Keywords: earthquake, random vibration, multiple excitation, long-span bridge.

Long span structures are usually important public facilities and so their safety during earthquakes has received much attention [1,2,3,4]. The seismic analysis of long-span bridges subjected to multiple ground excitations has long been a problem of great concern. However, it is rather difficult to compute because some special factors must be taken into account during their design, which include [1] the wave-passage effect caused by the different times at which seismic waves arrive at different supports; the incoherence effect due to loss of coherency of the motion caused by either reflections and refractions of the waves in the inhomogeneous ground medium or the difference in the manner of superposition of waves from an extended source arriving at various supports and; the local effect because of the differences in soil conditions at different supports and the manner in which these influence the amplitude and frequency content of the bedrock motion. The conventional response spectrum method neglects the spatial effects of ground motion, and so may result in questionable conclusions. In current practice, dynamic analysis for such spatially varying input motions is performed mainly by the time history method, of which the chief disadvantage is that the results rely heavily on the selected time history records. In the meanwhile, the analysis requires extensive computational effort, which makes it difficult to select a sufficient number of records. The conventional response spectrum method is based on a single excitation. Although some recently published extensions deal with the seismic analysis of long-span structures, the accuracy and efficiency of such extensions still require further improvements prior to their use in practical applications. The random vibration approach has been regarded as a better means, and has been adopted by European Committee for Standardization [5]. Unfortunately, so far some computational difficulties have not yet been satisfactorily solved [1,2,3,4].

This problem has been satisfactorily overcome by the Pseudo Excitation Method (PEM) described in this paper, which is accurate because the correlation terms between all participating modes and between all excitations have both been included [6,7]. It is also very easy to use because the stationary random vibration analysis is transformed into harmonic vibration analyses, while the non-stationary random vibration analysis is transformed into deterministic transient dynamic analyses. The most important advantage of the PEM is its extremely high efficiency. For an average 3D FEM based bridge model, the computing time for stationary seismic analysis is about a few minutes when using a Pentium 4 personal computer; and about an hour for the corresponding non-stationary seismic analysis. A case-study for a real cable-stayed bridge is given in this paper. The numerical computations show the good applicability of the PEM in dealing with the seismic spatial effects. In fact, this method has been widely used in China.

1

A.D. Kiureghian, A. Neuenhofer, "Response Spectrum Method for Multi-support Seismic Excitations", Earthquake Engineering and Structural Dynamics, 21(8), 713-740, 1992. doi:10.1002/eqe.4290210805

2

H.Z. Ernesto, E.H. Vanmarcke, "Seismic Random Vibration Analysis of Multi-support Structural Systems", Journal of Engineering Mechanics, ASCE, 120(5), 1107-1128, 1994. doi:10.1061/(ASCE)0733-9399(1994)120:5(1107)

3

M. Lee, J. Penzien, "Stochastic Analysis of Structures and Piping Systems Subjected to Stationary Multiple Support Excitations", Earthquake Engineering and Structure Dynamics, 11(1), 91-110, 1983. doi:10.1002/eqe.4290110108

4

M. Berrah, E. Kausel, "Response Spectrum Analysis of Structures Subjected to Spatially Varying Motions", Earthquake Engineering and Structure Dynamics, 21(6), 461-470, 1992. doi:10.1002/eqe.4290210601

5

European Committee for Standardization, "Eurocode 8, Structures in Seismic Regions - Design Part 2: Bridge", Brussels: European Committee for Standardization, 1995.

6

J.H. Lin, "A Fast CQC Algorithm of PSD Matrices for Random Seismic Responses", Computers and structures, 4(3), 683-687, 1992.

7

J.H Lin, W.S Zhang, J.J. Li, "Structural responses to arbitrarily coherent stationary random excitations", Computers and Structures, 50(5), 629-633, 1994. doi:10.1016/0045-7949(94)90422-7

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