Response Spectrum–Based Stochastic Method for Earthquake Analysis of Gravity Dams: Fid-Bau Portal

Response Spectrum–Based Stochastic Method for Earthquake Analysis of Gravity Dams

Gupta, Ishwer D. / Joshi, Sharad G.

Time-history response analysis is necessary to account accurately for the dam–foundation rock and the dam–reservoir water interaction effects in the earthquake response of gravity dams. This paper presents a response spectrum–based stochastic method for obtaining statistical estimates of various response quantities of gravity dams, in which foundation rock and reservoir interactions are modeled realistically using a substructure approach. The novel feature of the proposed method is that it can predict the amplitudes of several highest peaks of the response, which is useful in ensuring the safety requirements in an optimal way. The random vibration theory for computing the peak factors of ordered peaks in a stationary stochastic process, wherein the statistical parameters are defined in terms of the first few moments of the power spectral density function (PSDF) of the process, is used for this purpose. To apply this theory to gravity dams, expressions have been developed for the PSDFs of various response quantities in terms of the modal properties of the dam and the response spectrum–compatible PSDFs of input ground acceleration. The stochastic method has been validated by comparing the statistical estimates of the peak amplitudes of displacements and stresses in a typical dam section with the time-history solutions for several real accelerograms with widely differing characteristics.