Civil Engineering Reference
In-Depth Information
Using the available post-earthquake damage data, each element of a
DPM can be obtained from
(
)
NI
NI
DS
,
(
)
=
k
PI
DS
,
[29.1]
k
()
k
as the probability that damage state DS is observed in
k
-type buildings
when exposed to an earthquake of intensity
I
. In this equation
N
k
(DS,
I
)
stands for the number of
k
-type buildings in damage state DS, whereas
N
k
(
I
) stands for the total number of k-type buildings under earthquake
intensity
I
. The sum of the probabilities in each column of a DPM equals
1.0. The information contained in the damage probability matrix and in the
damage ratios can be combined as the mean damage ratio, MDR
k
(
I
), which
is expressed as follows:
∑
()
=
(
)
×
MDR
I
P
DS
,
I
CDR
DS
[29.2]
k
k
DS
where CDR
DS
=
central damage ratio corresponding to the damage state,
DS.
29.2.3 Pure risk premium
The expected annual damage ratio (EADR
k
) is used as a measure of the
magnitude of earthquake damage to a
k
-type of structure built in a certain
seismic zone and is defi ned as:
∑
()
×
EADR
=
MDR
I
SH
[29.3]
k
k
I
I
where MDR
k
(
I
)
average damage ratio for the
k
-type of structures sub-
jected to an earthquake of intensity
I
, and SH
I
=
annual probability of an
earthquake of intensity
I
occurring at the site. EADR
k
is a unitless quantity
and can be interpreted as the pure insurance premium for a unit property
replacement cost.
After calculating EADR
k
, the pure risk premium (PRP
k
) for the portfolio
of contracts is computed based on the insured value of the building (INSV)
under consideration from the following relationship:
=
PRP
=
EADR
×
INSV
[29.4]
k
k
29.2.4 Commercially priced earthquake
insurance premium
The commercially priced earthquake insurance premium (CPP
k
) that will
be charged by an insurance company for the
k
-type of structure is found
by increasing the PRP
k
by some margin as follows:
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