The Earthquake Engineering Online Archive

Stochastic analysis of offshore tower structures

Malhotra, Anil Kumar; Penzien, Joseph

UCB/EERC-69/06, Earthquake Engineering Research Center, University of California, Berkeley, 1969-05, 172 pages (541/M22/1969)

A general theory is developed for evaluating the response of offshore structures in deep water subjected to random wave forces or earthquakes. The analytical approach to this stochastic, fluid elasticity problem takes into account the nonlinearities arising from hydrodynamic drag forces and wave-structure interaction. In deep waters, flow characteristics are described by the linear wave theory and may be assumed to be zero-mean, Gaussian processes. The hydrodynamic forces on the structure are computed through the Morrison, O'Brien formula. The nonlinearities in the system due to wave-structure interaction and the drag forces are eliminated by a modified equivalent linearization technique, the essence of which is to alter the damping and drag coefficients in an optimal manner by minimizing the average mean square error. The consequent cyclic solution process is convergent, the rapidity of convergence depending upon the strength of the nonlinearities. The response of the linearized system to any arbitrary spectra of wave heights can be obtained through both the time and frequency domains. The response statistics, which have a Gaussian distribution, are used to estimate the probability distribution of the extreme peak values of displacement, stress, and/or any other response quantity of interest. In an extension of the theory, it is shown that a modified form of the system equations enables the determination of similar statistics for the response of tower structures in deep waters when excited by earthquake motions. A 1340 ft offshore tower in 1315 ft of water is analyzed for the wave-height spectra specified by Pierson and Moskowitz. The relevant peak value statistics are obtained. The importance of not neglecting the influence of wave-structure interaction and the nonlinear drag forces on response, especially at high wind velocities, is discussed. Studies of varying leg-spacings of the three-legged tower indicate that significant reductions in response may be achieved by proper spacings.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-69-06.pdf (32 MB)