Seismic risk management of insurance losses using extreme value theory and copula - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 766

of the mean yield and collapse maximum inter-story drift ratios are consid-
ered to capture their epistemic uncertainty (see Table 28.1). The mean
values are consistent with FEMA/NIBS (2003). The coeffi cients of variation
for D Y and D C are set to 0.15 and 0.3, respectively.
For loss estimation, d is transformed to seismic loss quantities through
damage-loss functions. For convenience, damage costs are categorised into
three types: repair/replacement costs related to damaged building parts
L RR (d) (RR type), costs for lost contents L CO (d) (CO type), and costs
related to business interruption L BI (d) (BI type). They are approximated
by power functions:

() = () = () =

L δ C δ

β

, L δ C δ

β

, and L δ C δ

β

, [28.13]

RR CO BI

RR RR CO CO BI BI

where C RR , C CO , and C BI are the replacement costs, and

BI are
the exponent parameters for damage cost types RR, CO, and BI, respec-
tively. To develop damage-loss functions that are applicable to wood-frame
houses in Vancouver, the use type defi ned by the City of Richmond is
related to the HAZUS-Earthquake occupancy type (FEMA/NIBS, 2003;
Ventura et al. , 2005), and the exponent parameters of the damage-loss func-
tions are determined by least squares curve fi tting. The parameters for four
prevalent occupancy types in Vancouver are summarised in Table 28.2. The
unit replacement costs are considered to be lognormally distributed with

β

RR ,

β

CO , and

β

Table 28.1 Mean yield and collapse maximum inter-story drift capacity ratios

UBC-SAWS
model

Yield capacity D Y : drift
ratio (weight)

Collapse capacity D C : drift ratio
(weight)

House 1 [0.004(0.25), 0.006(0.5),

0.008(0.25)]

[0.075(0.25), 0.1(0.5), 0.125(0.25)]

House 2 [0.004(0.5), 0.006(0.5)] [0.05(0.25), 0.075(0.5), 0.1(0.25)]

House 3 [0.004(0.5), 0.006(0.5)] [0.05(0.25), 0.075(0.5), 0.1(0.25)]

House 4 [0.002(0.5), 0.004(0.5)] [0.05(0.5), 0.075(0.5)]

Table 28.2 Model parameters of damage-loss functions for different occupancy
types

Replacement cost
(CAD/ft 2 ): [ C RR , C CO , C BI ]

Exponent parameter:
[ Occupancy β RR , β CO , β BI ]

Single-family dwelling [87.2, 21.8, 19.8] [0.754, 0.681, 0.568]

Multi-family dwelling [111.0, 27.8, 26.2] [0.810, 0.681, 0.617]

Store/commercial service [47.6, 26.4, 23.8] [0.808, 0.681, 0.426]

Restaurant [149.4, 74.7, 228.1] [0.851, 0.681, 0.541]