Probabilistic assessment of earthquake damage and loss for the City of Tabriz, Iran

2.1. Building inventory

Up to 2006, Iran’s population and housing census has been conducted every ten years [2]. The latest information is developed until 2011.

According to the HAZUS-MH classification of structures [5], there are 17 types of building in Tabriz, the characteristics of which are consistent with HAZUS-MH Structures. These structures are shown in Table 2. Structures are classified in three categories: steel, concrete, and masonry. Fig. 2 depict the area corresponding to each type of buildings. Since occupancy classes are reported in formal census in term of building area; In the present work, 6 major occupancy classes: residential, education, commercial (retail trade, personal and repair services), hospital and medical office, and government are considered. Since there is no information suggesting buildings age in previous censuses, all steel and concrete structures are assumed moderate-code buildings, while masonry structures are in low-code design level.

2.2. Demographic information and casualty model

Fig. 3 illustrates the distribution of population among different zones in 2011 [2]. We have used different occupancy classes to calculate MDR and economic losses. The population should be distributed using different zones and occupancy types. Due to the lack of sufficient formal data describing this distribution, probable earthquake casualties are calculated just in 2:00 a.m. One should keep in mind that the latter assumption means that the residential occupancy plays a significant role in the development of casualty model. The HAZUS methodology has been manipulated to estimate the probable earthquake casualties.

The applied methodology for calculating the number of human casualties, basically, follows the HAZUS approach but is somewhat simplified using the formulas given by Coburn and Spenceequation [4]:

where, is the number of casualties due to structural damage, is the number of casualties due to non-structural damage and is the number of casualties due to follow-on hazards such as landslides, fires, etc.

Equation can also be modified such that the level of injury (severity) is considered:

where $i$ represents the level of severity, ranging from light injuries, moderate injuries, heavy injuries to death.

A more detailed description of the severity levels is given in Table 1.

In order to consider several cases of occupancy which strongly depend on time of day (i.e., school occupied only during daytime), three different times are considered for prediction of the casualty numbers:

1) Nighttime scenario (called 02:00 am): i.e. earthquake striking during night time.

2) Daytime scenario (called 10:00 am): i.e. earthquake striking during day time.

3) Commuting time scenario (called 05:00 pm): i.e. earthquake striking during the commuting time.

Fig. 2Built area of steel, concrete, and masonry structures in Tabriz’s regions in 2011 (square meters) [2, 3]

Fig. 3Population of Tabriz’s regions in 2011 [2]

2.3. Development of economic loss model

In recent years, many public and government buildings have been retrofitted in Iran. Therefore, the costs of rebuilding of structures in earthquake-stricken areas have been estimated. These costs vary according to the type and height of structures. Table 3 presents a summary of mentioned costs. Retrofitting and rehabilitation of buildings after earthquake differs based on damaged level. In practice, costs of retrofitting equal 10, 20, 40, and 60 percent of those of rebuilding procedure for slight, moderate, extensive, and complete damage levels, respectively.

Economic loss for building renovation (and for reconstruction, in the case of complete damage) is computed based on the following equation [4]:

where $N_{OT}$ is the number of occupation types, $N_{BT}$ presents the number of building types and $N_{DS}$ is the number of damage states. In this equation, $C_r$, is regional cost multiplier (currently is set to 1.0, but can have different values for each geographical region in order to take into account the geographic cost variations); $A_{i,j}$ is the area of building type $j$ with type $i$ occupancy (in m²); $P_{j,k}$ is the damage probability of a structural damage type $k$ (slight, moderate, extensive or complete) in the building type $j$ and $C_{i,j,k}$ is the cost of renovation or reconstruction (per m²) for structural damage $k$ in building type $j$ with $i$ occupancy.

3.1. Damage and loss assessment method and applied software

In general, two approaches are available to estimate the earthquake damage suffered by a certain building. Traditional approach uses empirical parameters, such as macro seismic intensity or peak ground acceleration, to represent ground motion, whereas the more recent analytical method employs the entire response spectra, preferably, in the spectral acceleration-spectral displacement domain [8]. The capacity spectrum method has been applied to compute iteratively the inelastic spectral lateral displacement demand $S_d$, which is a measure of damage extent. In order to estimate the possible damage to the building stock of Tabriz, the analytical risk and loss assessment tool SELENA has been applied [4]. In SELENA, three user-selectable methods are incorporated to compute the damage: the traditional capacity spectrum method proposed in ATC-40 [9], a recent modification called the modified acceleration-displacement response spectra (MADRS) method, and the improved displacement coefficient method IDCM [10]. In the present study, we select the MADRS procedure. As mentioned above in this study we manipulated 17 types of HAZUS buildings. Capacity curves of these buildings are showed in Fig. 4.

The probability of being in or exceeding a given damage state is modeled as a cumulative lognormal distribution. For structural damage, given the spectral displacement, the probability of being in or exceeding a damage state, is modeled as:

where: $S_{d,ds}$ – median value of spectral displacement at which the building reaches the threshold of damage state $d_s$, ${\beta }_{ds}$ is the standard deviation of the natural logarithm of spectral displacement for damage states, $\mathrm{\Phi }\left(·\right)$ is the standard normal cumulative distribution function. Refer to HAZUS-MH technical manual to get Coefficients [5]. Probability of each damage level could be obtained from fragility curve. In Fig. 5 a typical fragility curve has been illustrated.

Fig. 4Capacity curves for selected model building types in the city of Tabriz

Fig. 5Typical fragility curve and damage probability

3.2. Probabilistic earthquake scenarios for Tabriz

In this article, an evaluation of the seismic risk of Tabriz is provided. There are several major faults surrounding Tabriz, each of which has caused at least one severe earthquake. These faults have the potential to generate high magnitude ground motions. Having a review of seismic risk of Tabriz, we can conclude that we cannot choose a specific fault for subsequent steps of our study, so, a probabilistic scheme is used. According to the Iranian Code of Practice for Seismic Resistant Design of Buildings [1], Tabriz is situated in a region with high seismic risk in Iran (Fig. 6).

3.3. Probabilistic seismic hazard parameters of Tabriz

According to Iranian Code of Practice for Seismic Resistant Design of Buildings [11], the peak ground acceleration proposed for seismic design of structures in Tehran as a high-risk region is 0.3 g. The methodology characterizes ground shaking using a standardized response spectrum shape as given in IBC-2006 [11], which consists of four parts:

PGA, a region constant spectral acceleration at periods from zero seconds to $T_{AV}$, a region of constant spectral velocity between periods from $T_{AV}$ to $T_{VD}$; and a region of constatnt spectral displacement for periods of $T_{VD}$ and beyond. In general, the elastic design spectrum $S_a\left(T\right)$ is defined by the following equations:

The period $T_{AV}$ is based on the intersection of the region of constant spectral acceleration and constant spectral velocity and its value varies depending on the values of spectral acceleration that define these two intersecting regions:

The period $T_A$ representing the left corner period of the spectral plateau can be determined as follows:

Fig. 6a) Iran’s probabilistic seismic hazard map [2], b) distribution of Tabriz’s faults [4]

a)

b)

The constant spectral displacement region has spectral acceleration proportional to $1/T^2$ and is anchored to the spectral acceleration value at the period $T_{AV}$, where constant spectral velocity transitions to constant spectral displacement. The period $T_{VD}$ is based on the reciprocal of the corner frequency $f_c$, which is proportional to stress drop and seismic moment:

where, $f_c$ is the corner frequency.

The response spectrum which is usually in terms of $S_a$ versus $T$ is converted to $S_a$ versus $S_d$. By definition, the values of $S_d$ are calculated from the following formula:

Eq. (12) gives the spectral displacement:

where: $A$ – design basis acceleration over bedrock (suggested value is 0.35 g for the entire Tabriz region), $B$ – the response factor representing both the amplifying effects of soil deposit and the structural response, simultaneously. Soil type is determined using the average shear wave velocity

Spectral accelerations for city of Tabriz for four different soil types are presented in Fig. 7.

As it is obvious in Fig. 8, there is an acceptable agreement between the results of Iranian Code of Practice for Seismic Resistant Design of Buildings [11] and those of IBC-2006.

Fig. 7Spectral acceleration of four soil types

Fig. 8Shear wave velocity domain using three references

4.1. Introduction of a function describing building damageability

Since damage estimates are provided as disaggregated numbers for distinct damage states (in this paper: slight, moderate, extensive, and complete), a one-to-one comparison of damage results is not easy to visualize. Consequently, damage and loss estimates are represented by total economic loss as well as mean damage ratio. Both parameters allow a one-to-one comparison between the results.

MDR can be computed for a certain area and building typology. Several MDRs can be defined for different purposes. In this study we calculated three types of MDR which are according below.

1) MDR for each geounit and all building types:

where $D{R}_j^k$ is the damage ratio of the model building type $k$ corresponding the damage state $j$ where $j=S$ for slight, $M$ for moderate $E$ for extensive and $C$ for complete. $N_{ji}^k$ is the damaged built area corresponding to the damage state $j$ ($S$, $M$, $E$, $C$) for the model building type $k$ at the geounit $i$. $N_{Ti}$ is the total built area at the geounit $i$. for all the model building types $i=$ 1,…, $mbt$.

This parameter helps us to compare different region in one city, and to determine which of regions must be in the top priority of rehabilitation process.

2) MDR for each model building types and all regions:

where $N_T^k$ is the total built area for the model building type $k$ and added to all the geounits $i=$1,…, $geounits$. Other parameters are according the above equation One of the criteria of city extension (both horizontally and vertically) is considering of its seismic vulnerability. This parameter demonstrates that between two years of study whether specific kind of structure has been built in less prone to earthquake area or not. Meanwhile, it can helps to authorities to determine the critical type of building for rehabilitation.

3) MDR for all model building type and all geounits:

This parameter which is only one number to the whole city, demonstrates the mean damage ratio of entire city. It could be useful to compare to different city; or one city in different years to demonstrate whether the rehabilitation policies would be affective or not.

4.2. MDR for regions of Tabriz in 2011

Mean damage ratio in each region in 2011 which are calculated through Eq. (11) are depicted in Fig. 9, respectively.

Fig. 9MDR of different regions of Tabriz in 2011

4.3. MDR for buildings of Tabriz in 2011

With reference to the Fig. 10, we can obtain mean damage ratio calculated for each type of building in Tabriz (According to Eq. (15)).

4.4. Monetary loss due to probable earthquake in Tabriz

A probable monetary loss due to the possible earthquake defined by Iranian Code of Practice for Seismic Resistant Design of Buildings [1] is presented in Fig. 11. Monetary loss has been computed for 2011 using the same currency unit.

Fig. 10MDR for each building type in Tabriz computed for 2011

Fig. 11Monetary loss due to probable earthquake in Tabriz in 2011 (millions dollars)