T.T. Bui and G. De Roeck
Department of Civil Engineering, KU Leuven, Belgium
Keywords: vulnerability assessment, fragility curve, ambient vibration, stochastic subspace identification.
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Vulnerability assessment of existing buildings in a seismic region requires a structural model and response spectrum at the building's site for estimating building damage arising from ground shaking. The output damage function includes fragility curves that describe the probability of reaching or exceeding different damage states for the given level of ground shaking. This probability is often modelled using a cumulative lognormal distribution.
The method described in this paper is based on experimental data, which can be identified from an ambient vibration test using the versatile covariance based stochastic subspace system identification algorithm (SSI-cov). By using SSI-cov, not only the modal parameters can be identified but also their statistical variance can be estimated. The structural response under ground shaking can be calculated by a mode superposition method using the first of several identified vibrational modes. Each mode is characterised by a frequency, a damping ratio and a mode shape. This calculation is known as the Duhamel integral in the time domain. From the response an important criteria of interstorey drift is computed and the result is compared with the threshold for the slight damage state. Based on that the probability of reaching or exceeding the slight damage state at a given interval of shaking can be fitted and the uncertainty arising from the ground shaking can be estimated. It is noted that the identified fundamental frequency is also employed in calculating the spectral displacement value, which was often assumed without field testing.
The total lognormal standard deviation is computed using a combination of different contributors. These include the variability in ground motion, the variability in structural model and the variability in damage threshold. Only the variability in damage threshold has to be assumed as the structural model uncertainty bound can be estimated directly from the experimental data.
The method is demonstrated using a frame building. Four modes are identified with their own variances. The fragility curve is delivered based on past strong motion data. Since the theory of superposition is only valid for linear vibration, this method is only applicable up to a slight damage state in a low-to-moderate seismic region.
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