JOINT CONFERENCE PROCEEDINGS 9th International Conference on Urban Earthquake Engineering/ 4th Asia Conference on Earthquake Engineering March 6-8, 2012, Tokyo Institute of Technology, Tokyo, Japan

EARTHQUAKE LOSS ESTIMATION OF STRUCTURES IN PAKISTAN

Naveed Ahmad1), Qaisar Ali2), Helen Crowley3) and Rui Pinho4)

1) PhD Graduate, ROSE School–IUSS Pavia, Pavia, Italy 2) Director, Earthquake Engineering Center, UET, Peshawar, Pakistan

3) Executive Committee, GEM Foundation, Pavia, Italy 4) Secretary General, GEM Foundation, Pavia, Italy

anaveed@roseschool.it, drqaisarali@nwfpuet.edu.pk, helen.crowley@eucentre.it, rui.pinho@eucentre.it

Abstract: Pakistan is an earthquake-prone region due to its tectonic setting resulting in high hazard with moderate to strong ground motions, vulnerability of structures and social vulnerability to ground motions; leading to the loss of life, property damage and economic losses. Earthquake related disaster in Pakistan is a regular and serious threat to the community however the country lack tools for earthquake risk reduction through early warning (pre-earthquake planning), rapid response (prompt response to locations of high risk) and pre-financing earthquake related risk (property insurance against disaster). This paper present models for physical, social and economic loss estimation of structures in Pakistan for earthquake induced ground motions which are derived using state-of-the-art earthquake loss estimation methodologies. The loss estimation methodologies are being calibrated with the site-specific materials and structures response whereas the derived models are tested and validated against recent earthquakes in the region. The models can be used to develop damage scenario for earthquakes (estimate damaged and collapsed structures, casualties and homeless) and estimate economic losses for the required repair and reconstruction (for a single earthquake event and all possible earthquakes). The models can provide help on policy- and decision-making towards earthquake risk mitigation and disaster risk reduction in Pakistan.

1. INTRODUCTION

Pakistan is one of the regions with the highest seismic risk due to its active tectonic features resulting in high hazard level, vulnerability of regional structures and infrastructures and social vulnerability to strong ground shaking. Being sixth amongst the highly populated countries of the world where urbanization is on rise as are future earthquake disasters which may lead to human casualties, direct economic losses due to repair and reconstruction of structures, indirect economic losses due to business downtime and loss of means of income.

On average the country can possibly experience a damaging earthquake every ten years (Ahmad 2011), however little effort has been made since in reducing the earthquake disaster risk in Pakistan. The drastic consequences of all these earthquakes in Pakistan are due to the lack of well planned preparedness activities in the country. The future risk of earthquakes in a country can be mitigated through retrofitting existing structures, well designing new structures and ensuring proper land use planning. On parallel rapid response planning, emergency planning and pre-financing earthquake risk can significantly reduce earthquake disaster risk and help early recovery.

The paper thus present tools for risk assessment and loss estimation of structures in Pakistan for site amplified ground motions to quantify the socio-economic impacts of

earthquakes (single event and all possible earthquakes) in the region. The tools presented herein can be used for policy- and decision-making towards earthquake risk mitigation and disaster risk reduction in Pakistan. 2. EARTHQUAKE LOSS ESTIMATION

FRAMEWORK 2.1 General Framework

Seismic risk assessment and economic loss estimation of structures in a region should takes into account all possible earthquakes which can occur and affect the region in future time (Abrahamson 2006, Bommer and Abrahamson 2006). Such analysis takes into consideration the impacts of all possible earthquakes in the region with their associated rate of activity i.e. the occurrence probability of earthquakes.

Also, the earthquake loss estimation tools must have the capabilities; to treat different sources of uncertainties systematically, provide estimate of losses for all possible earthquakes as well as single event earthquake, should be capable to provide estimate with different confidence level, it should be updatable and must consider at least two procedures for risk assessment (Calvi et al. 2006, Pinho et al. 2008). The following frameworks are thus developed in the present study for loss estimation considering all possible earthquakes and a single earthquake event:

Probabilistic Earthquake Loss Estimation Framework Considering All Possible Earthquakes: This framework includes seismic hazard curve, which quantify the annual probability of exceedance of different level of ground motions at a site form all possible earthquakes. It also includes the vulnerability curve, which provide estimate of the economic losses the structures can incur given the intensity of ground motions.

For loss estimation at a site, the hazard and vulnerability curves are convolved to compute the so called loss exceedance curve, which correlates the annual probability of ground motions with the likely economic losses of structures for that ground motions. On integrating the loss exceedance curve, the average annual economic loss (AAL) can be obtained, where AAL represents the losses the structures can incur in a given region on annual bases from all possible earthquakes. Figure 1 depicts different components involved in the loss estimation framework developed for structures in Pakistan. The AAL is estimated as a probability distribution, considering various sources and procedures for hazard and vulnerability curve derivation for a given region.

Figure 1 Probabilistic Earthquake Loss Estimation Framework,

Major Components Involved and Typical Shape of Curves. From Left to Right and Top to Bottom : Seismic Hazard Curve, Structure

Vulnerability Curve, Loss Exceedance Curve

Probabilistic Earthquake Loss Estimation Framework

for Single Event Earthquake: In some cases it is also important to quantify the socio-economic impacts of single earthquake e.g. historical events, for general awareness and retrofit prioritization to mitigate the risk. Single event loss estimation is also essential in real and near-real time for prompt response to areas with high damage potential for rescue prioritization and planning to reduce the disaster risk.

This framework includes the simulation of ground motions for the event, considering possible uncertainties in the ground motions. The framework also include structure vulnerability curve and fragility functions, where fragility functions define the probability of exceedance of specified level of physical damages in structures. Fragility functions

can help develop damage scenario, generate damage maps, provide estimate of casualties. Figure 2 depict components involved in the single event loss estimation framework with possible outputs for policy- and decision -making.

Figure 2 Probabilistic Earthquake Loss Estimation Framework for Single Earthquake and Possible Outputs. From Left to Right and

Top to Bottom : Scenario Ground Motions, Structure Vulnerability Curve and Fragility Functions, Damage Map and the Associated

Uncertainty, Distribution of Losses 2.2 Components of Earthquake Loss Estimation

Framework Seismic Hazard Curve: The seismic hazard curve for a

site requires the frequency estimate of site ground motions i.e. the rate at which a target ground motion level is exceeded on annual bases. Thus the objective of hazard analysis within the context of probabilistic earthquake loss estimation is to calculate the rate of potential ground motion levels from all possible future earthquakes. Seismic hazard curve is generally obtained for a given site using the probabilistic seismic hazard analysis (PSHA) procedure as outlined by Reiter (1990). The PSHA procedure adopted in the present study will be elaborated in the following related section.

Structural Vulnerability Curve: The vulnerability curves are derived by combining the structural fragility functions with the consequence factor (the cost of damage repair, as a fraction of structure replacement cost, to bring the structure to normal condition). For a specified ground motion the damage statistics of structures (the percentage of structures with different damage levels) is retrieved from the fragility functions which is convolved with consequence factor and integrated over the damage levels to calculate the corresponding MDR and help derive vulnerability curve for the structure class, see Figure 3 for graphical description.

Structural Fragility Functions: Fragility functions represents the probability of exceeding a given degree of damage of structures for a specified ground motion levels and thus represents the conditional exceedance probability of damage. Structural fragility functions can be obtained either

through statistical analysis of observed earthquakes, expert opinion based on observed structural response (experiments and/or earthquakes observations) and experimental investigation of structures (empirical), or analytical analysis, or a hybrid procedure which combines analytical with that of empirical procedure (Calvi et al. 2006). The present study considered two analytical probabilistic methodologies to derive fragility functions for structures in Pakistan. The following sections briefly present the methodologies and the parameters to derive fragility functions for application.

Figure 3 Graphical Description of Vulnerability Curves Derivation

from Structure Fragility Functions. From Top to Bottom and Anti-Clock Wise: Structure Fragility Functions, Damage Statistics for a Specified Ground Motion, Economic Consequence Factor

(from FEMA 2003 and Bal et al. 2010), and Vulnerability Curves

3. FRAGILITY FUNCTIONS FOR STRUCTRUES IN PAKISTAN

3.1 Structures Classification

On National scale the construction typologies in Pakistan is primarily based on the type of material used in the construction of walls, floors and roof, and the overall construction quality of a structure typology. This include the building units e.g. the type of masonry units, structural elements like wood/timber or concrete frame, binding material in construction of walls e.g. cement mortar, mud mortar, material constituent used in the construction of floors/roof e.g. reinforced concrete floors, reinforced concrete-brick floors, wooden logs provided with straw and heavy mud flooring, roof trusses of wood or steel.

The structures in Pakistan can be broadly classified in the three groups: masonry, timber and concrete structures. Masonry structures may be further classified in different categories (11 classes) depending on the type of masonry unit used in construction, floor/roofing (based on type e.g. wood/rc and weight) and presence of any seismic resistance features e.g. horizontal band beams at roof level, lintel level, plinth level, etc. Concrete structures are classified into two major groups; concrete bare frame structures with/without

masonry infill. Timber structure are classified into two groups; wooden structures with light roofing and braced wooden frame system e.g. Dhajji structures, and wooden structures of heavy roofing with poorly detailed timber frames. Thus a total of 15 classes of structures are considered for fragility functions derivation, as given in Table 1.

Table 1 Structure Typology Matrix Considered in The Present Study

Following the behavior of the considered structures and

their likely mechanism during moderate and strong ground shaking in past earthquakes (Ahmad 2011, Ali 2007, Javed et al 2006, Naseer et al 2010, UN-HABITAT 2008), 10 of the classes (1,2,4,5,7,9,10,12,13,14) are considered with in-plane response of structures and 5 of the classes (3,6,8,11,15) are considered with out-of-plane response of walls subjected to ground shaking.

3.2 Structures Assessment Methods

Probabilistic Displacement-Based Earthquake Loss Assessment Methodology (DBELA): The study included the DBELA methodology developed by Crowley et al. (2004, 2006) for fragility functions derivation. The method is calibrated with the regional-specific material properties and the likely structures response to ground shaking. Further details on the method for the derivation of fragility functions for both in-plane response and out-of-plane response of structures can be viewed in the available literature (Ahmad 2011, Ahmad et al 2010a, Crowley et al 2011a, 2011b).

Probabilistic Nonlinear Dynamic Reliability Based Method for Fragility Functions Derivation (NDRM): The study included also a dynamic reliability-based method which uses the incremental dynamic analysis (IDA) technique for structural analysis (Vamvatsikos and Cornell

2002) and the classical First-Order-Reliability-Method FORM approximation (Der Kiureghian 2005, Pinto et al. 2004) whereby the ground motions with different probability of target damage exceedance are quantified in order to derive structural fragility functions. Further details on the method is given in Ahmad (2011).

3.3 Fragility Functions for Case Study Structures

The two methods (DBELA and NDRM) are calibrated for assessment of case study structures. This includes the experimental investigation (laboratory testing of structural elements and structures at the Earthquake Engineering Center of Peshawar) and numerical investigation (nonlinear static and dynamic time history analysis NLTHA of structural models) of representative materials and structures.

The scope of the analyses is to develop displacement capacity model (obtained through experimental and numerical analyses), viscous damping model (obtained through experimental analysis) and secant period model (obtained through numerical analysis) for structures which are essential for the derivation of fragility functions using the DBELA methodology. The NDRM requires the development of mathematical framework for NLTHA of structural models. Table 2 reports the input parameters for fragility functions of the case study structures. Further details on the mathematical modelling and NLTHA of case study structures is given in Ahmad et al. (2010b, 2010c) and Ahmad et al. (2011a, 2011b).

Table 2 Input Parameters for Scalar-Based (Elastic Spectral

Acceleration at 0.30sec SA(0.30sec,5%)) Fragility Functions, Lognormal Distribution, Derived Using Static (DBELA) and

Dynamic (NDRM) Procedures. DS1 Represents Slight Damage; DS2 Represents Moderate Damage; DS3 Represents Heavy

Damage; DS4 Represents Collapse

3.4 Test, Validation and Calibration of The Fragility Functions

The derived structures fragility functions are tested against the real damage observations during the recent earthquakes in Pakistan. It included the recent 2005 Kashmir earthquake and the 2008 Balochistan earthquake. The scope of this test is to check the efficiency of the two methods and the derived fragility functions in damage prediction structure-by-structure class and per administrative units (District Level) for the damaged structure types in the earthquake affected region and carry out possible modification (adjustment), if necessary, to the basic fragility functions derived herein. This included the development of damage scenario for the case study structures within the earthquake damaged area.

Description of Case Study Earthquakes: The Kashmir earthquake had moment magnitude of 7.6 located at Latitude 34.49N and Longitude 73.63E, approximately 19 km north east of Muzaffarabad city of Azad Jammu Kashmir. The earthquake damaged more than 780,000 buildings were either destroyed or damaged beyond repair and more rendered unusable that needed demolishment and replacement (EERI 2005). The destruction was observed mainly over an area of 30,000 sq-km within rupture distance of about 10 km to 40 km. The Balochistan earthquake had moment magnitude of 6.4 located at Latitude 30.65N and Longitude 67.32E. This earthquake affected wide area where about 800 structures were collapsed, 5000 were heavily damaged, 2500 were moderately damaged and 2500 were minor damaged (UN-HABITAT 2008).

Earthquake Damage Statistics and Definition of Exposure: Information on the damaged statistics of structures is obtained from the available literature; Ali (2007) for Kashmir earthquake and UN-HABITAT (2008) for Balochistan earthquake, which are considered as a reference for the comparison. For Kashmir earthquake various Districts affected are considered while for Balochistan earthquake only three Districts mainly Harnai (23.42 km from source), Pishin (16.65 km from source) and Ziarat (28.96 km from source), are considered due to the obvious reasons of the availability of data on the damage statistics of structures. For Kashmir earthquake, the exposure of the affected building stock are obtained from Ali (2007); including 40% stone masonry (80% rural and 20% urban), 30% block masonry (100% urban), 20% brick masonry (100% urban) and 5% concrete structures (100% urban). These structure types were affected within about 10 to 40 km of earthquake source, which include the major affected Districts nearby. For Balochistan earthquake the damage statistics is provided in terms of the percentage of damaged structures per District which primarily comprised of adobe masonry structures.

Simulation of Ground Motions: Detailed and reliable data is not available on the actual observed ground motions in the nearby areas with their exposed structures. Thus, the ground motions for these earthquakes are simulated using empirical ground motion prediction equation (GMPE) of Boore and Atkinson (2008). The ground motions are

computed for type D NEHRP soil class with shear wave velocity Vs30 of 250m/sec, considering the total uncertainties in ground motion estimation. The ground motion is computed within 10 to 40 km for Kashmir earthquake where the exposed case study structures are considered distributed uniformly. For Balochistan earthquake the ground motion is simulated at the geometric center of each District where the exposure is lumped for assessment.

Fragility Functions for Damage and Collapse Assessment: For Kashmir earthquake, the global fragility functions of both floor types i.e. rc/wooden floor, for masonry, and lateral resisting system type (with/without masonry infill) for concrete structures are considered with weighting the estimated damage probability equally i.e. 0.50 factor is assigned to each fragility functions in order to obtain the total probability for a given structure type. The out-of-plane fragility functions are considered for rural rubble stone masonry structures collapse assessment only. For Balochistan earthquake, as mentioned earlier that it primarily include adobe masonry structures with relatively few structures of other material and construction type e.g. brick masonry, confined masonry, etc. Thus, only global fragility functions of adobe masonry structures are considered.

Damage Scenario Comparison: Figure 4, Figure 5 and Figure 6 reports the comparison of the estimated damage scenarios with the observation in the earthquakes.

Stone Masonry Block Masonry Brick MasonryConcrete Structures0

20

40

60

80

100

Structure Typology

Pe

rce

nta

ge

of

Str

uct

ure

s

DBELA-OriginalDBELA-AdjustedNDRM-OriginalNDRM-AdjustedObserved

Figure 4 Simulation of Structure Wise Damage Scenario for 2005 Kashmir Earthquake. Mean Estimate Using DBELA-Based and NDRM-Based Fragility Functions (Original and Adjusted) and

Comparison with the Observed Damaged and Collapsed Structures.

Figure 5 Simulation of District/Structure Wise Damage Scenario for 2008 Balochistan Earthquake: Observed Damaged and Collapsed

Structures and Mean Estimated Using DBELA-Based and NDRM-Based Fragility Functions for Adobe Masonry Structures

Figure 6 Simulation of District Wise Damage Scenario for 2005 Kashmir Earthquake. From Top to Bottom and Left to Right:

Observed Damaged and Collapsed Structures, after ERRA (2006a) (Top) and Mean Estimated Using DBELA-Based and

NDRM-Based Global Weighted Fragility Functions (Bottom). For both the earthquakes, the two methods provide

satisfactory estimate for the damaged and collapsed structures in most cases. The estimate of collapse for rubble masonry structures is relatively poor whereby the out-of-plane fragility function is systematically adjusted (reducing the ultimate displacement capacity) to provide reasonable estimate. The DBELA-based fragility functions provide relatively lower estimate of the damages for concrete structures, which are adjusted thereof. For District wise comparison in case of Kashmir earthquake, the fragility functions are weighted according to the structure type contribution while the information on the building stock is obtained from PCO (2010) for 1998 Census projected to year 2005. For Balochistan earthquake the methods provide somewhat similar estimate where the DBELA-based fragility functions provide relatively higher estimate (Positively). Overall the two methods (DBELA and NDRM) seems to be comparative for simulation of damage scenarios.

4. EARTHQUAKE LOSS ESTIMATION AT

NATIONAL SCALE 4.1 Definition of Exposure

The region under consideration consists of about hundred and ten administrative units, including eight Districts from the Azad Jammu and Kashmir (Figure 7), where each District consists of about a million, less or more population. Information on the building stock in each District is obtained from PCO (2010) and GAJK (2010) for the 1998 census essentially projected approximately to the end of 2011 year. For hazard and loss estimation the exposure is located at the geometric center of the administrative units, which although represents a very crude geographical resolution of urban exposure, can provide

reasonable estimate of mean damage ratio (MDR) estimate however may with higher estimate of uncertainties (Bal et al., 2010).

Figure 7 Definition of Exposure for National Scale Assessment: District Wise Exposure of Pakistan (Projected to Year 2011 From

The 1998 Census)

4.2 Seismic Hazard Analysis of The Entire Country The representation of ground motions and their severity

at the site for all possible earthquakes is carried out through the use of a classical probabilistic approach formulated by Cornell (1968). Although many features have since been added to the general framework of PSHA but the underlying procedure and concept remains the same.

The present study adopted the standard PSHA framework as outlined by Reiter (1990) where the hazard curve per District is derived using the hazard formulation of Bazzurro and Cornell (1999). The basic formulation is recently decomposed by Bommer and Stafford (2009) and which is approximated (after Stafford, 2007) herein for the numerical computation of the annual rate of exceedance ARE of specified ground motions, as given:

( ) [ ] ( ) ( )kjj k

kji

i rRPmMP,m|gmGMPνgmλ ==>≅ ∑∑∑ r (1)

[ ] ( )εΦ1r,m|gmGMP kj −=>

( ) ( )

σ

µlngmlnε

−=

where λ(gm) represents the total ARE of specified ground motion gm from all sources; νi represents the total number of earthquakes, great than a minimum specified magnitude Mmin, per year for a given seismic source; P(M=mj) represents the probability of a specified magnitude m, obtained using magnitude-frequency relationship for a given source; P(R=rk) represents the probability of each specified rupture location (hypocenter) over the source, resulting in a corresponding source-to-site distance r; ε represents the epsilon of standard normal distribution, estimate the deviation of specified ground motion gm from the median estimate µ using the standard deviation σ of ground motion variability for a specified ground motion intensity. The median estimate and ground motion variability both are defined using GMPEs.

The present study considered the seismicity model i.e. definition of seismic sources and temporal distribution of earthquakes (magnitude-frequency relationship, recurrence

law), developed by PMD (2007) and GSHAP (Giardini et al., 1999) for area seismic sources in Pakistan. Three GMPE’s (Abrahamson and Silva 2008, Boore and Atkinson 2008, Campbell and Bozorgnia 2008) developed under the PEER NGA Project are considered for the estimation of ground motions over stiff soil type D of NEHRP soil classification with shear wave velocity Vs30 of 250 m/sec. For earthquake loss estimation the hazard is expressed in terms of the probability of exceedance of ground motions. Thus, ARE of ground motions obtained for each District is converted to the exceedance probability of corresponding ground motions using the Poisson Model:

[ ] ( )tAREe1 ×−−=≥ 1NP (2)

where P[..] represents the probability exceedance of ground motions for a specified target time t, where t is considered unity for the estimation of annual average losses from all possible earthquakes. The Poisson model considers the earthquakes in time as a Possonian process, random occurrence with no memory of past earthquakes where ARE of an earthquake is not affected by the occurrence of similar earthquake in the past. Nevertheless, it has provided a very useful mean of converting ARE to exceedance probability PE and reasonably useful for the most practical seismic risk analysis studies (Cornell and Winterstein, 1986). Figure 8 reports the derived hazard curves for the case study 110 Districts in Pakistan.

Figure 8 Hazard Curve Derived Through PSHA. From Top to

Bottom: Mean Hazard Curves for Two Candidate Districts (in terms of ARE and PE of Specified Ground Motions) and The Whole 110

Districts using The Seismicity Model of GSHAP and PMD

4.3 Derivation of District Wise Vulnerability Curves The economic losses the structures can incur subjected

to ground shaking is estimated using the structures vulnerability curves, MDR correlated with the ground motion intensity. The convolution of MDR for a given structure class with the total number of structures and the replacement cost of an individual structure of that class provide an estimate of the mean absolute economic losses the group of structures can incur subjected to earthquake. The economic losses in a given region (say District) can be integrated over all structure classes to provide estimate of

mean total economic losses in a given District. Every District predominantly consists of different

building typologies e.g. adobe masonry, brick masonry, block masonry, stone masonry and timber structures. Vulnerability curves are derived for each material type structures where finally a single vulnerability curve is assigned to each District probability weighted by the structure type contribution. A single curve per District is employed in the framework primarily for the simplicity reason and due to the fact that it reduces the computational effort by one-fifth, giving the same results as obtained using class-by-class vulnerability curves.

In the present study the exposure data on each building types at Tehsil level (Sub-District) is obtained from Maqsood and Schwarz (2008) and ERRA (2006b) which is used to define structure wise exposure for each District. Each vulnerability curve is associated with the corresponding uncertainties arising due to the use of different methodology for fragility functions derivation and the economic consequence factor. The present study used the consequence factor proposed by FEMA (2003) and Bal et al., (2010). Figure 9 reports the Mean vulnerability curves derived for each case study District in Pakistan, where each methodology (DBELA and NDRM) and consequence factors are assigned equal weights.

Figure 9 Derived Mean Vulnerability Curves Correlated with

Elastic 5% Damped Spectral Acceleration at 0.30sec. From Left to Right: Weighted Curve for each 110 Districts and Two Candidate

Districts with Relatively Less (Muzaffarabad, Post-2005 Structures) and High Vulnerability (Pishin, Existing Structures)

4.4 Estimation of Average Annual Loss (AAL)

The economic losses the structures can incur over the design life from all possible earthquakes in a given region is quantified on annual bases. The annual economic losses in a given region (say District) can be integrated over all structure classes to provide estimate of average annual loss AAL. The AAL represents the annual specified amount needed to be arranged in order to be ready to pay for the repair and reconstruction of structures in a given region following any earthquake event. The District wise AAL integrated over the whole Districts provide estimate of AAL in the country.

The annual economic losses from all possible earthquakes at a site is computed by deriving loss exceedance curve per District which is integrated to estimate the AAL. The present study used the Simpson’s rule formulated for numerical integration to estimate AAL per District, after Crowley et al (2009):

( ) fCNMDR4MDRMDR6

PEPEAAL

n

1jjj1i0.5ii

i

i1i∑∑=

++∞→

+ ×++×

−= (3)

where PE represents the annual probability of exceedance of specified ground motion from all sources; MDR represents the repair to replacement cost exceedance for the specified ground motion; Nj represents the total number of structures of a given class; Cj represents the average cost of individual structure of a given class; f represents a correction factor, which is 1.0 in case of FEMA consequence factor and 1.05 in case of Bal et al consequence factor.

The f factor is required in the later model due to the fact that the vulnerability curve derived from fragility functions is normalized by 1.05 factor in order to perform fitting to the derived curve using standard lognormal cumulative distribution function. In this case, the repair cost ratio for the collapse is also considered as 1.05 instead of 1.04 originally proposed. Each District in Pakistan consists of two construction types (besides the construction material) which include Kacha and Pacca constructions (PCO, 2010). The present study considered average replacement cost of 2820 USD for Kacha construction and 7210 USD for Pacca construction. Figure 10 reports the mean AAL per District in Pakistan and the cumulative distribution of AAL at National level. Each component involved in the process is assigned with equal weights to estimate AAL.

Figure 10 Estimated AAL. From Top to Bottom: Mean Average

Annual Loss AAL (in Millions USD) at District Level and Distribution of Total AAL on National Levels

Considering the two seismicity models, two

vulnerability methods, three GMPEs, results in median estimate of AAL of about 603 millions USD with logarithmic standard deviation β of 0.81 for the whole country. The government should arrange every year a sum specified by AAL in order to be ready to pay for the repair

and reconstruction of structures following any earthquake event anywhere in the country, which seems significant losses for the country like Pakistan. 5. LOSS PREDICTION TABLES 5.1 Aim and Objective

The general loss estimation framework (Figure 2) require fragility functions in terms of seismic intensity SA(T=0.30sec, 5%) which are essential for earthquake loss estimation whereby the seismic intensity of ground motions is required to estimate losses for a given earthquake. However, considering the case of local government authorities, it will be utmost important to present the earthquake impacts in a convenient and easy to understandable form. For example as structure- independent and intensity-independent parameters, yet respecting the fundamentals of strong ground motions that can be generated by the considered earthquake and structures fragility and vulnerability to the earthquake induced ground shaking. It can then much facilitate the prompt assessment of a given region with minimal efforts essential for the quick response and emergency planning soon after the earthquake.

The best approach is to record the actual ground motions of earthquake, if possible, using a dense array of accelerographs and process the data (in real/near-real time) to obtain the seismic intensity required for damage scenario simulation using the fragility functions. For example the READY system for earthquake disaster management in Yokohama City, Japan (Midorikawa, 2005) and the IERREWS network for reduction of losses in disastrous earthquake in Istanbul Municipality, Turkey (Erdik et al., 2010) among others. Such initiative is also essential for major cities in Pakistan towards earthquake disaster risk reduction. 5.2 Earthquake Parameters for Direct Loss Estimation

Considering the fact that the simplest and readily available parameters soon after the earthquake could be the size of the earthquake (magnitude) and location (epicenter and depth of hypocenter) e.g. as reported by the USGS soon after the earthquake.

For this purpose large factitious earthquake scenarios are considered with different source–to–site distance and earthquake magnitude combination for loss estimation (distance and magnitude are divided into bins where the estimate are provided at the center) whereby the corresponding losses are presented in easy to read and usable tabular form. The present study thus carried out such analysis for the case study structures considering loss estimation at District level for scenario earthquakes, mainly structural damages, the economic losses as a percent of total building stock normalized by the unit cost of single structure, human fatalities, human injuries and number of people homeless. The tables are provided herein. These tables can be used given only the source–to–site distance and magnitude of earthquake event.

5.3 Uncertainties in Losses The provided tables can be used to estimate mean

losses for a given earthquake. Uncertainties in losses estimate need to be associated whereby the users can assess losses with different confidence level. It can help also in the probabilistic estimate of losses in earthquakes. Thus an attempt is made to correlate losses from scenario earthquakes with the associated uncertainties in the loss estimate, since it is observed that a simple relation can be establish in the loss estimate and uncertainties (Porter, 2010).

Figure 11 shows such correlation for MDR with the uncertainties in MDR estimate. It can be observed that the coefficient of variation C.O.V. decreases with increasing the MDR, as also observed previously (Porter, 2010) which can be approximated using an analytical decaying equation. However, the corresponding normal standard deviation is found to firstly increase with increase in the losses, as also observed earlier by Porter (2010), but it is also observed in the present study that the normal standard deviation saturate when loss increase enough and decrease essentially at higher estimate of losses. Thus, the formulation of normal standard deviation requires a complex functional form rather than an increasing only function as proposed by Porter (2010), which will provide inaccurate estimate of dispersion when the losses increase from earthquakes.

Figure 11 Correlation of Mean MDR with the associated uncertainties on MDR estimate. From left to right and top to

bottom: coefficient of variation, normal standard deviation σ and logarithmic standard deviation β

Alternatively, the present study also investigated the

correlation between logarithmic standard deviation β and MDR for uncertainty estimation on MDR. It is observed that like C.O.V. the logarithmic standard deviation also shows a decaying behavior with increasing losses which can be formulated easily. The present study thus uses logarithmic standard deviation β for measuring uncertainties on loss estimate due to its decaying only behavior with increasing losses. Thus β is formulated, for which analytical functions are derived, for estimating uncertainties on the losses estimate for the considered region. Also, for estimating

losses with different level of probability exceedance, the following Eq. (1) can be used approximately.

( )εβ0.5βMean

2

eLossLoss ±−= (4)

where Loss represents the estimate of losses; Lossmean represents the mean estimate as provided in the derived tables; β represents logarithmic standard deviation, the measure of uncertainties in the loss estimate; ε represents the number above/below median estimate e.g. ε 1.0 represents the 84th percentile estimate which has 16 percent chances of exceedance. The following analytical equations are derived through constraint nonlinear regression analysis for the case study structures for different type of loss estimate:

0.46lapseDamage/Col 11.05DSβ −= (5)

0.46MDR 0.76MDRβ −= (6)

0.36Fatalities 3.35Fβ −= (7)

0.36Injuries 4.93Iβ

−= (8)

0.51Homeless 12.21Hβ −= (9)

where DS represents the percentage of structures damaged and collapsed; MDR represents the mean damage ratio as a fraction of the total exposed structures in the considered District, normalized by the net average cost of a single structure; F represents the percentage of human fatalities, as a percent of total population in a given District; I represents the percentage of people injured, as a percent of total population in a given District; H represents the percentage of homeless people, as a percent of total population in a given District. The mean estimate of losses are tabulated for future applications which can be obtained from the provided web link LPO (2011).

6. CLOSURE

Summary: The paper present tools for earthquake loss modelling in Pakistan. It included development of probabilistic earthquake loss estimation framework for structures to quantify losses for site amplified ground motions, for both single earthquake events and all possible earthquakes expected in a given region. The framework require the structures fragility functions and vulnerability curves which are derived for the case study structures using state-of-the-art probabilistic analytical methodologies (DBELA static and NDRM dynamic). The derived fragility functions are tested and validated against recent observations in moderate earthquake (Mw 6.4 2008 Balochistan) and large earthquake (Mw 7.6 2005 Kashmir). Two seismicity models (GSHAP and PMD) are used to derive hazard curve per District in Pakistan using standard PSHA framework formulated herein. Case study application is carried out to estimate economic losses the structures can incur on annual bases in a given District (AAL) for the required repair and reconstruction after future expected earthquake events. Finally, various scenario earthquakes are considered for loss estimation in order to develop structure-independent and intensity-independent functions which are tabulated in easy to interpretable form for future applications for single

earthquake loss estimation. Conclusions and Findings: Overall the two methods for

structures assessment (DBELA and NDRM) are found comparable for damage and collapse assessment of existing structures. Comparison with earthquake observations shows that the methods provide reasonable estimate of damaged and collapsed structures in earthquakes (structure-by-structure class as well as District level comparisons). The observation shows that pure rigid rocking phenomenological model for out-of-plane collapse assessment of walls significantly underestimate the collapse of rubble masonry structures, like as observed for adobe structures (Ahmad et al 2011c), whereas a factor of 4% applied to reduce the ultimate displacement capacity can provide reasonable estimate. The weighted global fragility functions can reasonably simulate earthquake damage scenario at District level. For AAL estimation the use of weighted average (on National level and Provincial level) vulnerability curve can provide relatively less or more estimate as compared to District wise vulnerability curve weighted to the structure type contribution. Acknowledgements:

The work presented herein is based on the research carried out as part of the PhD study of the first author at the ROSE School–IUSS Pavia, Italy in collaboration with the Earthquake Engineering Center of UET Peshawar, Pakistan. References: Abrahamson, N.A. (2006), “Seismic Hazard Assessment: Problems

With Current Practice and Future Developments,” Proceedings of the First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland.

Abrahamson, N. and Silva, W. (2008), “Summary of The Abrahamson and Silva NGA Ground--Motion Relations,” Earthquake Spectra, 24(1), 67-97.

Ahmad, N. (2011), “Seismic Risk Assessment and Loss Estimation of Building Stock of Pakistan,” PhD Thesis, ROSE School ─ IUSS Pavia, Pavia, Italy.

Ahmad, N., Badrashi, Y.I., Ali, Q., Crowley, H. and Pinho, R. (2011a), “Development of Displacement-Based Method for Seismic Risk Assessment of RC Building Stock of Pakistan,” Proceedings of the International Conference on Earthquake Engineering and Seismology, Islamabad, Pakistan.

(http://www.vce.at/SYNER-G/pdf/publications/Ahmad_et_al_ICEES.pdf)

Ahmad, N., Ali, Q., Crowley, H. and Pinho, R. (2011b), “Displacement-Based Seismic Performance Evaluation of Dhajji Structural Systems,” 11NAMC, Proceedings of The Masonry Society, Minnesota, USA.

(http://www.dist.unina.it/proc/2011/NAMC11/data/papers/089.pdf)

Ahmad, N., Crowley, H., Pinho, R. and Ali, Q. (2011c), “Displacement-Based Earthquake Loss Assessment of Adobe Buildings in Pakistan,” In Cheung, S.O., Yazdani, S., Ghafoori, N. and Singh, A. (eds.) “Modern Methods and Advances in Structural Engineering and Construction,” Research Publishing Service, Singapore.

Ahmad, N., Crowley, H., Pinho, R. and Ali, Q. (2010a), “Derivation of Displacement-Based Fragility Functions for Masonry Buildings,” 14ECEE, Proceedings of The European Conference on Earthquake Engineering, Ohrid, Macedonia.

(http://www.vce.at/SYNER-G/pdf/publications/Ahmad_etal_14ECEE-327.pdf)

Ahmad, N., Crowley, H., Pinho, R. and Ali, Q. (2010b), “Displacement-Based Earthquake Loss Assessment of Masonry Buildings in Mansehra City, Pakistan,” Journal of Earthquake Engineering, 14(S1), 1-37.

Ahmad, N., Crowley, H., Pinho, R. and Ali, Q. (2010c), “Simplified Formulae for The Displacement Capacity, Energy Dissipation, and Characteristic Vibration Period of Brick Masonry Buildings,” 8IMC─Dresden Germany, Proceedings of the International Masonry Society , 11(2-H), 1385-1394.

(http://www.vce.at/SYNER-G/pdf/publications/Ahmad_et_al_IMS.pdf)

Ali, Q. (2007), “Case Study of Pakistan Housing Reconstruction,” Invited Lecture Presentation, ROSE School-IUSS Pavia, Pavia, Italy.

Bal, I.E., Crowley, H., Pinho, R., and Gulay, G. (2008), “Detailed Assessment of Structural Characteristics of Turkish RC Building Stock for Loss Assessment Model,” Structural Dynamics and Earthquake Engineering, 28 (10-11), 914-932.

Bal, I.E., Bommer, J.J., Stafford, P.J., Crowley, H. and Pinho, R. (2010), “The Influence of Geographical Resolution of Urban Exposure Data in an Earthquake Loss Model for Istanbul,” Earthquake Spectra, 26(3), 619-634.

Bazzurro, P. and Cornell, C.A. (1999), “Disaggregation of Seismic Hazard,” Bulletin of the Seismological Society of America,89(2), 501-520.

Bommer, J.J. and Stafford, P.J. (2009), “Seismic Hazard and Earthquake Actions,” In: Elghazouli, A.Y. (eds.) “Seismic design of buildings to Eurocode 8,” Spon Press, Oxfordshire, 6-46.

Bommer, J.J. and Abrahamson, N.A. (2006), “Why Do Modern Probabilistic Seismic Hazard Analyses Often Lead to Increased Hazard Estimates?,” Bulletin of the Seismological Society of America, 96(6), 1967-1977.

Boore, D.M. and Atkinson, G.M. (2008), “Ground–Motion Prediction Equations for The Average Horizontal Component of PGA, PGV, and 5%–Damped PSA at Spectral Periods Between 0.01s and 10.0s,” Earthquake Spectra, 24(1), 99-138.

Calvi, G.M., Pinho, R., Magenes, G., Bommer, J.J., Restrepo-Velez, L.F., and Crowley, H. (2006), “Development of Seismic Vulnerability Assessment Methodologies Over The Past 30 Years,” ISET Journal of Earthquake Technology, 43(3), 75-104.

Campbell, K. and Bozorgnia, Y. (2008), “NGA Ground Motion Model for The Geometric Mean Horizontal Component of PGA, PGV, PGD and 5% Damped Linear Elastic Response Spectra for Periods Ranging From 0.01 to 10s,” Earthquake Spectra, 24(1), 139-171.

Cornell, C.A. (1968), “Engineering Seismic Risk Analysis,” Bulletin of the Seismological Society of America,58(5), 1583-1606.

Cornell, C.A. and Winterstein, S.R. (1986), “Applicability of The Poisson Earthquake-Occurrence Model,” EPRI Research Report, Electric Power Research Institute (EPRI), Palo Alto, CA, USA.

Crowley, H., Pinho, R., and Bommer, J.J. (2004), “A Probabilistic Displacement-Based Vulnerability Assessment Procedure for Earthquake Loss Estimation,” Bulletin of Earthquake Engineering, 2(2), 173-219.

Crowley, H., Pinho, R., Bommer, J.J., and Bird, J.J. (2006), “Development of a Displacement-Based Method for Earthquake Loss Assessment,” Technical Report, ROSE School-IUSS Pavia, Pavia, Italy.

Crowley, H., Colombi, M., Borzi, B., Faravelli, M., Onida, M., Lopez, M., Polli, D., Meroni, F. and Pinho, R. (2009), “A Comparison of Seismic Risk Maps for Italy,” Bulletin of Earthquake Engineering, 7(1), 149-180.

Crowley, H., Colombi, M., Silva, V., Ahmad, N., Fardis, M., Tsionis, G., Papailia, A., Taucer, F., Hancilar, U., Yakut, A., and Erberik, M.A. (2011a), “D3.1. Deliverable: D3.1. Fragility Functions for Common RC Building Types in Europe,” WP3-Fragility Functions of Elements at Risk, SYNER-G 2009/2012.

(http://www.vce.at/SYNER-G/pdf/deliverables/D3.1_Syner-G_RC_final.pdf)

Crowley, H., Colombi, M., Silva, V., Ahmad, N., Fardis, M., Tsionis, G., Karantoni, T., Lyrantzaki, F., Taucer, F., Hancilar, U., Yakut, A., and Erberik, M.A. (2011b), “D3.2. Deliverable: D3.2. Fragility Functions for Common Masonry Building Types in Europe,” WP3-Fragility Functions of Elements at Risk, SYNER-G 2009/2012.

(http://www.vce.at/SYNER-G/pdf/deliverables/D3.2_Syner-G_MASONRY_final.pdf)

Der Kiureghian, A. (2005), “First- and Second-Order Reliability Methods,” In Nikolaidis, E., Ghiocel, D.M. and Singhal, S. (eds.), “Engineering Design Reliability Handbook,” CRC Press LLC, Chapter 14.

EERI (2005), “Learning From Earthquakes: First Report on The Kashmir Earthquake of October 8, 2005,” Technical Report, Earthquake Engineering Research Institute (EERI), Oakland, CA, USA.

Erdik, M., Fahjan, Y., Ozel, O., Alcik, H., Mert, A., and Gul, M. (2003), “Istanbul Earthquake Rapid Response and Early Warning System,” Bulletin of Earthquake Engineering, 1(1), 157-163.

ERRA (2006a), “No. of Houses Destroyed by Tehsil: Progress Up To 5 June 2006,” Technical Report, Earthquake Reconstruction and Rehabilitation Authority (ERRA), Islamabad, Pakistan.

ERRA (2006b), “Earthquake Reconstruction and Rehabilitation in Earthquake Affected Areas,” Web Report, Earthquake Reconstruction and Rehabilitation Authority (ERRA), Islamabad, Pakistan.

FEMA (2003), “Multi–Hazard Loss Estimation Methodology, Earthquake Model, HAZUS-MH Technical Manual, Federal Emergency Management Agency (FEMA), Washington, DC, USA.

GAJK (2010), “Population Features: District Wise Area, Population, Density, Growth Rate and House Hold Size in Azad Kashmir,” Web Report, Govt. Azad Jammu and Kashmir (GAJK), Muzaffarabad, AJK.

Giardini, D., Grunthal, G., Shedlock, K.M., and Zhang, P. (1999), “The GSHAP: Global Seismic Hazard Map,” Annali Di Geofisica, 42(6), 1225-1230.

Javed, M., Naeem, A., Penna, A., and Magenes, G. (2006), “Behavior of Masonry Structures During The Kashmir 2005 Earthquake,” Proceedings of the first European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland.

LPO (2011), “Loss Prediction Tables: Mean Estimate of Losses for Scenario Earthquakes,” http://www.4shared.com/folder/AzqJxWif/_online.html

Midorikawa, S. (2005), “Dense Strong-Motion Array in Yokohama, Japan, and Its Use for Disaster Management,” In: Gulkan, P. and Anderson, J.G.. (eds.) “Directions in Strong Motion Instrumentation,” Springer, Netherland, 197-208.

Naseer, A., Naeem, A., Hussain, Z., and Ali, Q. (2010), “Observed Seismic Behavior of Buildings in Northern Pakistan During The 2005 Kashmir Earthquake,” Earthquake Spectra, 26(2), 425-449.

PCO (2010), “Estimated Population of Pakistan,” Web Report, Population Census Organization (PCO), Islamabad, Pakistan.

Pinho, R., Bommer, J.J., and Crowley, H. (2008), “Open-Source Software and Treatment of Epistemic Uncertainties in Earthquake Loss Modelling,” Proceedings of the Fourteenth World Conference on Earthquake Engineering, Beijing, China.

Pinto, P.E., Giannini, R., and Franchin, P. (2004), “Seismic Reliability Analysis of Structures,” IUSS Press, Pavia, Italy.

PMD (2007), “Seismic Hazard Analysis and Zonation for Pakistan, Azad Jammu and Kashmir,” Technical Report, Pakistan Meteorological Department (PMD), Islamabad, Pakistan.

Porter, K. (2010), “Cracking an Open Safe: Uncertainty in HAZUS–Based Seismic Vulnerability functions,” Earthquake Spectra, 26(3), 893-900.

Reiter, L. (1990), “Earthquake Hazard Analysis,” Columbia University Press.

Stafford, P.J. (2007), “Basics of Seismology and Seismic Hazard Assessment: Probabilistic Seismic Hazard Analysis (PSHA),” Graduate Coursework, ROSE School-IUSS Pavia, Pavia, Italy.

UN-HABITAT (2008), “Balochistan Earthquake Initial Assessment Report October 2008,” Technical Report, UN-HABITAT, Islamabad, Pakistan.

Vamvatsikos, D. and Cornell, C. (2002), “ Incremental Dynamic Analysis,” Earthquake Engineering and Structural Dynamics, 31(3), 491-514.