river discharge, and location of an initial breach (Wood 1977;Moss and Eller 2007). Many studies focus almost exclusively on determining the appropriate probability distribution for flood events or a structural failure (Ang and Tang 1975;Van Manen and Brinkhuis 2005).…”

“…Delta levees can fail in several ways (Linsley and others 1964;Wood 1977;Mount and Twiss 2005;Moss and Eller 2007). Most commonly, levees fail from slumping, rupturing, erosion or overtopping during storm events, or when high winds create large waves at high tides.…”

Flood Defense Systems Design by Risk-Based Approaches

“…For examples, both hydrologic and hydraulic uncertainties were considered in the design of highway drainage structures (Mays, 1979;Tung and Mays, 1982;Tung and Bao, 1990), storm sewer systems (Yen and Ang, 1971;Yen and Jun, 1984;Tang et al, 1975), levee systems (Tung and Mays, 1981b), storm surge barrier (Voortman et al, 2003), and river diversion (Afshar et al, 1994). Inherent hydrologic uncertainty, along with parameter and model uncertainties were considered in the design of levee systems (Bodo and Unny, 1976;Wood et al, 1977).…”