Session: 07-13-01 Optimization, Uncertainty and Probability I

Paper Number: 73231

Start Time: Tuesday, 03:50 PM

73231 - Bounds of Reliability Function for Structural Systems Subjected to Imprecise Seismic Actions 

The analysis of ground motion acceleration plays a key role in earthquake engineering. It is well known that earthquake ground motions must be modelled as non-stationary processes in both time and frequency domains. Temporal non-stationarity refers to the variation of the intensity of the ground motion in time, whereas the spectral non-stationarity refers to the time variation of the frequency content [1]. However, accelerograms recorded on rigid soil present an almost linear variation of the cumulative number of zero level up-crossings in the strong-motion time duration, so that they can be reasonably modelled as zero-mean Gaussian stationary processes in this most dangerous time region. It follows that for structures built on rigid soil, the seismic excitation process can be characterized by an intensity parameter, strictly related to the energy of the seismic action, and by a power spectral density (PSD) function, which defines the frequency content of the action. It has also been recognized that the frequency content can be estimated once the number of zero level up-crossings and the number of peaks of an accelerogram are evaluated [1-3]. Since different accelerograms recorded by the same seismic station possess different frequency content, it is not possible to define an assigned PSD for a selected seismic site. 

In this paper, first a set of accelerograms, recorded on rigid soil, is analysed with the purpose of estimating a suitable PSD function for this kind of soil. Through the analysis of selected accelerograms it is shown that the three main parameters of the PSD function, namely the frequency of peaks, the frequency of zero level up-crossings and the variance of the stationary seismic process, can be reasonably described as interval variables [4]. Thus, the recorded accelerograms may be viewed as samples of a zero-mean stationary Gaussian random process whose PSD function is an interval function [4].

The main purpose of the present study is to perform reliability analysis of linear structures subjected to ground motion acceleration modelled as a zero-mean stationary Gaussian random process characterized by the previously defined imprecise PSD function. The reliability function for the extreme value response process is evaluated in the framework of the first-passage theory using the Vanmarcke model [5]. Since the PSD function of seismic excitation is an interval function, structural safety assessment involves the evaluation of the lower bound (LB) and upper bound (UB) of the reliability function which in turn has an interval nature. The LB (or right bound) and UB (or left bound) of the interval reliability function define a probability-box (p-box) [6] representative of the range of structural performance under prescribed variations of the uncertain parameters within their respective intervals. In the present paper, an efficient procedure for estimating such bounds is developed by taking advantage of the dependency of the imprecise PSD function of the input on three interval parameters only.

The accuracy of the proposed procedure as well as the influence of the imprecision of the seismic excitation on structural performance are illustrated through a numerical example.

References

[1] Saragoni G.R., and Hart G.C., 1973, Simulation of earthquake ground motions, Earthq Eng Struct Dynam; 2: 249–267.

[2]Conte J.P., and Peng B-F, 1997, Fully nonstationary analytical earthquake ground-motion model, J Eng Mech (ASCE), 123: 15–24.

[3]Muscolino G., Genovese F., Biondi G., and Cascone E., 2021, Generation of Fully Non-Stationary Random Processes Consistent with Target Seismic Accelerograms, Soil Dynam Earthq Eng 141: 106467.

[4]Moore, R.E., Kearfott, R.B., and Cloud, M.J., 2009, Introduction to Interval Analysis, SIAM, Philadelphia.

[5]Vanmarke E.H., 1975, On the distribution of the first-passage time for normal stationary random processes, J Appl Mech (ASME), 42, 215-220.

[6]Ferson S., Kreinovich V., Ginzburg L., Myers D.S., Sentz K., 2003, Constructing probability boxes and Dempster-Shafer structures, Sandia National Laboratories SAND2002–4015

Presenting Author: Federica Genovese University of Messina

Authors:

Federica Genovese University of Messina
Giuseppe Muscolino University of Messina
Alba Sofi University “Mediterranea” of Reggio Calabria