Probabilistic assessment of earthquake insurance rates for buildings - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 786

Table 29.1 Damage probability matrix

Intensity

Damage
state (DS)

Central damage
ratio (CDR) % V VI VII VIII IX

None 0 Damage state probabilities P(DS, I)

Light 5

Moderate 30

Heavy 70

Collapse 100

Source: Adapted from Yucemen (2005).

A DPM describes what will happen to buildings, designed according to
some particular set of requirements, during earthquakes of various intensi-
ties (Whitman, 1973; ATC, 1985). An element of this matrix P k (DS, I ) gives
the probability that a particular damage state (DS) occurs when the struc-
ture of k -type is subjected to an earthquake of intensity, I . The identifi cation
of damage states is achieved in two steps (Yucemen, 2005).

1. The qualitative description of the degree of structural and non-struc-
tural damage by words. Generally, fi ve levels of damage states are
specifi ed (Deniz and Yucemen, 2009): no damage (N), light damage (L),
moderate damage (M), heavy damage (H), and collapse (C) states. This
categorization of damage states is also used in this study.
2. The quantifi cation of the damage described by words in terms of the
damage ratio (DR), which is defi ned as the ratio of the repair cost due
to earthquake damage to the replacement cost of the building (exclud-
ing the value of the land on which the building is constructed).

Specifying a range of DRs instead of a single DR value for each DS
makes more sense from an engineering perspective to capture a range
of uncertainties associated with the assignment of DRs. However, for
computational convenience, a single DR (usually the average of the cor-
responding range), called the central damage ratio (CDR), is assigned to
each DS to represent the best estimate DR of buildings in that DS (Blong,
2003b; Gurpinar and Yucemen, 1980). Based on interviews with experts
who are in charge of damage evaluation and based on similar studies, the
damage ratios corresponding to the fi ve damage states were estimated by
Gurpinar et al. (1978). Based on these values the CDRs are computed and
shown in Table 29.1. In the present study, only DPMs for conventional
reinforced concrete frame buildings are considered, and the corresponding
matrices are constructed from observational and estimated data available
in Turkey.