Extending Normalized Gaussian Adaptive Hyperspherical Integration for Fast Computation of Accurate Unsatisfactory Performance Probability for Hydraulic Retaining Structures

Abstract

The probability of unsatisfactory performance (PUP) is taken into consideration during the design of the US Army Corps of Engineers hydraulic structures retaining earth. These structures possess multiple limit states. A reliability analysis of a structure is used to determine the PUP, given the variability in loads and resistances. An adaptive polar numerical integration procedure is being proposed that uses specified numerical precision and Gaussian normal distribution properties to optimize reliability calculations for PUP, providing good spatial coverage. This method uses the properties of the normalized Gaussian variable hyperspace to adjust the number of integration steps taken at each hyperspherical shell based on the overall probability of the hyperspherical shell and the desired PUP precision. Results from an example earth retaining structure problem show the normalized Gaussian adaptive hyperspherical integration method provides more accurate PUP values compared to a simulation method.