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obtained by simply averaging a large amount of strong earthquake acceleration response spectra and
making smooth. The coefficient of variation of the normalized mean response spectrum changes with
period. But for general site and the range of period of multistory dwelling brick buildings, according to
Ref. [8], it can be taken as PR = 0.26. The duration of strong motion is taken as the 1/2 peak
acceleration duration i. By calculating 24 strong earthquake records longer than 2.75s from Ref. [8],
we obtain that its mean value is 8.25s, and its coefficient of variation (3 T = 0.678. The standard response
spectrum in the code is the one with the damping ratio of 0.05. When the structural damping ratio isn't
0.05, the response spectrum is revised by the damping revising coefficient formula (12) specified in
Chinese "Design code for antiseismic of special structures" (GB50191-93).
In this paper, we don't consider the parametric uncertainties of laminated rubber bearings.
5 THE EARTHQUAKE LOAD-STRUCTURE SYSTEM
The Latin Hypercube Sampling technique is utilized to establish the earthquake load -structure system
used in nonlinear time history analysis. In the analysis, four parameters describing the structural model
and four parameters describing the earthquake model are considered. The uncertainties for each
parameter are expressed in terms of three representative values, i.e., mean, mean minus and plus one
standard deviation. So, for the ensemble of structural model, from the combinations of three
representative values of the four parameters, a total of 81 structural models can be established. For the
ensemble of earthquake time histories, from the combinations of three representative values of
response spectrum and damping ratio, nine response spectra are obtained. For each response spectrum,
three stationary time histories are generated. Thus, 27 stationary time histories are produced. It is noted
that 27 different sets of random phase angles are used to generate these time histories. And then three
envelope functions represented by strong motion duration are applied to each stationary time history to
generate three normalized nonstationary time histories. Three strong motion durations are taken as its
mean, mean minus and plus 0.8 times standard deviation [2]. Thus, a total of 81 normalized earthquake
acceleration time histories are generated. Finally, using the Latin Hypercube Sampling technique, these
earthquake time histories are matched to the structural models so that 81 samples of the earthquake
load-structure system are constructed for seismic response analysis.
6 STRUCTURAL VULNERABILITY ANALYSIS
6.1 Limit States and Structural Capacity
In this study, the limit state of structure is defined in terms of structural ductility factor, and five limit
states representing initial crack damage, slight damage, moderate damage, severe damage and collapse
of structure are considered. For each limit state, a corresponding capacity in terms of the ductility
factor can be established. The ductility factor of the brick wall is defined as the ratio of the maximum
TABLE 3
DUCTILITY FACTOR CAPACITY
Limit states
Initial crack damage
Severe damage
Collapse
Brick wall without
constructional column
PR °R
1.0 0.3
1.6 0.3
2.6 0.3
Brick wall with
constructional column
PR °R
1.0 0.3
2.6 0.3
4.8 0.3