Spatial correlation of ground motions in estimating seismic hazards to civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 69

For a given ground-motion amplitude generated for a cell, a single value
of expected direct loss EDL i,j was estimated for every building. The loss
values, which had been estimated for all buildings within a particular cell,
were summarised to obtain a cell-specifi c loss. Then, a single total loss
amount for a given generation of the ground-motion distribution was
obtained as the sum of losses from all cells. The generated set of total loss
values (10 000 generations) is used for the estimation of the Probability
Density Function (PDF) and Cumulative Probability Function (CPF) and
the analysis of the parameters of loss distribution. The structure-to-structure
correlation of damage (e.g. Lee and Kiremidjian, 2007) and the uncertainty
of replacement costs (e.g. Porter et al. , 2002) were not considered.
Figure 3.3 shows results of loss estimation and Table 3.2 presents charac-
teristics of loss distribution. Note that the value of total loss, which was
estimated using the mean PGAs without consideration of uncertainty, is
about US $80 Mln. As can be seen, only mean values of loss do not depend
on the correlation models but, of course, they are sensitive to standard
deviation of ground motion.
For every particular earthquake scenario, the between-earthquake vari-
ability changes the level of ground motion at all location in similar way,
i.e. the level will be lower or higher than the median estimates from a
predictive equation. The larger level of ground motion at all locations will
cause greater damage everywhere and higher total loss values and vice
versa. Thus, if all of the ground motion variability is treated as between-
earthquake ( ρ η = 1.0), this would lead to high variability of total loss. The

Table 3.2 Parameters of loss probability distribution (Mln US $) evaluated for
two extreme cases of ground-motion correlation (see text) and two values of
standard deviation σ of ground-motion variation

Ground-motion variability

All the variability is
between earthquakes

All the variability is
within earthquakes

Parameter of loss
distribution σ 0.3 σ 0.5 σ 0.3 σ 0.5

Mean 115 290 115 290

Median 70 70 150 290

Standard deviation 140 360 9.2 35

Coeffi cient of variation 1.22 1.24 0.08 0.12

P E = 0.1 270 580 135 330

P E = 0.05 390 970 140 345

P E = 0.01 670 1850 145 370

P E = probability of exceedence.