Seismic risk and damage prediction: case of the buildings in Constantine city (Algeria)

Abstract

Located at the North-Eastern part of Algeria (Tellian Atlas), Constantine has crucial administrative, economic, scientific and cultural importance. It has continuously experienced significant urban evolutions during the different periods of its history. The city is located in an active seismic region within Algeria and has been struck in the past by several moderate and strong earthquakes. The strongest earthquake recorded since the beginning of instrumental seismology took place on October 27, 1985 with a magnitude M$_\mathrm{S}=$ 5.9. Constantine presents a high seismic risk, because of its dense housing and high population density (2,374 inhabitants/km$^{2})$. This requires a risk assessment in order to take preventive measures and reduce the losses in case of potential major earthquake. For this purpose, a scenario based approach is considered. The building damage assessment methodology adopted for the Algerian context is adapted from HAZUS approach. In the present case, the effective Algerian seismic code response spectrum (RPA 99/2003) is considered as a seismic hazard model. The prediction of the expected damages is performed for a set of almost 29,000 buildings.

Appendix: Methodology for assessment of building damages expected from seismic effects

The global procedure adopted to estimate the expected damages under seismic effects (earthquake scenario) for Constantine city buildings is adapted from HAZUS (Hazard United-States) approach (The FEMA Tool Estimating Earthquake Losses) (FEMA 2002). Based on the capacity spectrum method, it is adopted worldwide (Mahaney et al. 1993; ATC-40 1996; Comartin et al. 2000; Chopra and Goël 1999; Fajfar 1999). The adaptation to the Algerian case relies mainly on the specificity of Algerian soils and their dynamic properties (local and site effects: seismic input) as well as the specific material properties and the structural types that govern the structural dynamic response (seismic output). According to the intersecting performance point between the seismic load (elastic response spectrum) and the structural response (capacity curve), the corresponding spectral displacement identifies and indicates the level of structural damage, as shown in Fig. 15. Actually, this spectral displacement provides the probability of damage level occurrence on the fragility curve adopted for the concerned structural type. Therefore, the probabilities of damage and their category levels are obtained for the considered structure under the given seismic input.

Fig. 15

Seismic damage estimation procedure (Boukri et al. 2013)

Fig. 16

General flowchart: seismic damage evaluation procedure (Boukri et al. 2013)

Figure 16 shows the flowchart used to evaluate the damage probabilities. This flowchart consists in seven (07) main steps which are:

• Step 1 Choice of the building type according to the height and the corresponding seismic code level.

• Step 2 Development of the elastic response spectrum ($\xi = 5\,\%$: dam**) adapted to the concerned site, and transformed into the format “Acceleration-Displacement Response Spectrum” (ADRS) using the following relationship:

$$\begin{aligned} S_\mathrm{dy} (T)=\frac{S_\mathrm{ay} (T)}{4\pi ^{2}}T^{2} \end{aligned}$$

(4)

where: $T$ [unit: s] represents the Period of the building; $S_{ dy}$[unit: m] and $S_{ay }$[unit: m s $^{-2}$] represent the spectral displacement and the spectral acceleration, respectively.

• Step 3 Generation of the capacity curve

The capacity curve relates the resulting shear effort acting at the building base to the top total displacement of the building. The push-over response depends on the geometry, the constitutive materials behaviour considered as linear or nonlinear with possible P-Delta effects, (Jerez and Mébarki 2011). This curve is transformed into ADRS format in order to be compared to the elastic response spectrum (Fig. 3). The main parameters of this capacity curve are:

• (1) Yield capacity point ($D_{y}, A_{y}$)

• (2) Ultimate capacity point ($D_{u}, A_{u}$)

$D$ and $A$ express the displacement and acceleration point of the capacity curve, respectively

• Step 4 Definition of the performance point

The performance point ($S_{d})$ represents the performance of the building or generic classes of buildings under the effect of a given seismic action level. It expresses the interaction between the capacity curve of the building and the elastic response spectrum for the considered soils conditions (FEMA 2002; ATC-40 1996). Once defined, this point provides the probability of damages occurrence by using fragility curves.

• Step 5 Generation of damage functions

The damage curves are commonly adopted as being lognormal fragility curves that express the probability $P[d_{s}{\vert }S_{d}]$ of reaching or exceeding a given level of structural or non-structural damage ($d_{s})$, for a spectral displacement ($S_{d})$ at the performance point. The cumulative distribution for a given damage level (d$_{s})$ gives therefore the probabilities for each category of damage $P[N{\vert }S_{d}]$, $P[S{\vert }S_{d}]$, $P[M{\vert }S_{d}]$, $P[E{\vert }S_{d}]$, $P[C{\vert }S_{d}]$ as expressed by Eq. 5 (Federal Emergency Management 2002):

$$\begin{aligned} P\left[ {d_s /S_d } \right] =\Phi \left[ {\frac{1}{\beta _{ds} }\ln \left( {\frac{S_d }{\overline{S} _{d,d_s } }} \right) } \right] \end{aligned}$$

(5)

where, $S_{d}$ is the spectral displacement (acting as seismic demand and input); $S_{d,ds }$represents the mean value of the spectral displacement for a given damage level taken equal to “$d_{s}$”; $\beta _{ds }$is the logarithm value of the displacement standard deviation “$d''$for the damage level or category $d_{s}; \Phi$(.) is the cumulative standardized Gaussian distribution function; $P[S{\vert }S_{d}]$ represents the occurrence probability of a slight damage “S”; $P[M{\vert }S_{d}]$ is the occurrence probability of a moderate damage “M”; $P[E{\vert }S_{d}]$ is the occurrence probability of an important and extended damage “E” and $P[C{\vert }S_{d}]$ is the occurrence probability of a complete damage “C”.

• Step 6 Calculation of the specific damage category probabilities

The specific damage category probability, corresponding to each category or level of damage, is then derived from the cumulative probabilities as follows:

$$\begin{aligned}&{ Complete}\ \hbox {damage} ``{{\varvec{C}}}'':\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad P[{{\varvec{C}}}] =P[C{\vert }S_{d}]\end{aligned}$$

(6)

$$\begin{aligned}&{ Important\ and\ extended} \, \hbox {damage} ``{{\varvec{E}}}'':\quad \quad \quad P[{{\varvec{E}}}{ ] = P[E{\vert }S}_{d}{ ] - P[C{\vert }S}_{d}]\end{aligned}$$

(7)

$$\begin{aligned}&{ Moderate}\ \hbox {damage} ``{{\varvec{M}}}'':\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad P[{{\varvec{M}}}{ ] = P[M{\vert }S}_{d}{ ] - P[E{\vert }S}_{d}] \end{aligned}$$

(8)

$$\begin{aligned}&{ Slight} \, \hbox {damage} ``{{\varvec{S}}}'':\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad P[{{\varvec{S}}}{ ] = P[S{\vert }S}_{d}{ ] - P[M{\vert }S}_{d}] \end{aligned}$$

(9)

$$\begin{aligned}&{ No\ or\ Very\ Slight}\ \hbox {damage} ``{{\varvec{N}}}'':\quad \quad \quad \quad \quad \quad P[{{\varvec{N}}}{ ] = 1-P[S{\vert }S}_{d}] \end{aligned}$$

(10)

• Step 7   Generation of the Damage probability matrix for the considered type (see Table 10).

Table 10 Damage probabilities matrix