A Compact Probabilistic Representation of the Chi-Chi Earthquake Ground Motion - Reinforced Soil Engineering: Advances in Research and Practice - page 475

Figure 6 The estimated response covariance matrix for an SDOF system with natural
frequency of 1 Hz and 5% critical damping.
the system. A comparison of the analytically estimated result from this procedure
is shown in Fig. 7 , versus the “exact” mean-square response computed by taking
the statistics of the numerically integrated convolution integral for each input
record. The “exact” result is therefore obtained effectively by Monte Carlo
simulation, where each record is a sample realization of the input process. The
accuracy of the method is clearly quite good, despite the acknowledged level of
error introduced in the condensation procedure. This type of result can be used to
obtain peak response statistics to quickly assess the impact of the event on certain
categories of structures. For this same structural system, the peak mean-square
response due to the 1994 Northridge earthquake ensemble was about 6.5 cm 2 ,
versus about 37 cm 2 observed here.
5 CONCLUSIONS
A powerful analytical tool, utilizing orthogonal decomposition approaches for
extracting the dominant features of a large ensemble of earthquake ground motion
records, is applied to a subset of the records obtained from the 1999 Chi-Chi
earthquake. The input covariance matrix eigenvalues and eigenvectors are