Keywords: uncertainty modelling, ground motion, stochastic seismic analysis, Kanai-Tajimi filter.

The complicated nature of the earthquake source mechanism, the highly irregular structure of the earth's mantle and crust and the difficulty of making significant measurements make it difficult to elucidate the real influences on the ground motion. Common design rules do not explicitly include the influence of the uncertainties associated with these fundamental features. For example for the Kanai-Tajimi-like filter, the choice of soil natural frequency, damping coefficient and the intensity of the ideal white noise excitation at the bedrock-overburden interface, is not straightforward. These parameters undergo fluctuations and should be modelled as random variables.

The purpose of this study is to investigate and propose methods to incorporate uncertainty into the analytical model of seismic input. Specific objectives are: to propose variation range of uncertain filter parameters to model earthquake ground motion and to study the influence of these uncertainties on structural response. This study considers as uncertain parameters, for each earthquake, the soil overburden effective natural frequency and damping coefficient.

The paper formulates the earthquake response maximum peak following a procedure based on the use of stochastic dynamics and representation of seismic ground motion as a filtered white noise [1,2].

Ground motion records of earthquakes in Southern-Italy are used to develop a procedure that quantifies uncertainties inherent to the ground motion [3,4]. In the proposed model, uncertainty is considered for filter parameters and quantified observing their probability density function. The ground motion accelerogram of each event, the comparison of the recording and the Kanai-Tajimi filter spectral moments provides filter parameters [5,6,7,8].

The proposed ground motion model is used to define uncertain seismic input for use in dynamic analyses of an example frame. The structure is considered as a deterministic system and the relationship between the structural response and the random filter parameters, i.e. the second order moments, are evaluated. The ground motion acceleration maximum peak used in the example is that proposed by current design codes. A structural design considering an uncertain dynamic load, allows an estimate of the real random nature of the earthquake ground motion, because of the uncertain soil characterisation, the statistically limited number of seismic records and the different local geological conditions related to each accelerogram. The resulting structural response maximum peak is compared to that obtained from the time dependent response [9,10,11,12,13].

1

N. Impollonia, G. Ricciardi, "Analysis of uncertain structural systems under white noise excitation by a response surface method", Proceedings of the ninth ICASP conference, San Francisco, California, USA, 2003.

2

G. Falsone, G. Muscolino, G. Ricciardi, "Combined dynamic response of primary and multiply connected cascaded secondary subsystems". Earthquake Engineering Structural Dynamics, 20, 749-767, 1991. doi:10.1002/eqe.4290200804

3

"European Strong-Motion Database", European Council, Environment and Climate Research Programme, 2000

4

N. Impollonia, G. Ricciardi, "Explicit solutions in the stochastic dynamics of uncertain structural systems", Probabilistic Engineering Mechanics, 21, 171-181, 2006. doi:10.1016/j.probengmech.2005.09.002

5

E.H. Vanmarcke, S.S.P. Lai, "Strong-motion duration and rms amplitude of earthquake records", Bulletin of Seismological Society of America, 70(4), 1293-1307, 1980.

6

S.S.P. Lai, "Statistical characterization of strong ground motions using power spectral density function", Bulletin of Seismological Society of America, 72(1), 259-274, 1982.

7

D.E. Newland, "An introduction to random vibrations, spectral and wavelet analysis", Longman Scientific & Technical, 1993.

8

H. Buchholdt, "Structural dynamics for engineering", Thomas Teldford, London, 1997.

9

A.G. Davenport, "Note on the distribution of the largest value of a random function with application to gust loading", Proc. Institution of Civil Engineering, 28, 187-196, 1964. doi:10.1680/iicep.1964.10112

10

S.O. Rice, "Mathematical Analysis of Random Noise", Bell System Technical Journal, 23, 282-332, 1944.

11

S.O. Rice, "Mathematical Analysis of Random Noise", Bell System Technical Journal, 24, 46-156, 1945.

12

C. Bucher, "Structural reliability and stochastic finite elements", NAFEMS Seminar "Use of stochastic in FEM analyses", 7-8 May 2003.

13

A. Der Kiureghian, P.L. Liu, "Multivariate distribution models with prescribed marginals and covariances", Probabilistic Engineering Mechanics, 1(2), 105-112, 1986. doi:10.1016/0266-8920(86)90033-0

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