Assessing seismic risks for new and existing buildings using performance-based earthquake engineering (PBEE) methodology - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 309

Table 12.2 Sample EDP matrix, X

GM number EDP 1 EDP 2 ··· EDP N

GM 1 0.66 1.07 ··· 0.75

GM 2 0.68 0.95 ··· 0.27

GM M 0.76 1.10 ··· 0.52

Evaluate the response of the building

With the selected ground motions, a series of dynamic analyses, including
nonlinear dynamic analysis if necessary, can be used to determine the earth-
quake response of the building. Depending on the EDP associated with
each performance group (defi ned in Step 1), peak values of the EDPs
obtained from dynamic analyses are summarized in an EDP matrix, X , as
shown in Table 12.2. The columns of X represent different EDPs of interest
(for example inter-story drift or fl oor acceleration) and the rows of X rep-
resent the peak EDPs recorded from the dynamic analysis of a single
ground motion. One EDP matrix will be defi ned for each intensity measure
considered.

Generate additional correlated EDP vectors

Computing additional EDP vector realizations using dynamic analysis is
hampered by the paucity of actual strong ground motions and the compu-
tational cost. Therefore, to circumvent running additional nonlinear dynamic
analyses, a joint lognormal distribution is fi tted to the EDP matrix. Cor-
related EDP vectors can then be generated using a computationally inex-
pensive procedure presented in Section 12.3.4.

Compute the total repair cost

With the generated correlated EDP vectors, the total repair quantities for
all repair items in the building due to each earthquake scenario can be
calculated. Depending on the values of the EDP associated with the per-
formance group, a random number generator with a uniform distribution
is used to select the damage state for the damaged model defi ned in Step
1. Once the damaged states have been identifi ed, the repair quantities for
each item in the performance group are obtained from the repair quantity
table, such as the one shown in Table 12.1. This process is repeated for all
performance groups and the total repair quantities for each item are
summed from the quantities obtained from each performance group.