earthquake loss estimation of residential...

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Earthquake Loss Estimation of Residential Buildings in Pakistan

Naveed Ahmad1,*, Qaisar Ali1, Helen Crowley2. Rui Pinho2

1Earthquake Engineering Center, UET Peshawar, KP Pakistan. 2GEM Foundation, Pavia, Italy. *E-mail: [email protected]

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 infrastructures 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 observed 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 as well as all possible earthquakes). The models can provide help on policy- and decision-making towards earthquake risk mitigation and disaster risk reduction in Pakistan.

Key words: Earthquake Loss Modelling, Earthquake Preparedness Planning, Earthquake Risk Mitigation, Disaster Risk Reduction

1 Introduction 1.1 Motivation for Earthquake Engineering Research in Pakistan

Pakistan is one of the regions with the highest seismic risk because of its dynamic tectonic characteristics resulting in high hazard level (Bilham 2004, Chandra 1992), vulnerability of regional structures and infrastructures to strong ground shaking and social vulnerability of communities (lack of disaster coping capacity) (Khan 2007, Naseer et al. 2010, Rossetto and Peiris 2009). Being sixth amongst the highly populated countries of the world, the present population of about 180 millions with average annual growth rate of 1.6 percent (PCO 2010), where urbanization is on ascent as are future earthquake disasters which will 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), which can result in huge losses and can devastate important cultural heritage (see Figure 1). The fatality model shown in Figure 1 is developed by Ahmad (2011) based on the major historical earthquakes observed in Pakistan, which provide the estimate of fatalities in earthquakes given the magnitude of an earthquake:

( )εσ.expaM D b ±= (1)

where D represents the number of deaths in an earthquake event; M represents the magnitude of earthquake event; a and b represent coefficients obtained through best fitting to the data; σ represents logarithmic standard deviation, an estimate of dispersion, in loss prediction; ε represents the number of standard deviation above the median prediction. Ahmad (2011) obtained though statistical analysis on historical earthquakes, a value of 0.03 for coefficient a and 6.56 for coefficient b with σ of 1.68. This model is compared with a casualty model developed by Vacareanu et al. (2004) for worldwide

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use under the Risk-UE Project. It can be observed that the Risk-UE model will highly underestimate casualty for Pakistan which is perhaps due to the fact of high structure vulnerability in Pakistan as compared to structures in the European towns.

(Fatality Estimation Model for Pakistan)

(Jinnah road Quetta before 1935 earthquake)

(Jinnah road Quetta after 1935 earthquake)

Figure 1 Impact of historical earthquakes on the communities in Pakistan. From Left to Right: fatality estimation model developed by Ahmad (2011) and the devastation caused by 1935 Balochistan earthquake in Quetta. It has been urged recently by scientists (Avouac et al. 2006, Bilham 2004) that the Himalayan belt is capable to produce large earthquakes in the near future of magnitude 8.0 or even greater. Eq. (1) shows that, it can result in the human fatalities in Pakistan as great as 0.13 million which is enormous. However despite the high level of risk, little effort has been made since in reducing the earthquake disaster risk in Pakistan. The drastic consequences of all these earthquakes in Pakistan are also due to the lack of well planned preparedness activities in the country (Khan 2007). 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 (Coburn and Spence 2002, Erdik et el. 2003, Lobo 2010, Mahul 2010, Midorikawa 2005, Phillips et al. 2010, Wyss 2005). All these important activities require state-of-the-art tools for risk assessment and loss estimation of the built environment against earthquake induced strong ground shaking. 1.2 The Need for Earthquake Loss Modelling in Pakistan

The key message that emerged from the Kobe-Hyogo Conference 2005, second world conference on disaster reduction organized under the Hyogo Framework for Actions (2005-2015), is that disaster risk reduction is a cross-cutting issue in the context of sustainable development and needs to be mainstreamed into the development agendas of nations (Briceno 2010). In fact the first step in the design of an efficient disaster risk management framework for a country is the risk identification that involve hazard mapping and risk modelling for that country (Balassanian 2000, Erdik et al. 2010, Mahul 2010, McGuire 2004, NDMA 2007). The Nature of Start-of-The-Art Earthquake Loss Modelling

It is worth to clarify that the aforementioned simple loss model do not take in to account the strong ground shaking effects at a site and the structure vulnerability systematically (but rather treat them implicitly based on the past observations), thus possess a huge dispersion in loss estimation due which it cannot be used for future applications with confidence. Also, such models cannot be used for

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disaster planning and mitigation activities as the regional variability in ground motions and uncertainty in structure vulnerability (from one place to other) cannot be directly incorporated in to the model. Furthermore, the improved performance of re-built and retrofitted structures cannot be easily incorporated into the model. This clearly indicate the indeed for research on the development of an earthquake loss model which is robust and dynamic for risk assessment. It must be capable to characterize the earthquake hazard of any region, should be flexible to incorporate seismic vulnerability of any structure and infrastructure types and it should be able to be employed for risk characterization of any communities across the country. Ideally, it should be extendable to include risk of communities due to other hazards (e.g. floods, landsliding, etc.) for community multi-hazards risk assessment. Earthquake Loss Model for Pakistan

Considering the case of Pakistan which has experienced numerous significant earthquakes over the past history (see Figure 1) but unfortunately lacks detailed and wide spread reliable data on strong ground shaking and structures vulnerability in order to setup an empirical earthquake loss model. Also, in many situations the observation-based methods cannot be applied, considering the change in the design and construction practices, and the experimental investigations for large structural portfolio is too expensive. Furthermore, the recent disaster experiences, 2005 Kashmir earthquake and recent floods, has significantly, if not all, modified the construction practices in the country. This situation gives an indication that an analytical and engineering mechanics-based tool is the only prudent choice to be developed for Pakistan. Also, considering multi-hazard disaster planning for a country, where either of the disaster event can alter the exposure of the country by large proportion with all other risk assessment models being left outdated make analytical tools the only reasonable choice for planning and decision making in the country due to the inherent dynamic nature of the analytical tools.

Thus, the main objective of the present research work is to develop a state-of-the-art, conceptual and uniform analytical framework for seismic risk assessment and socio-economic loss estimation of residential structures in Pakistan. It can provide probabilistic loss estimates (estimate with chances of exceedance) both for a single earthquake event as well as all possible future expected earthquakes. It is presented for future applications in the region towards effective risk mitigation and disaster risk reduction of communities. It included developing framework for seismic vulnerability and risk assessment of prevailing residential structure typologies in Pakistan. The tools presented herein are multi purposes which can best provide help on policy- and decision-making for public awareness and training, country risk communication, decision making and land use planning, training of task forces, emergency and response planning, insurance of property against earthquake risk, enforcing building codes, etc.. The loss model can be extended to include risk due to other hazards (e.g. floods among others). These characteristics of the present loss model define the state-of-the-art nature of the tools.

Scope and Limitation of The Earthquake Loss Model for Pakistan

The tools presented herein provides estimate of earthquake losses for four different levels depending on the level of knowledge of earthquake event and exposure with varying degree of accuracy of final estimate. It included fatality estimation in earthquakes given information only on the magnitude of earthquake Level-0; estimate of casualties, structure damageability and economic losses, including earthquake impact maps, per Administrative Units (Districts wise) given information on the magnitude of earthquake and source-to-site distance (epicentral distance for convenience) Level-1 or given the severity level of earthquake induced shaking (obtained using the ground motion prediction model, knowing source-to-site distance, magnitude, hypocenter depth for earthquake event) and exposure data (number of structures and their quality of construction i.e. good and poor) per District (Administrative Unit) Level-2 or municipality level (Sub-administrative Unit) Level-3. Level-4 analysis requires detail information on the structure typologies besides the construction quality e.g. stone masonry (good and poor), block masonry (good and poor), concrete structures, etc. Level-5 analysis is a structure-by-structure assessment which is not considered herein. The accuracy of final loss estimate increases from Level-0 to Level-4. Except the Level-0 analysis which is derived on the bases of historical earthquake impacts on the society, all other levels require the development of models derived based on the analytical analyses of structures for fragility and vulnerability

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characterization and hazard characterization. It is worth to mention that these levels are not equivalent to the risk analysis levels used in ELER by Erdik et al. (2003) or similar studies.

An earthquake loss models may ideally include all of the possible hazards from earthquake that can affect the built environment and contribute to the overall losses from that earthquake. Such earthquake hazard, other than ground shaking, include landsliding, liquefaction, surface faulting, tsunami and seiche (Coburn and Spence 2002, Kramer 1996) and other effects such fire following earthquakes. However, the overall contribution of these hazards to total losses from the earthquakes may be the order of ten percent or less which can be ignored looking at the scale of loss modelling and the approximation in the available data which otherwise will require more detailed information for the site. Thus only the site amplified ground shaking hazard, its impact on the structures, is considered for earthquakes in the present study which is by far the most important for disaster risk reduction in the urban areas (Bird and Boomer 2004, Boomer et al. 2002, Mumtaz et al., 2008). It is worth to mention that all of the aforementioned hazards and phenomenon can be incorporated in the loss model. 2 Earthquake Loss Estimation Framework Seismic risk assessment exercises mainly contribute in the pre-seismic and post-seismic phases of earthquake events (Erdik et al. 2010), providing estimate of the consequent losses of earthquake disasters which can guide planner for the disaster preparedness through public awareness and training, national code development for design and retrofit of structures, design of earthquake insurance and reinsurance models. Furthermore, the generation of ground shaking maps and earthquake impact maps may be produced soon after an earthquake event for early response management and emergency action in order to reduce casualties. 2.1 General Framework

Community risk characterization requires collection of databases on the regional earthquake activity, site conditions, shaking intensity characterization models, exposure definition and vulnerability characterisation, building damage repair costs and human casualties. Each of these components of the database carries large uncertainties which reflect as randomness in the final estimate. Thus, the loss model should be capable also to provide estimate with different confidence level (i.e. estimate with its exceedance level). The construction practices and building stock characteristics in a region may change overtime, for example significant proportion of reconstructed residential building have practiced timber construction in the devastated area of Pakistan after 2005 Kashmir earthquake that previously used rubble stone masonry (ERRA 2006a). Thus, the loss model should be updatable (capable to incorporate response of various constructions) to provide accurate estimate for community risk characterization. It has been observed that for a similar construction type different fragility functions may exist (Bradley 2010) because of the modellers using distinct hypothesis to simulate the structures behavior and assess the seismic performance. For this reason, it was proposed earlier that the loss estimation framework 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, keeping in mind the importance of the aforementioned loss model characteristics and its inclusion in the application process, for loss estimation considering all possible earthquakes and a single earthquake event. Probabilistic Earthquake Loss Estimation Framework Considering All Possible Earthquakes

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, Cornell 1968). 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).

Figure 2 depicts the probabilistic-based structure risk assessment framework for all possible damaging earthquakes that can be experienced in future at a given site which can possibly bring losses to the community. This framework includes seismic hazard curve, which quantify the annual probability of

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exceedance of different level of ground motions at a site form all possible earthquakes, which can occur and affect the community in future. It also includes the vulnerability curve, which provide estimate of the economic losses (structure restoration cost) the structures can incur given the intensity of ground motions.

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Figure 2 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, probability distribution of average annual loses.

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. The AAL, in case of Level-5 analysis, for a structure refer to the amount (on average) the owner should arrange by each year over the useful life of structure, that will made the owner able to pay for any level of required repair (structure restoration) following an earthquake. At community level loss estimation, the AAL refers to the amount the authority should arrange by each year in order to be prepared to pay any required cost for community restoration following an earthquake event. The AAL may be quantified as a probability distribution when epistemic uncertainties are included in hazard and vulnerability curves derivation. For example, considering various sources (input models) and procedures (hypotheses) for hazard and vulnerability curves derivation for a given region.

The AAL is a vital parameter used in insurance modelling of community for pre-financing earthquake risk. For example the micro-insurance model that is used to setup the annual premium per household

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which can help in early restoration of community following an earthquake that can help achieve the disaster risk reduction goal (Shah 2009, 2010). Also, the AAL plays an essential rule in selecting an optimum design solution for constructions in a seismically active regions. For example, the benefit-cost model, called as benefit-cost ratio (Crowley et al. 2004, Rose et al. 2007), that can help in risk reduction of constructions (i.e. reducing AAL) through increasing structure resistance (e.g. strength, ductility and energy dissipation) against earthquakes by spending on the retrofitting of structure (or replacing whichever is feasible) until a tolerable estimate of ALL is achieved. The reduction achieved in the AAL through quantifying the difference of the AAL before and after retrofitting, that represents the annual benefit which is summed over the design life of structure (presented in terms of the net present value of the future benefits) and normalized over the retrofitting cost, when provide estimate higher than unity is considered viable. This can help policy-makers for earthquake risk management in achieving the goal of community risk mitigation. The framework can thus help policy- and decision- makers in risk mitigation and disaster risk reduction of communities in high risk regions. Probabilistic Earthquake Loss Estimation Framework for Single Event Earthquake

In some cases it becomes essential to quantify the socio-economic impacts of single earthquake event. For example, in case of pre-event phase assessing the associated risk for an historical event for general awareness, preparedness and retrofit prioritization to mitigate the risk. In case of post-event phase, in real and near real time, the earthquake risk assessment facilitate the generation of loss maps to help guide emergency response planning in prompt response to areas with high damage potential for rescue prioritization and planning to reduce the disaster risk. Single earthquake risk characterization can also help provide estimate of temporary shelters need to accommodate homeless. The seismic risk assessment framework for single event is also probabilistic, as the future expected ground motions cannot be quantified with certainty. For example the fault rupture mechanism, rupture orientation, accurate measure of earthquake energy i.e. magnitude, depth and location of hypocenter, etc, cannot be modelled as a fixed quantity. The associated impacts of a single earthquake should be quantified thus with all possible uncertainties.

Figure 3 depicts the scenario-based probabilistic risk assessment framework for a single damaging earthquake expected in future (for pre-event risk assessment) or a damaging earthquake which has been just occurred (for post-event risk assessment in near real time for response) with possible outputs (e.g. loss maps, loss statistics). This framework includes the simulation of ground motion fields for the event, considering possible uncertainties in the ground motion estimate. 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.

For structure damage evaluation, the ground motion fields are analyzed to retrieve the severity of ground motion with the likely variability in the severity (e.g. the temporal and spatial variability of ground motions) (Abrahamson and Youngs 1992, Boore et al. 2003, Youngs et al. 1995) at various sites. The ground motion representation depends on the scale of assessment e.g. per administrative units in case of Level-2 analysis or per sub-administrative units in case of Level-3 and Level-4 analyses or at the building site for Level-5 in structure-by-structure assessment. The ground motion characterized at a site is convolved with the structure fragility to help develop damage scenario (obtain damage statistics, the observation of buildings in various damage states i.e. slight damage, moderate damage, heavy damage and collapse), generate damage maps, and provide estimate of casualties with the probabilistic distribution of losses (e.g. the probability of exceedance of various fatality estimates). The site ground motion is convolved with the structure vulnerability to quantify the economic losses, which may be represented in the form of loss maps and probabilistic distribution showing the occurrence chances of losses. Besides the variability in ground motion, epistemic uncertainty may be included by employing various models for ground motion characterization. Similarly, for a given class of structures various fragility functions and vulnerability curves may be employed to include the epistemic uncertainty in fragility and vulnerability estimate. The economic losses obtained represents the cost required to repair/replace the damaged buildings (whichever is feasible) and restore the community from the devastation caused by the event.

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72 72.2 72.4 72.6 72.834.5

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Figure 3 Probabilistic earthquake loss estimation framework for single earthquake and possible outputs. From Left to Right and Top to Bottom: ground motion field and scenario ground motions at one of the sites, structure vulnerability curve and fragility functions, damage map showing median collapsed buildings and the associated uncertainty, and distribution of losses.

The scenario-based earthquake risk assessment and loss estimation, in post-seismic phase, is of prime importance to identify locations with the highest seismic risk. It is of particular use in emergency planning and prompt response to disaster site for rescue operation to rescue trapped people from the debris of the collapsed buildings. Experiences on the recent past earthquakes have shown that a prompt response to disaster site and early treatment of injured people can reduce the casualties by a factor of 10 (Coburn and Spence 2002) that can help achieve the disaster risk reduction goal of earthquake risk management (Erdik et al. 2010, Midorikawa 2005). The scenario-based risk assessment is also important to estimate the number of injured who require immediate hospitalization, the number of homeless people quantified help provide estimate of the size and numbers of temporary shelters needed and the economic loss estimated help to know the community restoration cost. These estimates provided in the pre-event phase can help in community awareness, disaster preparedness, risk prioritization and land use planning, which can help in risk reduction. The framework thus can help in policy-making for disaster risk reduction of communities and post-disaster management.

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2.2 Components of Earthquake Loss Estimation Framework

Seismic Hazard Curve

Seismic Hazard refers to any situation that poses a level of threat to properties, human settlements and their economic activities and which can be harmful to human life and health, property and the built environment caused by any of the primary (fault rupture, site amplified ground motions), or secondary (liquefaction, landsliding, ground spreading, etc) or tertiary effects (floods, fires, etc) caused by an earthquake. Generally, most of the contribution to the overall earthquake disaster losses arise from the site amplified strong ground shaking, even in disasters followed by numerous other earthquake’s effects (Bird and Bommer 2004). For example, the 2005 Kashmir earthquake which was followed by numerous landsliding that by and large contributed only 10% to the total losses (Mumtaz et al. 2008). Seismic hazard for earthquake risk assessment is thus characterized in terms of the severity of ground shaking.

For probabilistic-based risk assessment, seismic hazard is represented as the probability of occurrence of earthquake, earthquake effects (e.g. site amplified ground motions) of a certain degree of severity, within a specific future time period in a given area. The occurrence of an earthquake or its effect is represented in terms of its annual recurrence rate (number of occurrence per year) or inversely as an average return period (number of years per single occurrence). Seismic hazard for a given region is defined in terms of the earthquake characteristics (e.g. acceleration, velocity and displacement) and the annual exceedance probability of that earthquake by means of seismic hazard curve. The seismic hazard curve for a site requires the frequency estimate of site ground motions, the rate at which a specified ground motion level is exceeded on annual bases (Bommer and Stafford 2009, Cornell 1968, Kramer 1968, McGuire 2004). Thus the objective of hazard analysis within the context of probabilistic-based 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), based on the pioneering idea of Cornell (1968). The PSHA procedure adopted in the present study will be elaborated in the following related section.

Structural Fragility Functions and Vulnerability Curve

Seismic vulnerability thus refers to the susceptibility of an element, property, society and their economic activities to earthquake’s effects (i.e. primary, or secondary, or tertiary effects) caused by earthquake of a given severity. For seismic risk assessment herein, fragility of an element refers to the extent of damage caused to that element given the severity level of earthquake hazard. Different structural systems attain different level of damage for a given earthquake considering a structure’s portfolio and different degree of damage considering different earthquake and hazard (e.g. the degree of damage in a structure increases with increasing seismic demand). Thus for community risk assessment a database is required to give the number of damaged, collapsed, etc structures given the intensity of ground motions (Kircher et al., 1997), which is called in the present study as 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 structure fragility functions for application.

Seismic vulnerability of an element is defined as the degree of loss to that element for a given severity level of hazard which is expressed as a percentage i.e. the ratio of its expected loss to the maximum possible loss on a scale from 0 to 1 or 0 to 100 % (Coburn and Spence 2002). Structural fragility and vulnerability are often used interchangeably, in the present study fragility refers to physical damages in structures whereas vulnerability refers to the economic loss the structure can incur for a given received damage. The vulnerability curves are derived by combining the structural fragility functions

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with the consequence factor (the cost of damage repair, as a fraction of structure replacement cost, to bring the structure to normal useable 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 the economic consequence factor and integrated over the damage levels to calculate the corresponding repair cost ratio and help derive vulnerability curve for a structure class, see Figure 4 for graphical description. The economic consequence factor (Bal et al. 2010, FEMA 2003) provides a mean to transform structural physical damages to monetary loss. Structures with different construction material and practice, which have different dynamic properties, shows different pattern and level of damage (with different required repair cost) for a given earthquake considering a given region. Thus number of different vulnerability curves has to be prepared and used to estimate earthquake losses for that region. For community risk assessment, in a given earthquake different structure types will receive different level of damages requiring different repair cost (presented in term of repair cot ratio) which may be integrated over the total structure types to obtain the measure of mean damage ratio (MDR) describing the level of risk of the community.

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Figure 4 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. (2008), and vulnerability curves.

The measure of earthquake loss depends on the element at risk, and accordingly may be expressed as a percentage of casualties i.e. the numbers killed or injured to the total population, as a repair cost ratio or as the degree of physical damage i.e. minor, moderate, heavy, etc defined on an appropriate scale. For community risk assessment it may be quantified in terms of the proportion of structures/infrastructures experiencing some particular level of damage. It may be quantified also as

Vulnerability Curves Fragility Functions

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the percentage of casualties or homeless. For a given earthquake the percentage of collapsed structures are retrieved from the fragility functions which is convolved with the social consequence factor (Spence 2007) to calculate the extent of casualties in a given structure type, which is integrated over the total structures in the community to quantify the causalities in the community due to earthquake. Social consequence factor provides the mean to transform the number of collapsed buildings to the expected casualties (i.e. injured people, fatalities). The survivors from the debris of the collapsed structures and the occupants in the heavily damaged structures (non-usable) collectively represent the homeless people.

Uncertainties in Earthquake Risk Modelling

The probabilistic seismic risk assessment framework presented earlier (Figure 2 and Figure 3) requires the collection of databases on the regional seismicity, site conditions, ground motion characterization models, definition of exposure and their vulnerability, damage repair costs and human casualties. Each of these components of the framework carries large associated uncertainties which need to be propagated through the analysis, such that the total uncertainty in the resulting risk estimates can be obtained, which makes the sensitivity analysis possible to help decision making for earthquake risk management (Bommer et al. 2006a, Pinho et al. 2008). The earthquake loss estimation tools must have the capabilities to treat different sources of uncertainties systematically. Uncertainties are generally classified in three categories for modelling and probabilistic analysis of a process which included Aleatory Variability (i.e. inherent randomness of earthquake phenomenon), Epistemic Uncertainty (i.e. reflects our lack of knowledge, the way the real process is simulated by means of a model), Ontological Uncertainty (i.e. unknown or unexpected, not known previously) (Elms 2004). An earthquake loss model should at least take into account the first two types of uncertainties in risk assessment. Ontological uncertainty cannot be modelled by definition, however it may be reduced through peer review process and experts opinion. For probabilistic-based risk assessment considering all possible earthquakes, the aleatory variability is included within the derivation of seismic hazard curve and seismic vulnerability curve. For example, the effects of the randomness of the earthquake process is included in the hazard curve derivation and the impacts of the geometric and material properties randomness of a given structure type is included in the vulnerability curve derivation, to help include the total aleatory variability in final risk estimate. The impacts of using different hypotheses or models for hazard and vulnerability characterization, to capture the epistemic uncertainties, are included employing hazard and vulnerability curves derived using different procedures. At least two procedure may be used to take into account the epistemic uncertainty in the risk estimate (Calvi et al. 1999, Pinho et al. 2008). 3 Fragility Functions For Structures In Pakistan 3.1 Structures Classification

Characteristics of Building Constructions

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 construction units (e.g. the type of masonry units), structural load bearing elements like (masonry walls, wooden frame, concrete frame), binding material used 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). Figure 5 shows the proportioning of structure typologies in Pakistan. Figure 7 shows, the construction typologies predominantly found in most of the areas of Pakistan, which are briefly described below. Figure 8 shows various floor and roofing systems employed for these constructions.

Brick Masonry Construction: unreinforced brick masonry buildings is a recent construction form popular in the urban and civilized plan areas of the country (Ali 2006). These buildings are generally built by ordinary masons using thumb rules of constructions. It is commonly found in the region from

11

one to three storeys (since the municipal authority restrict masonry construction higher than three storeys in the municipality), however in few cases brick masonry up to four and even five storeys may

Bricks/Blocks/Stone, 59% Adobe/Earth Bound, 34%

Wood/Bamboo, 5%Others, 2%

(Material used in Exterior Walls)

Iron Sheet, 13%

Wood/Bamboo, 58%

Others, 8%RCC, 21%

(Material used in Floors and Roof)

Kacha, 35%Pacca, 65%

(Quality of Construction) Figure 5 Characteristics of structure typologies in Pakistan on national scale – based on 1998 Census (PCO 2011). From left to right: proportion of the construction type based on material used in walls and floors/roof and construction quality of structures.

be seen (Ahmad et al. 2010). These building types use fired brick units in cement mortar for the construction of one-wythe load-bearing masonry walls. The building is generally provided with reinforced concrete slab floors and roof. However, buildings may be found also using light beam-girder and steel joists or using light wooden-beam and wooden joists and may be provided with the wooden/steel roof trusses and GI sheeting. Horizontal rcc bands (thin beam with light nominal reinforcement) at lintel and sill level and ring beam at floor level are also provided to increase the building integrity. Very recent construction also use lightly reinforced vertical confining elements at the corners of the walls and junctions to ensure better structural integrity. In rural areas some of the constructions may be found built using brick units in mud mortar and provided with heavy wooden roof that also included thick mud topping.

Block Masonry Construction: unreinforced block masonry buildings is also a recent construction system in the country (Stephenson 2008). These buildings are constructed in similar fashion of brick masonry construction, using concrete block units in cement mortar for the construction of one-wythe walls. This construction type also practice similar floor and roofing systems that of brick masonry constructions. The recent construction of block masonry make use of light vertical reinforcement (i.e. a 12 m steel bar provided at 1.20 m center-to-center distance). In rural areas block masonry is constructed either in mud mortar or in dry form and provided with heavy wooden roof and mud topping.

Stone Masonry Construction: unreinforced stone masonry buildings is an old construction form of masonry (Ali 2007). In case of urban construction, these buildings use fully or partially dressed stone blocks in cement mortar with coursed masonry practice for the construction of one- or two-wythes walls and provided with rcc slab floors and roofing, wooden joists, steel joists and wooden/steel truss roof system with GI sheeting. In rural constructions undressed local field stones are practiced in random rubble masonry in mud mortar or in dry form and provided with heavy wooden roof and mud topping.

Adobe Masonry Construction: it is also a common construction type in most of the rural and sub-urban areas, mostly adopted by poor people. This construction type consists of load-bearing masonry walls provided with heavy mud roof. The walls are constructed either using sun dried clay units in mud mortar or straw-mixed earth material mud lumps stacked in a wall. In the former type of construction, light roofing systems of wooden joists and steel joist with wooden truss roof are also practiced.

Concrete Construction: very recently people in cities started construction in concrete structures. Majority of these constructions for residential and mix commercial-residential purposes are found in two to five storeys, however concrete structures are also observed with 10-15 stories in the region. In some large cities like Karachi concrete structures are found also with 15-20 stories in the order of 10 to 20 percent (Badrashi et al. 2010).

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(Brick Masonry Constructions)

(Block Masonry Constructions)

(Stone Masonry Constructions)

(Adobe Masonry Constructions)

(Concrete Constructions)

(Wooden & Timber Constructions)

Figure 6 Typical examples of construction typologies in Pakistan. From top to bottom: brick masonry, block masonry, stone masonry, adobe masonry, reinforced concrete structures, wooden and timber constructions (Ali and Muhammad 2007, Bothara and Brzev 2011, Javed et al. 2006, Lodhi 2010, UN-Habitat 2008).

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(RCC Slab Floor)

(Steel Joist Light Floor)

(Wooden/Bamboo Light Floor)

(Wooden Truss Light Floor)

(Galvanized Iron GI Sheet)

(Wooden Heavy Floor)

Figure 7 Typical examples of floor and roof types used for building constructions in Pakistan. From left to right and top to bottom: rcc slab floor , steel joist floor, wooden/bamboo floor, wooden truss roof, galvanized iron sheet, heavy wooden roof.

Commercial purpose concrete structures like plazas, hotels, hospitals etc in cities are constructed mainly of rc frame structures. The typical construction systems consists of mostly regular, both in plan and elevation, gravity designed rc moment resisting frames which are provided with unreinforced masonry infill, in cement mortar or lime mortar. Irregular structures with open ground floor can be also found rarely in the region. This construction type is mostly provided with infill-frame at least in the three sides (two parallel and one orthogonal) where the front frame in the fourth side is left open for access, shops, etc. However, the intermediate parallel frames in the orthogonal direction are provided with masonry infills. Masonry infills are provided in such a manner that no separation exist between infill and concrete frames. Structures with storey stiffness irregularities and overhangs can be also found in Karachi (Lodhi 2010).

Wooden and Timber Constructions: traditional forms of construction also exist in the mountainous region that makes use of wood material for construction besides local available stone units and mud (Langenbach 2009, Schacher and Ali 2008, Schacher 2005). In remote areas it included structures having parallel un-braced timber frame walls with rubble stone masonry infill. The walls are constructed of regularly placed vertical wooden posts with or without horizontal post, and filled with random rubble masonry. These constructions are provided with heavy wooden roof. Other form of traditional wood construction included Taq, locally called as Bhattar, which consists of load bearing masonry walls and infill walls, with horizontal wood runners/bands at multiple levels used to tie the walls together and with the floors, all of which is locked together by the weight of the masonry overburden. Another wooden construction type consist of timber-braced frame with random rubble masonry infill. It is provided with light wooden floor and wooden truss roof system. The wooden frame of walls are form of vertical wooden posts, provided with horizontal post at the top, that is provided with horizontal and diagonal wooden braces, later filled with masonry infill. The Taq type of construction can be found in the mountainous regions however its use is not widespread like that of Dhajji structures, which is employed in large numbers (Stephenson 2008).

Observed Behavior of Constructions in Recent Past Earthquakes

Before classifying constructions for fragility analysis, it is essential to understand the likely mechanism and behavior of these construction in past earthquakes. The recent 2005 Kashmir earthquake has been experienced in a wider areas of Pakistan whereby almost every construction type found in the country, as discussed earlier, was subjected to ground motions of moderate to high shaking intensity. It included mainly low-rise masonry constructions and low- to mid-rise gravity designed reinforced concrete structures (Ali 2007, Javed et al. 2008, Naseer et al. 2010). Figure 8 shows the percentage of each construction type found in the affected regions and their observed

14

vulnerability, in terms of damaged and collapsed structures. Figure 9 show the damages observed in various masonry and concrete structures in the affected region.

Stone Block Brick Concrete0

10

20

30

40

50

Structure Typologies

Perc

enta

ge o

f S

truc

ture

s 45%

32.5%

22%

5%

(Constructions Exposure)


20

40

60

80

100


Perc

ent

age o

f Str

uct

ures

95%

60%

40%

50%

(Absolute Vulnerability)


20

40

60

80

100


Perc

enta

ge o

f Str

uct

ures

100%

63.16%

42.11%

52.63%

(Relative Vulnerability)

Figure 8 Statistics on the structure damages in 2005 Kashmir earthquake. From left to right: exposure of structures in the affected region, observed absolute and relative vulnerability (heavy damages and collapse) of structures (Ali 2007).

Behavior of Masonry Structures: Typical damages observed in poor quality masonry constructions included total structure, collapse, predominant out-of-plane failure of walls, vertical cracks at wall corners and junctions, and delamination of material from facade-walls. Similar damages are also observed in 2008 Balochistan earthquake for adobe masonry structures (Un-Habitat 2008). Damages observed in good quality masonry construction included shear damages in walls (X type cracks, sliding or complex), flexure rocking and toe crushing of walls, combined in-plane/out-of-plane failure modes (corner damages). Such mechanisms are also observed for few adobe buildings in the region during 2008 Balochistan earthquake (UN-Habitat 2008). A prominent feature of out-of-plane failure of walls also included the effect of structure and floor amplified ground motions (Ali 2007, Javed et al. 2008, Naseer et al. 2010, Peiris et al. 2008).

Behavior of Concrete Structures: The observed high vulnerability of reinforced concrete structures may be attributed to the non-seismic design rules and poor quality of construction practice. It included poorly compacted concrete with inappropriate mix ratio of cement-sand-gravel resulting in low strength concrete, insufficient longitudinal reinforcement in beams and columns of structures, insufficient and poor quality of lateral confining reinforcement (particularly in columns), strong-beam to weak-column construction practices. These factors contributed to the structure poor performance. Typical damages observed in this construction type included damage to masonry infill, damage to columns at the top and bottom due to infill diagonal axial strut mechanism due to frame lateral movement, concrete crushing and bond failure of columns, out-of-plane failure of infill on upper stories, soft-storey failure, total structure collapses (Ali 2007, Javed et al. 2008, Naseer et al. 2010, Peiris et al. 2008). The affected sites also had few traditional structures made of wood and stone masonry, mainly Taq and Dhajji structures, which performed extremely well and survived the earthquake with no damage or very light damages (Ali et al. 2012, Langenbach 2010, Schacher 2005).

Final Remarks on The Observed Behavior: It can be observed that despite the low resistance of masonry against large earthquakes, some of the masonry structures meeting the minimum requirements to ensure resistance against lateral load (Magenes 2006, Tomazevic 2000) and constructed with good effort and using engineering principles survived the earthquake with moderate damages. However, it is also worth to mention that the seismic demand to each structure type is not known certainly. Also, different proportion of construction type was found in different parts, cities, affected by the earthquake. these structures are generally formed in semi-engineered fashion having proper load path, respond to earthquake shaking through in-plane force/deformation demand in masonry walls. In the present study this construction type is assessed using global assessment procedures. Structures that are built in an irregular and random fashion without paying attention to ensure in-plane connectivity of load bearing elements (e.g. walls in masonry structures) result in out-of-plane failure of portion of walls or complete walls. Since in this case the resistance of elements is relatively lower while on the other hand the seismic demand to these elements is filtered/amplified by

15

Masonry Constructions Concrete Constructions

In-Plane Damage Mechanisms Out-of-Plane Damage Mechanisms

Figure 9 Observed damages in buildings during 2005 Kashmir earthquake. From left to right and top to bottom: typical in-plane and out-of-plane damages observed in masonry structures and damages observed in concrete structures (Ali 2007, Javed et al. 2008, Naseer et al. 2010, Peiris et al. 2008).

the structure itself, which is due to the likely load transfer path (Menon and Magenes 2011, Priestley 1985). Such constructions are assessed using out-of-plane assessment procedure. In case of masonry infill reinforced concrete structures (which is the most common for residential purposes), the

16

resistance to earthquake shaking is generally provided by masonry walls through in-plane diagonal strut type mechanism, as evidenced by the predominant diagonal shear damage in the infill walls. These structure types are found in a collapse or near collapse state (critical) after the complete spalling of infills. Wooden structures those of traditional good construction practice (Dhajji and Taq) have generally performed well during large earthquakes. However, structures provided with vertical wooden posts without proper connectivity and large masonry panels (random rubble masonry in most cases) have performed poorly with out-of-plane failure modes of walls, delamination of infill material and complete structural collapse.

Structure Typology Matrix for Fragility Analysis

The structures in Pakistan can be broadly classified in three groups: masonry, timber and concrete structures (see Figure 10). Masonry structures may be further classified in different categories (11 classes) depending on the type of masonry unit used in construction, floor/roofing system and presence of any seismic resistance features (e.g. horizontal band beams at roof level, lintel level, sill level, etc.). Concrete structures are classified into two major groups; reinforced concrete bare frame structures with and 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 un-braced timber frames. A total of 15 classes of structures are considered for fragility functions derivation, as shown in Figure 8 and described in Table 1. Following the above discussion on the observed 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. 2008, Naseer et al. 2010, UN-HABITAT 2008), the structures are classified as follow: 10 of the classes (1,2,4,5,7,8,10,12,13,14) are considered with in-plane response of structures and 5 of the classes (3,6,9,11,15) are considered with out-of-plane response of walls subjected to ground shaking.

Wooden Struccture Concrete Structures Masonry Structures

Timber Braced Infill Frame Wooden Struccture

W1 W2

RCC Infill Frame RCC Bare Frame

RC1 RC2

CB1 CB2

RS1 RS2

M1 M2

Wooden Light Floor Wooden Heavy Floor

FB2 FB3

Struccture Typologies

Brick Masonry

Block Masonry

Stone Masonry

Adobe Masonry

RCC Floors/Roof

FB1

CB3

RS3

W6 W7 C3L C4L

UFB5 UFB4 UFB1

UCB

DS4 RS1

A2 M1

Wooden Light Floor Wooden Heavy FloorRCC Floors/Roof

Wooden Light Floor Wooden Heavy FloorRCC Floors/Roof

Wooden Light Floor Wooden Heavy Floor

Figure 10 Diagram showing major typologies and classification of structures for fragility analysis and vulnerability assessment in Pakistan. Each typology is labeled and compared with the building construction taxonomy of PAGER-WHE (label from PAGER-WHE is provided, in light, where applicable).

Furthermore, the masonry buildings are classified in two classes based on their damage mechanism (In-Plane and Out-of-Plane) developed during earthquake induced ground motions. For example for masonry structures FB1/CB1/RS1, FB2/CB2/RS2/M1, FB3/CB3/RS3/M2. FB1/CB1/RS1 corresponds to the building type which provide in-plane integrity, produces in-plane damages (shearing of masonry in-plane walls) and finally collapse abruptly due to in-plane mechanism (due to disintegration of masonry in-plane walls). In case of stone masonry, delamination of masonry material may also take place before the failure. This type of mechanism is common for public schools, office

17

Table 1 Structure typology matrix considered for fragility analysis in the present study

S. No. Label Height (m) Storeys Structural Description

Brick Masonry Constructions

1 FB1 5.40 2 Unreinforced fired brick masonry, cement mortar, reinforced concrete floors and roof slabs, lintel beam, with or without ring beam.

2 FB2 5.40 2 Unreinforced fired brick masonry, cement mortar, timber floors or steel joist floors and wooden/steel roof truss.

3 FB3 2.96 1 Unreinforced fired brick masonry, mud mortar (or dry), heavy wooden floor, thick mud topping.

Block Masonry Constructions

4 CB1 5.51 2 Unreinforced concrete block masonry, cement mortar, reinforced concrete floors and roof slabs, lintel beam, with or without ring beam.

5 CB2 5.51 2 Unreinforced concrete block masonry, cement mortar, timber floors or steel joist floors and wooden/steel roof truss.

6 CB3 5.40 1 Unreinforced concrete block masonry, mud mortar (or dry), heavy wooden floor, thick mud topping.

Stone Masonry Constructions

7 RS1 5.40 2 Unreinforced cut stone block masonry, cement mortar, reinforced concrete floors and roof slabs, lintel beam, with or without ring beam.

8 RS2 5.40 2 Unreinforced cut stone block masonry, cement mortar, timber floors or steel joist floors and wooden/steel roof truss.

9 RS3 2.96 1 Unreinforced field stone block masonry, mud mortar (or dry), heavy wooden floor, thick mud topping.

Adobe Masonry Constructions

10 M1 2.96 1 Unreinforced adobe block masonry, mud mortar, timber floors or wooden joist floors and wooden/steel roof truss.

11 M2 2.96 1 Unreinforced mud masonry, heavy wooden floor, thick mud topping.

Concrete Constructions

12 RC1 9.00 3 Reinforced concrete frame with masonry infill walls, lightly reinforced beams and columns, rcc floors and roof slab.

13 RC2 9.00 3 Reinforced concrete frame without masonry infill walls, lightly reinforced beams and columns, rcc floors and roof slab.

Wooden & Timber Constructions

14 W1 4.90 2 Wooden diagonally braced frame with mud-stone-masonry infill, light wooden floors and wooden roof truss.

15 W2 2.40 1 Wooden un-braced frame with load-bearing mud-stone-masonry infill, heavy wooden roof and mud topping.

buildings and residential buildings in urban areas. FB2/CB2/RS2/M1 corresponds to the building type which initially provide moderate in-plane integrity, producing in-plane damages (shearing and sliding of masonry in-plane walls) but finally collapse due to combined in-plane and out-of-plane mechanisms (disintegration of masonry in-plane walls, partial and total out-of-plane failure of walls). This type of mechanism is common for residential buildings. FB3/CB3/RS3/M2 corresponds to the building type that cannot provide in-plane integrity, due to the fact that the masonry is in either mud mortar or dry form where the building walls are built just placing one unit (bricks, blocks, stones) over another. This building predominantly damage and collapse due to out-of-plane mechanism. The FB1/CB1/RS1 and FB2/CB2/RS2/M1 building types are assessed using in-plane global assessment procedures whereas the FB3/CB3/RS3/M2 type of buildings are assessed using out-of-plane assessment procedure.

3.2 Structures Assessment Methods

Recent investigation on earthquake loss models for different input (modelling options) sensitivity analysis shows that (besides the seismicity model, site soil classification, ground motion prediction model), the use of different vulnerability methods can result in large differences in damage estimate of structures which can reach even up to 98 percent (Pinho et al. 2008). Thus, every earthquake loss

18

model for a country or region should consider at least two or more vulnerability assessment methodologies (in order to take into account the epistemic uncertainties in loss modelling), which is also pointed earlier by Calvi et al. (2006), with other uncertainties in loss model being considered for each of the method. Thus two methods are considered in the present study: a European standard nonlinear static displacement-based probabilistic earthquake loss assessment (DBELA) methodology and another fully probabilistic and nonlinear dynamic vulnerability assessment approach developed herein. Both of the methods are analytical which uses basic principles of the mechanics of materials and structures to assess the seismic vulnerability of structures. These methodologies are calibrated for the predominant structural typologies in Pakistan. This include the experimental (laboratory testing of structural elements and structures) and numerical (nonlinear static and dynamic time history analysis of structural models) investigation of representative materials and structures. The following sections describe the fundamentals of selected methodology for vulnerability assessment of structures.

The analytical methods are considered for detailed assessment due to the reason that expert opinion–based or empirical methodologies do not take into account the relationship between the frequency content of ground motions and the dynamic characteristics of structures. Also, empirical methods require large database on the observed behavior of structures during past earthquakes in the region, which is not possible considering the case of Pakistan where detailed and reliable data is not available to develop empirical methods confidently. Also, in most cases these methods cannot be extended for various applications in earthquake disaster management. Additionally, empirical methods cannot be extended to new designed structures or retrofitted structures which limit also the scope of the methodology. Since, cost-benefit analysis and code calibration may be required in the region.

Probabilistic Displacement-Based Earthquake Loss Assessment Methodology (DBELA) for Fragility Functions Derivation

Rationale of Method for Vulnerability Assessment: the study included the DBELA methodology for fragility functions derivation of structures for future applications in seismic risk/loss modelling. The methodology makes use of the existing displacement based approaches, developed mainly for the design and assessment of structures at the University of Pavia, EUCENTRE and the ROSE School-IUSS Pavia which is calibrated herein for unreinforced masonry structures and masonry-infill concrete structures in Pakistan. The displacement-based method is originally proposed and developed elsewhere for concrete and masonry structures (Bal et al. 2008, Bommer et al. 2006b, Borzi et al. 2008a,b, Calvi 1999, Crowley et al. 2004, 2006, Glaister and Pinho 2003, Pinho et al. 2002, Restrepo-Velez and Magenes 2004). However, it is further developed to derive region-specific mechanical models and fragility functions for case study structures considering their global and local vulnerabilities.

Recently, the collected earthquake damage data in Italy over the past 30 years has led to the development of an extensive database from which empirical vulnerability predictions for the Italian building stock was possible to perform. Colombi et al. (2008) have recently processed the post-earthquake damage surveys from the most important earthquakes that have occurred in Italy: Irpinia 1980, Eastern Sicily 1990, Umbria-Marche 1997, Umbria 1998, Pollino 1998 and Molise 2002. The data has been used in the generation of empirical vulnerability functions which are compared then with the vulnerability functions derived using the DBELA methodology (Colombi et al. 2008, Crowley and Pinho 2008). It was observed that DBELA which has been originally developed for reinforced concrete structures performed satisfactory in vulnerability assessment of concrete structures whereas relatively performed better for masonry structures (Positively). Thus, increasing the confidence to calibrate DBELA method for semi-engineered and non-engineered masonry structures. Furthermore, very recently the DBELA methodology has been used for fragility functions derivation of non-engineer adobe buildings (Tarque et al. 2012). It is also used in case study application for damage evaluation and casualties estimation in scenario earthquakes (Ahmad et al. 2010, Bal et al. 2010a).

Fundamentals of The DBELA Methodology: The DBELA methodology is a response spectrum based method, where displacement demand on the structural systems is used as an indicator for the prediction of structural performance level for a given earthquake. Seismic displacement demand on

19

structures subjected to earthquake induced ground motions is dependent on the structural properties itself. The fundamental structural parameters controlling the seismic displacement demand on the structural system are the stiffness, strength, ductility and energy dissipation capacity of that system (Elnashai and Di Sarno 2008, Priestley et al. 2007).

DBELA Global In-Plane Assessment Procedure: In the DBELA methodology the seismic response of structures on regional scale is assessed through the use of a substitute, as proposed by Shibata and Sozen (1976), single-degree-of-freedom (SDOF) idealized system with simplified representation which has equivalent properties of an actual structures in terms of its lateral displacement capacity at the center of seismic force, secant vibration period and equivalent damping for a given seismic demand on that structure (Figure 11).

(Single Degree of Freedom Idealization)

(Displacement Capacity Simulation) Figure 11 Substitute-Structure for seismic response simulation of real structure. From left to right: Single degree of freedom (SDOF) idealization of a structure and displacement capacity representation by the linear SDOF system.

For a given earthquake, the secant period of structure is considered to compute the displacement demand from the elastic 5 percent damped displacement response spectrum, further overdamped through equivalent viscous damping, utilized to predict whether a given target performance limit state of a structure is exceeded by comparing the limit state (threshold) displacement capacity with the displacement demand. For seismic assessment, the SDOF is completely defined by secant vibration period, limit state displacement capacity and energy dissipation characteristics (equivalent viscous damping) of structures:

α−αµ+µ=

1TT yLS

(2)

( )εβ±= expaHT bTy (3)

( ) s2yLST1yLS hkHk θ−θ+θ=∆ (4)

hysteleq ξ+ξ=ξ (5)

µ−µ=ξ 1

Chyst (6)

where TLS represents the limit state secant vibration period; Ty represents the structure yield vibration period; a and b represent coefficients having distinct values for different structural systems; β represents the total logarithmic standard deviation, which is the measures of period variability for a given structure class due to uncertainties in material and geometric properties of structures and record-to-record variability; ε represents number of standard deviation above/below median value; µ = ∆LS/∆y represents the limit state ductility; ∆y represents the yield displacement capacity; ∆LS represents the specified limit state displacement capacity; θy represents the inter-storey yield drift; θLS represents the specified limit state inter-storey drift; k1 and k2 represent the displacement coefficients to convert structural system to an equivalent SDOF system and simulate the displacement capacity real structural system at the center of seismic force (Bal et al. 2010b, Calvi 1999, Priestley 1997, Restrepo-Velez and Magenes 2004); ζeq represents the equivalent viscous damping of structural system; ζel represents the elastic damping of the system (pre-yield); ζhyst represents the hysteretic

20

contribution of system damping due to nonlinear response of structural components, different values can be assigned to coefficient C depending on the structural capability to dissipate seismic energy (Priestley et al. 2007).

The limit state parameter values are selected, considering a given damage scale (e.g. Bal et al. 2010b, Calvi 1999, Crowley and Pinho 2008, Restrepo-Velez and Magenes 2004), to predict the corresponding damage states of structures for the derivation of fragility functions. The inter-storey drift limits can be defined for different structural systems using experimental (obtained from laboratory investigation on model walls and structures) models (Calvi 1999, Restrepo-Velez and Magenes 2004), or analytical (based on masonry compression strain limits which are used to obtain section curvature, wall chord rotation and interstorey drifts) as proposed by Kappos et al. (2002) for Greek masonry or based on strain limits of beam/column as proposed by Crowley et al. (2006), empirical model (Javed 2008), or numerically using more or less sophisticated tools recommended by experts.

DBELA Out-of-Plane Assessment Procedure: Generally, the structures are predominantly excited in orthogonal directions by real seismic excitations, with translation and rotational motions. The structural component walls are subjected to loadings in both principal directions. The in-plane walls at the structure edges transmit the ground motion to the floors which is taken further to the out-of-plane walls (Priestley 1985). Similarly, a SDOF system is developed for the vulnerability assessment of masonry structures with out-of-plane failure modes of masonry walls. The methodology adopted herein for the out-of-plane assessment is also a displacement-based approach for which the mechanical characteristics are formulated following the recommendations of (Doherty et al. 2002).

(Single Degree of Freedom Idealization, Out-of-Plane Failure)

(Out-of-Plane Seismic Input Path) Figure 12 Out-of-Plane assessment of masonry walls. From left to right: Single degree of freedom (SDOF) idealization of a out-of-plane responding wall (Doherty et al. 2002) and load path for seismic input to out-of-plane walls (Priestley 1985).

where ai represents the peak acceleration of input excitation; ar represents the response acceleration of wall; M represents total mass of wall; g represents acceleration due to gravity; t represents the wall thickness; ∆1, ∆2 and ∆3 represent the limit state displacement capacities of out-of-plane responding masonry wall that corresponds to the cracking, joint opening and collapse of wall (Doherty et al. 2002). The methodology considers the ultimate displacement capacity as the controlling parameter to define the collapse of out-of-plane.

The resistance of out-of-plane responding wall to earthquake excitation is governed by the wall geometry, boundary condition, selfweight and pre-compression level of rocking portion of wall while less affected by the masonry material properties (Griffith et al. 2003). The out-of-plane stability and collapse of pre-cracked wall can be relatively well assessed by using the secant stiffness (i.e. Ksec), at the beginning of the third degrading branch of the nonlinear force-displacement response, and 5 percent damped elastic floor response spectrum. Thus, the secant period for out-of-plane mechanisms can be formulated as follow:

( )5.0

e

uoop c1

c2T

−λ∆π= (7)

21

where c = ∆2/∆u = 0.50 represents the ratio of the limit state displacement capacity; ∆2 represents the displacement capacity at the bed-joint crack opening; ∆u = φ.t represents the displacement capacity at the collapse limit state; ɸ represents a reduction factor; t represents the wall thickness; λe = F/Me represents the effective collapse multiplier having unit of m/sec2, it is obtained for the identified collapse mode; F represents the lateral force at the incipient rocking; Me represents the effective seismic mass of wall. The ultimate displacement capacity of the out-of-plane wall is mainly governed by the thickness of the wall (Doherty et al. 2002), however a factor of φ = 0.8 is recommended to respect the actual boundary condition and reduce conservatively the ultimate displacement capacity (Griffith et al. 2003, Restrepo-Velez and Magenes 2004) which can be used with 5 percent viscous damping for seismic assessment and collapse prediction. The above equation considers the displacement capacity at the center of seismic force.

DBELA Fragility Functions Derivation Methodology: Generally, for a given limit state, fragility function is derived considering a standard normal cumulative distribution function of the logarithmic difference of the seismic intensity and threshold capacity of limit states with certain level of standard deviation (Kircher et al. 1997):

( )

βΦ==≥

LSLS im

IMLn

1imIM/dDP (8)

where P(D ≥ dLS/IM = im) represents the probability of reaching or exceeding a given limit state dLS; ɸ represents the standard normal cumulative distribution function; IM represents the seismic intensity/demand (e.g. PGA, SA, etc.); imLS represents the median intensity at which the structure exceeds the specified limit state capacity of the system; β represents the natural logarithmic standard deviation which define the total uncertainties in the fragility function. The median intensity imLS may be obtained either experimentally or numerically using sophisticated numerical tools. The standard deviation β is obtained from the square-root-square-sum or similar combination of individual uncertainties, or the consideration of β = 0.6 (commonly), which do not have clear rationale and justification behind. Similar other procedures exist which make use of constraint criterion to derive analytical fragility functions. Thus, an explicit approach is presented to derive analytical fragility functions for regional structures, taking into account different sources of uncertainties explicitly (at local level), without making use of any constraint, in order to obtain the global uncertainty of fragility functions (i.e. β). Various steps involved in the derivation of fragility functions are shown in the flowchart (Figure 13 for in-plane global mechanism and Figure 14 for out-of-plane mechanism). For out-of-plane assessment, the capacity-demand check is performed using the absolute displacement spectra along with the out-of-plane amplification function (Figure 15) as proposed by Priestley et al. (2007). The absolute spectrum is anchored at the peak ground displacement (pgd) and linearly increased to maximum displacement demand at corner period following the recommendation of Priestley et al. (2007). Different recommendations can be used to compute pgd, corner period and corner displacement for worldwide regions (e.g. Gregor and Bolt 1997, Bommer and Martinez-Pereira 1999, Faccioli et al. 2004, Lam and Chandler 2005 and Campbell and Bozorgnia 2008) among others. Fragility functions for both global and local vulnerability of structures can be derived directly following the procedures outlined above. However, to facilitate the future application of fragility functions for developing damage scenarios within the context of risk/loss modelling. It becomes essential to perform fitting of existing simplified distribution functions to the data. The present study thus considered, as also common, lognormal distribution of fragility functions using the model given in Eq. (8). Only two parameters are required to completely define the fragility model (i.e. the median imLS and logarithmic standard deviation β. The median value corresponds to the intensity measure that has 50 percent probability of exceedance while the β is computed using the following formula, after HAZUS FEMA (2003),

( ) ( ) ( ) ( )( )16505084 imLnimLn,imLnimLnmean −−=β (9)

since,

22

( )β−= expimim 5016

( )β= expimim 5084

where im84 represents the seismic intensity corresponding to 84 percent probability; im50 represents the intensity corresponding to 50 percent probability; im16 represents the intensity corresponding to 16 percent probability.

Compute median Ty and ∆y of theconsidered building class

Obtain SD(Ty) from the 5% dampedelastic displacement response

spectrum at Ty

SA = SA(Ty)

Select a given class of buildings withgeometric and material properties

Generate random building propertiesfollowing the prescribed distributions

using controlled Monte Carlosimulation

Generate random population ofconsidered building class (i=1,....,n)

Generate random 5% damped lineardisplacement reponse spectra with

increasing slopes

For each random spectrum

For each limit state, j

i = 1

Obtain ∆i , ξi and Ti from thegenerated building population

Obtain SD(Ti) from the overdampeddisplacement response spectrum at Ti

Is SD(Ti) > ∆i ?

Pfi = 1 Pfi = 0

Is i = n ?

NY

Pfj = Σ Pfi /ni = 1

n

i = i + 1N

Plot Pfj against SA

YSymbols:

n = number of generated buildings

i = random building from generation

j = limit state

? y = yield limit state

Ν = the condition is not satisfied

Y = the condition is satisfied

∆ = displacement capacity

ξ = viscous damping

T = vibration period

SD = spectral displacement demand

SA = spectral acceleration demand

Pf = probability of exceedance

Obtain the corresponding SA(Ty)using the pseudo relationship

Figure 13 Flow chart for the derivation of structure-specific scalar-based fragility functions for global in-plane damage mechanism using DBELA methodology.

23

Compute median Ty and Tout of theconsidered building class

Obtain SD(Ty) from the 5% dampedabsolute elastic displacement

response spectrum at Ty

Compute the out-of-planeamplification S(Ty/Tout) for 5%

damping






increasing slopes


Obtain Ti , ∆outi and Τouti from thegenerated building population

Compute SD(Touti) from the amplifiedspectrum at Touti

Is SD(Touti) >∆outi ?

Pfi = 1 Pfi = 0

Is i = n ?

NY

Pf = Σ Pfi /ni = 1

n

i = i + 1N

Plot Pf against SA

Y

i = 1

Obtain SD(Ti) from the 5% dampedabsolute displacement response

spectrum at Ti

Compute SD(Tout) by amplifyingSD(Ty) with S(Ty/Tout)

Symbols:



?y = in-plane yield limit state



∆out = out-of-plane displacement capacity

T = in-plane vibration period

Tout = out-of-plane vibration period


S(Ty/Tout) = out-of-plane amplification



SA = SA(Tout)

Obtain the corresponding SA(Tout)using the pseudo relationship

Figure 14 Flow chart for the derivation of structure-specific scalar-based fragility functions, for out-of-plane collapse of walls using DBELA methodology.

It is worth to mention that the fragility function derivation adopted herein is distinct to the HAZUS methodology. Since, besides the uncertainties in the seismic capacity and demand the spatial variability of ground motions is also considered in HAZUS type fragility which is essentially separated herein in order not be specific-to a given earthquake scenario and/or region. The spatial variability of ground motions can be considered later in the development of damage scenario and/or risk/loss modelling for a given region using the fragility functions derived herein.

24

Period (sec)

Resp

ons

e S

pect

ral D

ispl

ace

ment

pgd

Corner displacement

Corner Period

Absolutedisplacement

Relative displacementresponse spectra

Absolute displacementresponse spectra

In-Plane Period

(Absolute Displacement Response Spectra)

0 1 2 3 4 50

2

4

6

8

10

12

TIP

/TOOP

Dis

place

ment

Am

plif

icatio

n F

act

or

5% Damped AmplificationFunction

(Absolute Displacement Amplification Function)

Figure 15 Definition of seismic displacement demand on the out-of-plane walls. From left to right: absolute displacement spectrum and out-of-plane amplification spectrum, after Priestley et al. (2007).

Probabilistic Nonlinear Dynamic Reliability Based Method for Fragility Functions Derivation (NDRM)

At present the available computing tools can provide an affordable means to assess the vulnerability of structures using inelastic and dynamic analysis technique. However certain approximations are required in the preparation of structural models for analysis but which nevertheless may provide significantly accurate estimate of structural response. Thus, the present study included a fully probabilistic and nonlinear dynamic approach, respecting all sources of uncertainties, for the fragility analysis of structures in Pakistan. For this purpose and to understand the seismic behavior of structures over the full range of seismic demand and most importantly to develop the full capacity of the system subjected to ground shaking, Incremental Dynamic Analysis (IDA) technique is used as proposed earlier by Vamvatsikos and Cornell (2002). The scope of the structural analysis is to quantify ground motions with different level of probability, exceeding a target performance of structures in order to develop structural fragility functions. Classical reliability method is used for the derivation of fragility functions. Figure 16 shows the NDRM framework for fragility derivation. The following sections describe the use of IDA technique for structural analysis and the derivation of fragility functions of structures using classical reliability method.

Incremental Dynamic Analysis: IDA is a computational analysis method for structures to estimate more thoroughly the structure performance under dynamic seismic loading i.e. acceleration time histories representing strong ground shaking. IDA technique involves subjecting a structural mathematical model to a suite of ground motion records which are scaled to multiple levels of increasing intensity in order to produce curves of response parameters versus intensity level of input excitations (Vamvatsikos and Cornell 2002). The scaling levels are appropriately selected to force the structure through the entire range of behavior, from elastic to inelastic and finally to global dynamic instability, where the structure essentially exceed the collapse capacity. Figure 16 shows the IDA curve for a structure subjected to ten natural accelerograms for multiple intensity levels. The general concept of fragility functions derivation through IDA adopted herein, is based on the generation of demand distribution. The present study considered the inter-storey drift as the response quantity for damage measure in structures. For a given IM, the demand is convoluted then with the capacity to obtain a measure of probability exceeding a target damage in structures till the complete exceedance of that target damage state, such analyses are carried out in a fully probabilistic fashion. The capacity-demand convolution is performed using classical reliability approach and first-order-reliability-method (FORM) approximation. The following sections describe the damage exceedance probability estimation for random variables using basic reliability formulation and FORM.

Classical Reliability Method and FORM Approximations: If a structure element has random value of resistance capacity R that is subjected to random load demand S. Also, assuming that R and S are

25

non-negative quantities having joint probability distribution. Failure of the element is defined as the event R ≤ S and the probability of the element failure can be obtained then as follow:

( )[ ] ( )drrr/sF1P0

Sf f∫∞

−= (10)

where FS (s/r) represents the conditional cumulative distribution function (CDF) of S given R = r; f (r) represents the probability density function (PDF) of variable R. Figure 16 shows graphically the failure probability computation.

Str

uctu

ral M

ode

l

Ma

the

ma

tica

l Mod

el

(Structure Mathematical Model)

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

PGA (g)

Pro

babi

lity

of E

xce

eda

nce

Point Obtained ThroughNDRM

Curve Fitting

(Derived Fragility Function)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Drift (%)

PG

A(g

)

(Structure Response Curve)

(Capacity-Demand Convolution)

Figure 16 Probabilistic NDRM framework for fragility functions derivation. From top to bottom anticlockwise: mathematical modelling of structure system and nonlinear time history analysis (NLTHA) using accelerograms, derivation of structure response curves through IDA, estimation of exceedance probability of ground motions for specified limit state and fragility function development.

The first- and second-order reliability methods (i.e. FORM and SORM), have found wide popularity for the solution of Eq. (10) (Der Kiureghian 2005, Pinto et al. 2004). These approximations work well for most practical cases due to the reason that the neighbourhood of the design point makes the dominant contribution to the probability integral (Der Kiureghian, 2005). In case if the two random variables are not statistically independent, and if the closed form solution is possible for the failure probability computation. The probability of failure can be computed as follow:

( )β−Φ=fP (11)

where ɸ represents the standard normal cumulative distribution function; β represents a factor, called reliability index, that provide estimate of the nearest point on the limit-state surface, approximated through FORM. If capacity and demand both are considered being lognormal distributed, then the logarithmic of R and S will be normally distributed, the β can be obtained:

2S

2R

SR ζ+ζ

λ−λ=β (12)

( )∫∫≤

=sr

drdssr,fP RSf

C-D

Con

volu

tion

NLT

HA

IDA

Fragility

26

where

( ) 2RR 5.0ln ζ−µ=λ

( )2R1ln δ+=ζ

R

RR µ

σ=δ

Where μR represents the mean value of R, σR represents the standard deviation of R Knowing β for the two variables, the specified limit-state failure probability can be obtained (Figure 17). Repeating the procedure for multiple level of intensity, where the limit state exceedance probability can be correlated with the seismic intensity to develop fragility functions (Figure 16). Fitting to the fragility functions and the derivation of fragility functions parameters are performed similarly as explained earlier. Figure 18 and Figure 19 describe the NDRM procedures for the derivation of fragility functions for both in-plane global mechanism and out-of-plane collapse mechanism.

(FORM and SORM Approximation)

(Standard Normal Cumulative Distribution Function)

Figure 17 Limit-state failure probability estimation through FORM approximation. From left to right: the limit-state function in the standard space for computation of β and standard normal cumulative distribution function ɸ for failure probability estimation.

3.3 Mathematical Modelling for Case Study Structures

The two methods selected for the fragility analysis require the calibration of the procedures to derive fragility functions for case study structures. The NDRM is a fully dynamic approach and requires the nonlinear mathematical modelling of the structures for dynamic seismic analysis, derivation of structure response curves and estimation of limit state probability of exceedance for various limit states. The DBELA methodology requires modeling of structures to obtain the vibration period model of the structure for fragility analysis. The following sections describe the modelling of structures for fragility functions derivation.

Modelling of Masonry Structures for Global In-Plane Mechanisms

Modelling Hypothesis, Equivalent Frame Method (EFM): The method used for the mathematical modelling and nonlinear dynamic analysis of masonry structures in the present study is based on the equivalent frame idealization of masonry walls with rigid offsets as proposed earlier by Magenes and Fontana (1998) and further investigated and developed by Magenes et al. (2000) and Magenes (2000) for the simplified in-plane/global analysis of masonry buildings (SAM). Magenes et al. (2000) have carried out many comparisons of the SAM with numerical and experimental predictions which showed reasonable agreement in terms of global behavior (i.e. initial stiffness, lateral strength and ductility). The present study thus formulated the same method with simplified constitutive laws which

27

Compute median Ty and ∆y of theconsidered building class

Obtain SD(Ty) from the 5% dampedelastic displacement response

spectrum at Ty

SA = SA(Ty)






increasing slopes


For each limit state, j

i = 1

Obtain ∆i , ξi and Ti from thegenerated building population

Obtain SD(Ti) from the overdampeddisplacement response spectrum at Ti

Is SD(Ti) > ∆i ?

Pfi = 1 Pfi = 0

Is i = n ?

NY

Pfj = Σ Pfi /ni = 1

n

i = i + 1N

Plot Pfj against SA

YSymbols:



j = limit state

? y = yield limit state



∆ = displacement capacity

ξ = viscous damping

T = vibration period




Obtain the corresponding SA(Ty)using the pseudo relationship

Figure 18 Flow chart for the derivation of structure-specific scalar-based fragility functions for global in-plane damage mechanism using NDRM methodology.

28

Compute median Ty and Tout of theconsidered building class

Obtain SD(Ty) from the 5% dampedabsolute elastic displacement

response spectrum at Ty

Compute the out-of-planeamplification S(Ty/Tout) for 5%

damping






increasing slopes


Obtain Ti , ∆outi and Τouti from thegenerated building population

Compute SD(Touti) from the amplifiedspectrum at Touti

Is SD(Touti) >∆outi ?

Pfi = 1 Pfi = 0

Is i = n ?

NY

Pf = Σ Pfi /ni = 1

n

i = i + 1N

Plot Pf against SA

Y

i = 1

Obtain SD(Ti) from the 5% dampedabsolute displacement response

spectrum at Ti

Compute SD(Tout) by amplifyingSD(Ty) with S(Ty/Tout)

Symbols:



?y = in-plane yield limit state



∆out = out-of-plane displacement capacity

T = in-plane vibration period

Tout = out-of-plane vibration period


S(Ty/Tout) = out-of-plane amplification



SA = SA(Tout)

Obtain the corresponding SA(Tout)using the pseudo relationship

Figure 19 Flow chart for the derivation of structure-specific scalar-based fragility functions, for out-of-plane collapse of walls using NDRM methodology.

29

based on the experimental investigations on local materials and structural elements, for frame elements representing piers and spandrels. The present method use the idea of modelling the masonry spandrels and piers as one dimensional beam-column elements with bending and shear deformation with infinitely stiff joint element offsets at the ends of the pier and spandrel (Figure 20) which is employed also earlier by Ahmad et al. (2010). A similar type modelling approach, constitutive law being defined at the section level, is also used by Kappos et al. (2002) for the vulnerability assessment of masonry structures. This modelling ignores the stiffness and strength contribution from the out-of-plane walls, which is conservative for shear dominated damage in masonry walls, as demonstrated through experimental investigation (Tomazevic 2000). Experimental investigation on structure has shown that this type of modelling approach may underestimate the lateral strength by 30 percent (Shahzada et al. 2012) when considering the response of overall structure. However, it is a conservative approximation for vulnerability assessment on regional scale for the existing structures which may not result in larger lateral resistance due to other couple effects (e.g. aging, low strength of materials, structural idealization in modelling, etc.).

Figure 20 Equivalent frame method for in-plane global assessment of masonry buildings. From left to right: equivalent frame idealization of masonry structural wall and nonlinear force-displacement response of frame element, with bi-linear and multi-linear inelastic behavior, after Ahmad et al. (2010).

Strength Evaluation of Masonry Walls: The masonry walls of structures are generally pierced by doors and windows opening forming short piers which carry both gravity loads and lateral loads. These piers provide lateral resistance by rocking of the pier, diagonal tension failure of the units, mortar and/or combination of units and mortar, and shear sliding at the mortar joints (Magenes and Calvi 1997, Tomazevic 2000). The ultimate mechanism governed in a pier depend primarily on the pier geometry, boundary conditions of wall, applied vertical loads, mechanical properties of unit, mortar and unit-mortar interface. From the point of view of stiffness, strength, and ductility of masonry walls, which are the fundamental structural parameters for seismic performance evaluation (Elnashai and Di Sarno 2008), the primary mechanism is of less importance. The ultimate mechanism can better represent the maximum available capacity of walls in terms of strength and ductility. The yield stiffness can be obtained, reasonably approximate, through the use of crack section properties for the consideration of ultimate mechanism of wall Magenes et al. (2000). Thus, obtaining the response quantities for complete description of masonry wall for a given ultimate mechanism. The available mechanical models (CEN 1994, Magenes and Calvi 1997, Turnsek and Sheppard 1980) that can predict the ultimate mechanism of piers, considering the assessment of existing structures, are employed. These strength models are primarily developed for clay unit masonry, which have recently been found to work significantly well for in-plane lateral strength evaluation of stone masonry (both regular and random rubble masonry) walls (Vasconcelos and Lourenco 2009). Different possible strength models for spandrels and their appropriate uses can be found in Magenes (2000) and Magenes et al. (2000), which are used to compute the shear strength of the spandrel require in the EFM of structure.

Frame-Element Constitutive Law: For all the frame elements the yield shear force is considered to be 90 percent of the value estimated using the above strength models based on the recommendations of (Magenes and Calvi 1997, Tomazevic 2000). The reduction is required for possible bi-linearization of non-linear force-displacement curve for masonry walls. If the structures has rc ring beams and/or band beams, these should be considered as rigid except where openings are found on the top and bottom sides of the element. The nonlinear behavior, force-displacement response of the frame element is

30

idealized as elastic-perfectly-plastic for the masonry piers as per recommendation of Magenes and Calvi (1997) and Tomazevic (2000), also used by Magenes (2000) for nonlinear static pushover analysis and Menon and Magenes (2011) for dynamic analysis. The frame element is assigned with a limited deformation capacity at which the strength of the element goes to zero (defining the failure of pier). The ultimate displacement of frame element is computed approximately at the ultimate drift capacity of walls, 0.40 percent for brick masonry walls failing in shear and 0.8 percent for the flexure/rocking mechanism (Magenes et al. 1995) or three times the crack displacement capacity for shear dominated failure (Tomazevic 2000). However, in the preset study the ultimate drift limit of masonry wall is computed using the pre-compression dependent model of ductility (Frumento et al. 2009, Ahmad 2011).

Modelling of Timber Structures for Global In-Plane Mechanisms:

Equivalent Frame Method (EFM): similar like the masonry structure, EFM modelling approach is also developed for dynamic seismic analysis of timber braced masonry (TBF) structures based on the macro-modelling approach common for masonry structures (Galasco et al., 2002). Other detailed and sophisticated modelling approaches exist for the in-plane nonlinear static pushover analysis of timber frame masonry structures (Kouris and Kappos 2012). In the present study, the TBF masonry wall is idealized as one dimensional elastic stiff beam-column frame element, which is provided with lumped plasticity moment-rotation (M-θ) hinges to simulate the inelastic behavior of wall. The frame element simulate in-plane rocking behavior of TBF wall on lateral translation whereas the wall inelastic force-displacement behavior is simulated through the M-θ plastic hinges (Ahmad et al. 2012a, 2013). The formulation is depicted in Figure 21.

Dhajji Wall: Timber Braced Frame Masonry Wall

Dhajj Wall Panel Kinematic Model

θ

θ

Beam Type Element(Elastic Bending Element with EndLumped Plasticity Hinges)Simulating Dhajji Wall Panel.

Equivalent Frame Element

M

N

V

M

N

V

Equilibrium of ForcesDhajji wall plasticity is modelledusing nonlinear moment-rotationconstitutive law.

Figure 21 Equivalent frame idealization of timber braced frame masonry wall. From left to right: timber braced frame masonry wall, kinematic model for lateral loading, equivalent frame element with moment-rotation plastic hinges and equilibrium of forces (Ahmad et al. 2012a).

Frame Elements Constitute Law: the lateral in-plane force-deformation response of TBF masonry wall depends on the overturning moment resistance of element and chord rotation which in turns depends on M-θ constitutive law of plastic hinges. A trilinear M-θ constitutive law is calibrated from the experimental tests conducted at the Earthquake Engineering Center of UET Peshawar on full scale walls (Figure 22). Figure 22 also shows the comparison of proposed hysteretic model with the observed cyclic response of full scale wall. Other recent experimental investigation on full scale TBF masonry wall for timber buildings in Portugal has shown similar type of lateral force-deformation response (Meireless et al. 2012).

Fmax

y u

F

dd

ki

ki

µβ

md

f.Fm

mF

r.dm

d

Fcr

α1.ki α2.ki

e.Fcr

maxd

ki

ki

α1.kiα2.ki

30.0e

50.0f

65.0r

0.1

F5.0F

05.0

13.0

maxcr

2

1

====β

==α=α

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

Drift (%)

F/F

max

ExperimentalAnalytical Model

Figure 22. Frame element constitutive law for TBF masonry wall panel. From left to right: hysteretic rule for M-θ plastic hinges and comparison of lateral force-drift response with the test results (Ahmad et al. 2012a).

31

M-θ Constitutive Law for TBF Masonry Walls: previously non-linear static pushover analysis tool SAP2000 (CSI 1999) was calibrated with the experimental results (Ahmad et al. 2012a), which is employed to derive the lateral force-displacement capacity curve of TBF masonry walls (Ahmad et al. 2013). It included TBF masonry wall panels of various geometry and loading conditions, which are analyzed to obtain the corresponding maximum moment capacity and drift limits to help develop M-θ constitutive law for TBF walls. The following models are derived based on the experimental behavior and nonlinear static pushover analyses of various TBF walls.

Maximum Rotational Resistance SCF2.44L M 1.70max ×= ; 0.034P0.80 SCF += (13)

Elastic Limit State -0.30y 0.25L =θ (Fcr = 0.50Fmax) (14)

Idealized Yield Limit State -0.300.82L =θ (15) Maximum Strength Limit State -0.30

max 2.25L =θ (16) Near Collapse Limit State -0.303.70L =θ (F = 0.80Fmax) (17)

Collapse Limit State -0.30u 6.41L =θ (18)

where Mmax(kN-m) represents the lateral strength of wall; L(m) represents the in-plane total length of wall panels; P(kN) represents the total axial load pre-compression on walls; SCF represents the strength correction factor; θ(%) represents various limit states drift capacity of wall.

Modelling of Masonry Structures for Out-of-Plane Mechanisms:

Hypothesis for Out-of-Plane Assessment: the non-engineered structures with predominant out-of-plane failure mechanism can be best analyzed for fragility derivation using a fully dynamic experimental and analytical investigations on structural model (Ali et al. 2013, Ahmad et al. 2012b) but which is however expensive when considering various typologies. These structures are analyzed dynamically in the present study following the hypothesis proposed by Priestley (1985). It include subjecting the out-of-plane facade walls to input ground motions that are filtered by the in-plane walls and structure floor (i.e. the acceleration input to the out-of-plane walls are modified by the global response of structures), as mentioned earlier. The mathematical model used for fragility analysis is based on the proposal of Menon and Magenes (2011). This include the dynamic analysis of structure to compute the structural amplified ground motion (i.e. floor acceleration), that is used as an input to the out-of-plane facade walls for linear dynamic analysis. Mathematical Formulation of Out-of-Plane Wall: following the hypothesis proposed by Priestley (1985) for the determination of seismic demand on faced walls, the problem may be formulated as a secondary structural elements (out-of-plane walls) attached to primary structure (global structure system). However, it is worth to mention that the problem cannot be treated as a combined primary-secondary system using a conventional dynamic method for analysis, which results in an inaccurate simulation of the phenomenon (Villaverde 1997, 2004). The present study thus considered primary-secondary uncoupled systems in series, as adopted elsewhere (Menon and Magenes 2011), respecting the fundamentals of the problem. In the present study, it included primary structure system idealized as an equivalent in-plane frame (nonlinear), as discussed already, and secondary system idealized as an elastic SDOF system with rocking response. The vibration period of the out-of-plane SDOF system is computed using Eq. (7), which requires the definition of λe (lateral strength factor, called as collapse multiplier) for the considered structures. Griffith et al. (2003) has observed that the material properties less affect the lateral resistance of out-of-plane loaded walls but it is in fact dependent on the wall geometry, boundary conditions and pre-compression. Thus, the collapse multiplier obtained experimentally by Restrepo and Magenes (2009) for dry masonry building models are assumed in the present study. It is worth to mention that most of the out-of-plane failure mechanisms investigated by Restrepo and Magenes (2009) have been observed also for the Pakistani building stock in the recent earthquakes.

32

Modelling of Concrete Structures for Global Assessment

Modelling of Hypothesis: this construction type is mostly provided with infill-frame at least in the three sides (two parallel and one orthogonal) where the front frame in the fourth side is left open for access, shops, etc. Also, the intermediate parallel frames in the orthogonal direction are provided with masonry infills. Thus, it is reasonable to consider only rc frame structures with masonry infill for Level-4 risk analysis. However, although rare, rc structures with bare frames can also be found in some cases. Thus, both concrete structures (i.e. structures with and without infill) are considered for analysis. As discussed earlier that rc frame construction practice is generally non-engineered or only gravity design-based frame structures. In this construction type, the frame elements (beams/columns) detailing are significantly deficient. The relative minimum dimensions, deficient longitudinal reinforcement, larger spacings of transverse reinforcement and low quality of transverse reinforcement confinement (90 degree hook ends in the ties) make the structural elements weaker, especially columns. Also, the infills are provided in such a manner that no separation exist between infill and surrounding frame. In this construction type only the masonry infill provide resistance to lateral loading (i.e. provide and strength stiffness and strength). It is also noticed in recent earthquake observations that concrete frame structures were found in a collapsed or critical (near collapse) state upon the spalling of infill (Ali 2007, Naseer et al. 2010, Rossetto and Peiris 2009). However local buckling of longitudinal reinforcement, opening of confining ties and early brittle failure of columns (at the top and bottom ends) are noticed in columns before the spalling of infill besides significant damage in the infill (see Figure 9). Thus, it was considered to model infill structures respecting the fundamentals of the problem (i.e. the stiffness and strength is primarily contributed by the infill and the structure ductility is governed by the infill failure). The damage mechanism of infill include cracking and damage in the diagonal of panel. Mathematical Modelling of Concrete Structures: The method used in the present study for mathematical modelling and nonlinear dynamic analysis of rc structures is based on the equivalent frame idealization of reinforced concrete elements (beam/columns) and masonry infill. It included idealization of concrete frame with fiber-based inelastic beam-column elements and idealization of masonry infill with tension-compression axial diagonal strut element (see Figure 23, a macro-modelling technique for infill). The present study followed the proposed modelling approach of (Kadysiewski and Mosalam 2009).

Figure 23. Mathematical modelling of rc-infill structures. From left to right: structural idealization of masonry infill rc frame and details of masonry infill macro-modeling, after (Kadysiewski and Mosalam 2009). In this framework the rc beams and columns are modeled using the regularized forced-based fiber-section elements with distributed plasticity formulation (over specified inelastic regions; at the ends of member), beamwithhinges beam-element developed by (Scott and Fenves 2006), which is computationally efficient and which avoid also the localization and nonobjectivity issues common with softening behavior of rc members (Calabrese et al. 2010, Scott and Fenves 2006). The elastic part of the beamwithhinges is provided with 50 percent crack section stiffness properties. Such modelling technique is also used for rc bare frames.

33

Strength Evaluation of Masonry Infill: A nonlinear axial stress-strain hysteretic rule (for the middle nonlinear fiber section hinge portion), cross sectional area of the strut and masonry moduli (used for the elastic part of strut) are required to completely define the masonry infill model. A number of analytical models are available to compute the required width of the strut for different types of masonry typology (Crisafulli 2008, Smyrou et al. 2011, 2006), the present study used the model developed by Mainstone (1971):

( ) 40.0n

Hcos

L175.0W

λθ= (19)

25.0

ncc

m

HIE4

2sinbE

θ=λ (20)

where W represents the width of diagonal strut; Ln represents the net horizontal dimension of infill panel; θ = arctan(Hn/Ln); Hn represents the infill height; H represents the column height; b represents the thickness of infill; Ic represents the moment of inertia of the exterior frame columns; Ec represents the concrete Young modulus; Em represents the masonry Young modulus in the diagonal direction (Kappos et al. 1998, Sacchi and Riccioni 1982). The maximum axial strength of strut is obtained using the empirical strength model proposed by Fardis and Calvi (1994). A tri-axial stress-strain hysteretic rule is assigned to diagonal strut (nonlinear hinge at the middle of the strut). The cracking strength is assumed as 60 percent of the maximum axial strength:

θ=θ cos

bfaLP cn (21)

where Pθ represents the axial strength of diagonal strut; Ln represent the horizontal length of infill; b represents the infill thickness; fc represents the diagonal compression strength; a represents the reduction coefficient varies between 1 and 1.3. In the absence of the diagonal strength of panel, Kadysiewski and Mosalam (2009) recommend to consider a as 1 and fc considered as the shear strength of masonry which is a widely available parameter for masonry material. A hinge length of 40 percent is assumed for diagonal strut length in order to provide a moderate ductility. A test case study has been performed on typical Pakistani bare concrete frame model to check if shear failure may occur in the columns, which is confirmed (Ahmad et al. 2011). However, such failure occur soon after the upper bound strain and drift limits generally recommended (Crowley et al. 2006) for ultimate limit state of existing structures. Thus, only the flexure type of modelling for frame element coupled with the proposed limit states for existing structures are used for fragility analysis. 3.4 Fragility Functions for Case Study Structures

Design of Case Study Structures for Analysis:

Due to unavailability of detailed case study structural models besides the complexity and huge computational cost required for dynamic analyses of 3D complex structures. 2D Prototype structural models are designed for static and dynamic seismic analysis (i.e. derivation of IDA curves, computation of vibration period, limit state drift limits and consequently derivation of analytical fragility functions). The structural models are generated using Monte Carlo simulation. It included 50 structural models for a given class of structures. The generated prototype structures are designed with structural characteristics prevailing in the considered region. The uncertainty in material and geometric properties is defined in a probabilistic fashion (i.e. for each structural design parameter 50 random values are generated using specified likelihood function). Conservatively, lognormal distribution function is considered in the present study. Table 2 shows the various parameters and their uncertainties considered in the present study. Acceleration Time Histories for Dynamic Analysis:

In order to calibrate the selected methodologies for the case study structures, non-linear dynamic analysis of structure models is performed using ten natural acceleration time histories extracted from the PEER NGA database. The selected records are obtained mainly for soil type C and D of NEHRP

34

soil classifications, soil types recommended for the regions in Pakistan in case of unavailability of detailed site data. The mean acceleration response spectrum of records is also compatible to the code specified acceleration response spectrum for type D soil, as per specification of BCP (2007). Figure 24 shows the characteristics of accelerograms used in the present study.

Table 2 Geometric and material properties and probabilistic distribution type of case study structure models

Parameter Mean COV (%) Min. Max. Distribution

Brick Masonry Constructions

Compressive Strength fmc (Mpa) 5 10 4 6 Truncated Lognormal

Tensile Strength ft (Kpa) 150 10 120 180 Truncated Lognormal

Effective Young Modulus Eeff (Mpa) 1750 10 1400 2100 Truncated Lognormal

Effective Shear Modulus Geff (Mpa) 700 10 560 840 Truncated Lognormal

Masonry Unit Weight γm(kN/m3) 18 10 15 21 Truncated Lognormal

Wall Density Wd (%) 6.04 30 3.30 9.21 Truncated Lognormal

Floor Area Af (%) 67.43 62 24.42 172.13 Truncated Lognormal

Block Masonry Constructions

Compressive Strength fmc (Mpa) 2.33 10 1.63 3.03 Truncated Lognormal

Tensile Strength ft (Kpa) 69.90 10 48.90 90.90 Truncated Lognormal

Effective Young Modulus Eeff (Mpa) 815.50 10 570.50 1060 Truncated Lognormal

Effective Shear Modulus Geff (Mpa) 326.20 10 228.20 424.20 Truncated Lognormal




Stone Masonry Constructions



Effective Young Modulus Eeff (Mpa) 1148 10 1057 1256 Truncated Lognormal



Wall Density Wd (%) 17.91 30 9 40 Truncated Lognormal

Floor Area Af (%) 59.11 62 24.51 133 Truncated Lognormal

Adobe Masonry Constructions



Effective Young Modulus Eeff (Mpa) 165.38 10 132.72 212.32 Truncated Lognormal


Masonry Unit Weight γm(kN/m3) 18 - - - Truncated Lognormal



Concrete Constructions

Concrete Crushing Strength fc (Mpa) 14.16 27.16 8.15 22.82 Truncated Lognormal

Steel Tensile Strength fy (Mpa) 260.09 27.40 13.82 465.69 Truncated Lognormal

Strut Compressive Strength fmθ (Mpa) 1.22 24.75 0.81 1.95 Truncated Lognormal

35

Strut Width WS (m) 0.58 - - - Truncated Lognormal

Strut Axial Strength Pθ (kN) 162.78 24.75 107.54 260.31 Truncated Lognormal

Concrete Young Modulus Ec,eff (Mpa) 9327 13.43 7136 11944 Truncated Lognormal

Strut Young Modulus Em,θ (Mpa) 915.90 24.75 605.10 1465 Truncated Lognormal

Wooden & Timber Constructions

Lateral Strength fy (Mpa) 14.16 27.61 8.15 22.82 Truncated Lognormal

Effective Stiffness ky (Mpa) 260.10 27.40 13.82 465.69 Truncated Lognormal

Seismic Mass M (Ton) 1.22 24.75 0.81 1.95 Truncated Lognormal

Wall panel Length LW (m) 0.58 - - - Truncated Lognormal

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Period (sec)

Spect

ral A

cce

lera

tion (

1/P

GA

)

BCP-2007, D SoilMean SpectrumIndividual Record

(PGA-Normalized Spectrum)

0 1 2 3 4 50

0.5

1

1.5

2

Period (sec)

Spe

ctra

l Dis

pla

cem

ent

(1/

PG

D)

BCP-2007, D SoilMean SpectrumIndividual Record

(EC8 Specified PGD at Target PGA 0.4g-Normalized Spectrum)

(Details of Individual Record)

Figure 24 Characteristics of the accelerograms used in the present study. From left to right and top to bottom: acceleration response spectrum, displacement response spectrum and details of the individual record.

The acceleration time histories are linearly scaled for dynamic analysis, contrary to the cloud approach (where large number of un–scaled accelerograms are employed), for the simplicity reason in order to facilitate incremental dynamic analysis. The linear scaling of accelerograms may results in a biased prediction of response parameters. Nevertheless, different contradictory findings i.e. over prediction (Carballo 2000) and under prediction (Naeim and Lew 1995) with linear scaling have been observed in the past. A recent detailed study conducted by Hancock et al. (2008) using different scaling approaches observed that each of the scaling and matching approaches are able to adequately capture the expected response of the structure. However, the variability of the observations decreases consistently as one scales and matches the records using more stringent criteria, (i.e. as one moves from linear scaling to the target acceleration at the initial period of the structure to spectrally matching to multiple damping ratios). Thus, linear scaling will result in relatively higher estimate of dispersion (large uncertainties) in seismic demand, which is positive.

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Vibration Period of Case Study Structures:

The DBELA method presented earlier, make use of the response spectra and secant vibration period (see Eq. 2) of structure to compute seismic displacement demand on that structure. It is used then for the capacity demand check at different limit states in order to assess the damage state of structure for a given seismic demand and derive vulnerability functions, when considering group of structures. The vibration period is thus an essential parameter in displacement-based vulnerability assessment of structures. Many building design codes suggest simplified empirical relationships for the estimation of vibration period of structures as a function of the height of the structure, number of storeys of structures, length of lateral force resisting walls and/or cross-sectional area of walls. Similar relationships can be found also in the current building code of Pakistan (BCP 2007). These code-specified relationships have been recommended for force-based design of structures which generally provide conservative (lower) estimates of period whereby the base shear force is predicted conservatively (higher). However recent investigation of existing structures have shown that the code specified equation may underestimate the period by more than 20 percent (Ahmad et al. 2011, Crowley and Pinho 2004, 2010, Goel and Chopra 1998) among others. Thus, the use of code specified period equations may result in lower estimate of structure vulnerability and consequently reduced earthquake losses using displacement-based assessment (Crowley et al. 2004, Priestley et al. 2007). Thus, the estimation of vibration period of structures under evaluation is essential with due consideration of actual field condition.

Equivalent SDOF system and the Yield Vibration Period: Recently, Ahmad et al. (2010) extended the idea of Priestley et al. (2007) and Crowley and Pinho (2004) for the single degree of freedom idealization of structures using dynamic analysis. The procedure included dynamic analysis of case study structures for a suite of acceleration time histories. For each of the analysis the base shear demand and lateral floor displacements are obtained which are converted to the equivalent properties in terms of lateral force and displacement to represent the structure lateral response as an equivalent SDOF system. The equivalent displacement is obtained using Eq. (22) and the corresponding equivalent lateral force is obtained using Eq. (23) which are used to compute the lateral force-displacement response of structure.

∑

∑

=

=

∆

∆=∆

n

1i ii

n

1i

2ii

eqM

M (22)

eqeq M

VBVB = (23)

eq

n

1i iieq

MM

∆

∆= ∑ = (24)

eq

eqy VB

2T∆

π= (25)

where Δeq represents the equivalent displacement at the centre of seismic force; Mi represents the ith floor mass; Δi represents the ith floor displacement for a target damage state at the critical storey; VB represents the base shear force demand on structure for the target damage state; VBeq represents the equivalent lateral force and Meq represents the equivalent mass of the equivalent SDOF system. Once VBeq and Δeq are obtained for the considered accelerograms, the vibration period of the structure can be computed using Eq. (25).

This procedure have few advantages: 1) the deformed shape is not pre-assumed but obtained actually from the observed response (this also helps to develop the actual nonlinear mechanism in the structure), 2) it takes into account the record-to-record variability in the observed deformed shape of the structure and hence the vibration period, and 3) it can provide estimate of vibration period exactly at the specified damage state regardless of any arbitrary idealization of lateral force-displacement curve, by this it can relate directly the critical storey damage state to the global capacity parameters

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(i.e. displacement capacity and vibration period). The first point may not be very crucial for low-rise and regular structures where higher modes are not significant to affect the deformed shape of structure. However, the second and third points are important to provide an estimate of record-to-record variability in the capacity parameters and carry out capacity demand check exactly at the specified damage state. The nature of the procedure (equivalent single degree of freedom idealization) also make it compatible with the fundamentals of DBELA methodology which uses substitute-structure idealization. The procedure also has ease in the computation of vibration period for a target damage state, no matter if the structure has even exceeded the higher damage levels. However, the target damage state must be reached/exceeded at least. Other procedures common for the structure vibration period estimation are also used. For example, the Eigen Value Analysis (EVA), Fast Fourier Transformation (FFT), and Time History Analysis (THA) for Predominant Period Estimation from the structure response history.

It is worth to mention that, the two procedures FFT and THA based predominant period estimation both results in very similar estimate of vibration period due to the fact that both use the time history of response for a specified ground motions. Slight differences may arise simply due to the use different hypothesis to compute the predominant period, as the one FFT uses the frequency domain while the other THA uses the time domain. Thus, only the THA based predominant period and initial period are considered for comparison. Figure 25 shows the elongation of yield vibration period relative to the initial crack period and comparison with the code-specified period formulae.

Figure 25. Comparison of the estimated yield vibration period. From top to bottom: Vibration period elongation mean value in SDOF systems relative to initial crack period and the ratio of yield vibration period mean value to the period obtained using code specified formulae.

Period-Height Relationship: The present study included the linear regression technique to develop the period-height relationship, obtaining the coefficients in the equation. It included fitting a curve to the data (observed period value) obtained for each structure type which is presented as a function of the height of structure. Considering the general form of empirical equation of vibration period (Eq. 26), it can be seen that it is non-linear as the height is given a certain power. Presenting the equation in a logarithmic form, it can be deduced to linear form as given,

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bTaHTy = (26)

( ) ( ) ( ) iiTy OHlog.balogTlogi

++= (27)

iii ObXAY ++= (28)

( )Aexpa =

where Tyi represents the observed ith vibration period; Oi represents error of the function for a given ith observation. The general regression analysis technique include the identification/quantification of equation/coefficients that minimize the error in the functions (i.e. the sum of the squares SSE of the error):

( )∑∑==

−−==n

1i

2ii

n

1i

2i bXAYOSSE (29)

The above equation can be differentiated with respect to A and b respectively to derive explicit functions for the two coefficients,

XY bA µ−µ= (30)

( )( )XVar

Y,XCOVb = (31)

( ) ( )[ ] ( )[ ]∑=

µ−µ−=n

1iii YYXX

N

1Y,XCOV

( ) ( )XXVar 2σ=

where COV represents the covariance of vectors (i.e. X and Y); Var represents the variance of vector (i.e. X). This hypothesis will provide estimate of coefficients that will provide best estimate of structure vibration period for the considered case. The study also included the constraint regression analysis for period-height relationship, where b is set to unity 1.0, following the proposal of Crowley and Pinho (2010). Figure 26 shows the derived empirical equations for the case study structures using un-constraint regression analysis. Table 3 report the period-height function coefficients derived using both constraint/un-constraint regression analysis. it can clearly observed that the code-specified equation may should not be used directly for assessment purposes without modification. It is worth to mention that these relationships are derived only for low-rise structures but which is nevertheless practised the most in the country. The derived period-height relationships are intended for the displacement-based assessment of considered structures. These relationships cannot be directly employed for code specified force-based design of structures.

(Masonry and Timber Structures)

(Concrete Structures)

Figure 26. Comparison of the derived period-height relationships with code specified relationships. From left to right: masonry and timber structures (height-based period only) and concrete structures (height-based and shear area-based).

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Table 3 Period-height relationships for case study structures. Case-I and Case-II represent heavy floor and light floor structures for masonry and timber structures and infill and bare frames for concrete structures.

Structure Type

Un-Constrained Regression Constrained Regression

Case-I Case-II Case-I Case-II

a b a b a b a b

Brick Masonry 0.019 1.397 0.011 1.546 0.038 1.000 0.028 1.000

Block Masonry 0.005 2.321 0.005 2.242 0.054 1.000 0.041 1.000

Stone Masonry 0.025 1.330 0.021 1.375 0.044 1.000 0.039 1.000

Adobe Masonry 0.084 0.934 0.066 0.950 0.079 1.000 0.063 1.000

Timber Structures 0.261 1.000 0.112 1.000 0.261 1.000 0.112 1.000

RC Structures 0.042 1.000 0.125 1.000 0.042 1.000 0.125 1.000

IDA of Case Study Structures

the NDRM method included herein for the fragility analysis of structures, as presented earlier (see Figure 16), require the derivation of IDA curves for structures. The case study structural models (50 structures for each typology) to a suite of ground motion records, scaled to multiple levels with increasing intensity, to derive curves of response parameters (inter-storey drift demand) versus target intensity of ground motions (Vamvatsikos and Cornell 2002). The drift demand obtained from non-linear dynamic analysis included primarily the record-to-record variability in demand considering a particular random structure. It considers the geometric and material uncertainties in the drift demand, hence total uncertainties, since various case study structures are considered.

Structural Fragility Functions

For DBELA-based fragility functions, controlled Monte Carlo simulation is used to generate random structures with different geometric and mechanical properties considering lognormal probability density function (pdf) for all the parameters involved in the capacity evaluation (i.e. limit state displacement capacity, viscous damping and vibration period). The distribution function parameters (i.e. mean and coefficient of variation and/or standard deviation) are used in the random generation. The lognormal pdf is considered for simplicity reasons and to be conservative in structural capacity estimation. The distribution parameters for vibration period (as presented earlier), viscous damping and drift limits are obtained from the available experimental investigation and numerical analysis. For dynamic-based fragility functions through reliability method, the definition of inter-storey drift demand in terms of median and dispersion (logarithmic standard deviation) is required for a given structure types (Eq. 12). The inter storey drift limits for masonry structures are obtained for each of the individual structural system in the random generation. The drift limit corresponding to DS1 (first limit state at the attainment of 60 percent shear strength force in the storey) is obtained by computing the storey stiffness (50 percent cracked) and the cracking storey shear strength (60 percent of the maximum strength); DS2 (yielding limit state) is obtained similarly at the development of full yielding force at the story level; DS3 (maximum damage state) is considered as 3/4 of the ultimate drift limit, however a 10 percent reduction is made in order to be conservative; DS4 (ultimate damage state: collapse of the system) is computed using the ductility model of (Frumento et al. 2009). It is worth to mention that this model was particularly developed for solid fired brick units and cement mortar, which is further modified (reduction is made conservatively) based on the performance prediction of the tested structure. However, the concept can be reasonably generalized for an unreinforced pressure material like masonry (i.e. the ductility capacity reduces with increasing pre-compression on the masonry walls). For timber structures, the drift limits are obtained in similar fashion using the simplified models (mainly the model for lateral strength, yield displacement, and ductility estimation i.e. Eq. 14 to Eq. 18) developed through experimental and numerical investigation of full scale timber framing

40

systems. The DS1 drift limit state for timber structures is considered as 80% of the yield drift capacity, the ultimate drift limit is obtained using Eq. (17) while the DS3 is computed in similar fashion as the masonry (i.e. 2/3 of ultimate drift capacity). For the case of concrete structures the drift limits derived by Rossetto and Elnashai (2003) for non-ductile concrete frames and concrete infill-frame structures obtained through experimental investigation are considered. However, the drift limits are reduced by 50 percent for collapse and heavy damage limit states and 80 percent for yield limit state in order to be conservative in fragility functions derivation. Table 4 shows the drift limit states considered for fragility fucnoitons derivation. Table 4 Drift limits for global limit states of case study structures. Case I and Case II represent heavy floor and light floor structures for masonry and timber structures while infill and bare frames for concrete structures.

Structure Type

Calculated Drift Limits (%)

Case-I Case-II Case-I Case-II

DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4

Brick Masonry

Mean 0.06 0.09 0.29 0.44 0.04 0.06 0.26 0.39

Std. Dev. 0.12 0.13 0.08 0.08 0.11 0.10 0.13 0.13

Block Masonry

Mean 0.09 0.13 0.37 0.55 0.06 0.10 0.35 0.52

Std. Dev. 0.17 0.18 0.08 0.08 0.14 0.15 0.07 0.07

Stone Masonry

Mean 0.09 0.13 0.61 0.92 0.07 0.11 0.59 0.89

Std. Dev. 0.04 0.05 0.04 0.04 0.05 0.05 0.04 0.04

Adobe Masonry

Mean 0.05 0.08 0.37 0.55 -- -- -- --

Std. Dev. 0.03 0.04 0.04 0.04 -- -- -- --

Timber Structures

Mean 0.40 0.50 1.50 2.25 -- -- -- --

Std. Dev. 0.06 0.06 0.06 0.06 -- -- -- --

RC Structures

Mean 0.08 0.24 0.57 1.39 0.44 0.80 1.16 2.05

Std. Dev. 0.05 0.05 0.12 0.12 0.07 0.06 0.15 0.14

For derivation of fragility function in case of DBELA methodology, inelastic displacement demand i.e. overdamped displacement spectrum is considered for the capacity demand comparison. This includes the limit states capacity demand comparison at the secant vibration period where overdamping of the 5 percent damped elastic displacement spectra is performed using the spectral overdamping/reduction factor as proposed by EC8 CEN (2004) and the system viscous damping:

eq5

10

ξ+=η (32)

where η represents the spectral overdamping/reduction factor. This factor actually takes into account the energy dissipation capability of structural system by lowering the seismic demand on that system. The energy dissipation is provided by the nonlinear hysteretic response of elements in real structures for a given earthquake demand. The hysteretic damping mentioned earlier can be best obtained through experimental investigation. This include the investigation of structural elements through

41

cyclic tests for the derivation of lateral force-displacement hysteretic response where the energy dissipation of the element is computed in terms of the hysteretic damping coefficient using Eq. (33), which aim at quantifying the ratio of energy dissipated by the element due to nonlinear behavior in a complete stable cycle to the input energy required to force that element to the target lateral displacement:

e

hhyst A4

A

π=ξ (33)

where Ah represents the area within one stable complete cycle at a given level of deformation in the element under investigation; Ae represents the area of the elastic response for the same peak deformation level and peak force observed during the cycle. In the present study fitting is performed to various available experimental data to derive a simplified model for the viscous damping model (as shown in Eq. 5 to Eq. 6). Table 5 reports the viscous damping for different structural types, used herein, obtained from the available literature. In case of block masonry and stone masonry the viscous damping for brick masonry is used in the DBELA-based vulnerability assessment. It is worth to mention that the ζel term assigned with 0.05 in Eq. (5) does not represent 5% elastic damping but rather 2% elastic damping, the value 0.05 is assigned only to obtain a best fit model to the observed damping of structural systems.

Table 5 Viscous damping coefficient, C in Eq. (6), used herein for different structural types.

Structure Type C Source Remarks

Brick Masonry 0.32 Javed (2008) The total viscous damping include also 2% elastic damping.

Adobe Masonry 0.41 Tarque et al. (2012) The damping obtained for the Peruvian adobe masonry is reduced by 10% in order to be conservative.

Timber Structures 0.74 Ali et al.(2012) The total viscous damping include also 2% elastic damping.

RC Frames 0.51 Priestley et al. (2007) The damping obtained for concrete frames is reduced by 10% in order to be conservative.

RC–Infill Frames 0.62 Priestley et al. (2007)

The damping obtained for concrete frames is increased by 10% to include the additional damping may be provided by damage to infill.

Once the two methods were developed, fragility functions were derived using the step by step procedures as explained earlier. Figure 27 and Figure 28 reports the derived fragility functions using the two methodologies and best fitting to the data to obtain the parameters for fragility derivation model (i.e. Eq. 8) for future applications.

3.5 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) Level-3 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.

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Figure 27 Fragility functions derived through DBELA method for the case study structures.

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e


(W1) (W2)

Figure 28 Fragility functions derived through NDRM method for the case study structures.

44

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. Heavy/Light 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 29 and Figure 30 reports the comparison of the estimated damage scenarios with the observation in the earthquakes. 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

45

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.

Stone Masonry Block Masonry Brick MasonryConcrete Structures0

20

40

60

80

100

Structure Typology

Perc

enta

ge o

f S

truct

ure

s

DBELA-OriginalDBELA-AdjustedNDRM-OriginalNDRM-AdjustedObserved

(2005 Kashmir Earthquake)

(2008 Balochistan Earthquake)

Figure 29 Simulation of Structure-Wise Damage Scenario for 2005 Kashmir Earthquake and District/Structure-Wise Damage Scenario for 2008 Balochistan Earthquake. Mean Estimate using DBELA-Based and NDRM-Based Fragility Functions (Original and Adjusted) and Comparison with the Observed Damaged and Collapsed Structures.

(Observed Damages, 2005 Kashmir Earthquake)

(Estimated Damages, 2005 Kashmir Earthquake)

Figure 30 Simulation of District Wise Level-3 Damage Scenario for 2005 Kashmir Earthquake. From Top to Bottom and Left to Right: Observed Damaged and Collapsed Structures, after ERRA (2006a) and Mean Estimated using DBELA-Based and NDRM-Based Global Weighted Fragility Functions.

46

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 31), 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 31 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 rRPmMPr,m|gmGMPνgmλ ==>≅ ∑∑∑ (34)

[ ] ( )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

47

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), Rafi et al. (2012), 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:

[ ] ( )tAREe11NP ×−−=≥ (35)

where P[N ≥1 ] 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 3232 reports the derived hazard curves for the case study 110 Districts in Pakistan.

(Ground Motions ARE)

(Ground Motions PE)

(Ground Motions PE, GSHAP Seismicity Model)

(Ground Motions PE, PMD Seismicity Model)

Figure 32 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.

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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 33 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 33 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∑∑=

++∞→

+ ×++×

−=

(36)

49

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. (2008) 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, which is nevertheless conservative. 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. The individual cost of a building for a given class is decided based on the expert opinion (i.e. by interviewing experts involved in constructions and re-constructions of buildings in the region). In this regard we considered the Earthquake Engineering Center and the Department of Civil Engineering of UET Peshawar as a reference. Figure 34 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. 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.

Figure 34 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.

5 Loss Prediction Tables Aim and Objective

The general loss estimation framework (Error! Reference source not found.) 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

50

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.

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 (i.e. magnitude) and location (i.e. epicentre and depth of hypocenter), 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.

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 35 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.

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. (37) can be used approximately.

( )εβ0.5βMean

2

eLossLoss ±−= (37)

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

51

Figure 35 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

are derived through constraint nonlinear regression analysis for the case study structures for different type of loss estimate:

0.46lapseDamage/Col 11.05DSβ −=

0.46MDR 0.76MDRβ −=

0.36Fatalities 3.35Fβ −=

0.36Injuries 4.93Iβ

−=

0.51Homeless 12.21Hβ −=

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

52

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. 2011), whereas a factor of 4 percent 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 (i.e. for Level-3 analysis). 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.

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.

Abrahamson, N.A., and Youngs, R.R. (1992), “A stable algorithm for regression analyses using the random effects model,” Bulletin of the Seismological Society of America, 82(1), 505-510.

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

Ahmad, N., Ali, Q., Umar, M. (2013), “Seismic vulnerability assessment of multistorey timber braced frame traditional masonry structures,” Advanced Material Research, 601, 168-172.

Ahmad, N., Ali, Q., Umar, M. (2012a), “Simplified engineering tools for seismic analysis and design of traditional Dhajji-Dewari structures,” Bulletin of Earthquake Engineering, 10(05), 1503-1534.

Ahmad, N., Ali, Q., Ashraf, M., Alam, B. and Naeem, A. (2012b), “Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures, experimental and analytical Studies,” Natural Hazards and Earth System Sciences, 12(11), 3441-3454.

Ahmad, N., Crowley, H., Pinho, R., Ali, Q., (2011), “Displacement-based earthquake loss assessment of adobe buildings in Pakistan,” Contribution to Book Chapter “Seismic Performance and Response” 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. (2010), “Displacement-Based Earthquake Loss

53

Assessment of Masonry Buildings in Mansehra City, Pakistan,” Journal of Earthquake Engineering, 14(S1), 1-37.

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

Ali, Q. (2006), “Unreinforced brick masonry residential buildings,” EERI Housing Report, World Housing Encyclopedia, Oakland, CA, USA.

Ali, Q. and Muhammad, T. (2007), “Stone masonry residential buildings,” EERI Housing Report, World Housing Encyclopedia, Oakland, CA, USA.

Ali, Q., Schacher, T., Ashraf, M., Alam, B., Naeem, A., Ahmad, N. and Umar, M., (2012), “In-plane behavior of Dhajji-Dewari structural system (wooden braced frame with masonry infill),” Earthquake Spectra, 28(03), 835-858.

Ali, Q., Naeem, A., Ashraf, M., Ahmed, A., Alam, B., Ahmad, N., Fahim, M., Rahman, S., Umar, M. (2013), “Seismic performance of stone masonry buildings used in the Himalayan Belt,” Earthquake Spectra, 29(4), November Issue.

Avouac, J., Ayoub, F., Leprince, S., Konca, O., and Helmberger, D.V. (2006), “The 2005 Mw 7.6 Kashmir earthquake: Sub-pixel correlation of ASTER images and seismic waveforms analysis,” Earth and Planetary Science Letters, 249(3-4), 514-528.

Badrashi, Y., Ali, Q., and Ashraf, M. (2010), “Reinforced concrete buildings in Pakistan,” EERI Housing Report, World Housing Encyclopedia, Oakland, CA, USA.

Bal, I.E., Crowley, H., Pinho, R. (2008), “Displacement-based earthquake loss assessment for an earthquake scenario in Istanbul,” Journal of Earthquake Engineering, 12(1), 12-22.

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. (2010a) “The Influence of Geographical Resolution of Urban Exposure Data in an Earthquake Loss Model for Istanbul,” Earthquake Spectra, 26(3), 619-634.

Bal, I.E., Crowley, H., and Pinho, R. (2010b), “Displacement-based earthquake loss assessment: Method development and application to Turkish building stock,” Technical Report, IUSS Press, Pavia, Italy.

Balassanian, S. (2000), “Seismic risk reduction strategy in the XXI century,” In Balassanian, S., Cisternas, A., and Melkumyan, M.(eds.), Advances in natural and technological hazards research: Earthquake hazard and seismic risk reduction, 12(1), 1-11.

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

BCP (2007), “Building code of Pakistan: Seismic provisions-2007,” Technical Report, Ministry of Housing and Works, Islamabad, Pakistan.

Bilham, R. (2004), “Earthquakes in India and in the Himalaya: Tectonic, Geodesy, and History,” Annals of Geophysics, 47(2/3), 839-858.

Bird, J.F. and Bommer, J.J. (2004), “Earthquake losses due to ground failure,” Engineering Geology, 75(2), 147-179.

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.

54

Bommer, J.J. and Martinez-Pereira (1999), “The effective duration of earthquake strong motion,” Journal of Earthquake Engineering, 3(2), 127-172.

Bommer, J., Spence, R., and Pinho, R. (2006a), “Earthquake loss estimation models: time to open the black boxes?,” Proceedings of The First European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland.

Bommer, J., Pinho, R., and Crowley, H. (2006b), “Using a displacement-based approach for earthquake loss estimation,” In Wasti, S. T. and Ozcebe, G. (eds.), Advances in Earthquake Engineering for Urban Risk Reduction, 489-504.

Bommer, J.J., Spence, R., Erdik, M., Tabuchi, S., Aydinoglu, N., Booth, E., Del-Re, D., and Peterken, O. (2002), “Development of an earthquake loss model for Turkish catastrophe insurance,” Journal of Seismology, 6(3), 431-446.

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.

Boore, D.M., Gibbs, J.F., Joyner, W.B., Tinsley, J.C. and Ponti, D.J. (2003), “Estimated Ground Motion From the 1994 Northridge, California, Earthquake at the Site of the Interstate 10 and La Cienega Boulevard Bridge Collapse, West Los Angeles, California,” Bulletin of the Seismological Society of America, 93(6), 2737-2751.

Borzi, B., Crowley, H., and Pinho, R. (2008a), “Simplified pushover-based earthquake loss assessment (SP-BELA) method for masonry buildings,” International Journal of Architectural Heritage, 2(4), 353-376.

Borzi, B., Crowley, H., and Pinho, R. (2008b), “Simplified pushover-based vulnerability analysis for large-scale assessment of RC buildings,” Engineering Structures, 30(3), 804-820.

Bothara, J. and Brzev, S. (2011), “A Tutorial: improving the seismic performance of stone masonry buildings,” EERI Technical Report, Earthquake Engineering Research Institute (EERI), Oakland, CA, USA.

Bradley, B.A. (2010), “Epistemic uncertainties in component fragility functions,” Earthquake Spectra, 26(1), 41-62.

Briceno, S. (2010), “Investing today for a safer future: How the Hyogo Framework for Action can contribute to reducing deaths during earthquakes,” In Garevski, M. and Ansal, A. (eds.), Earthquake Engineering in Europe, 17(6), 441-461.

Calabrese, A., Almeida, J., and Pinho, R. (2010), “Numerical issues in distributed inelasticity modeling of rc frame elements for seismic analysis,” Journal of Earthquake Engineering, 14(S1), 38-68.

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.

Calvi, G. M. (1999), “A displacement-based approach for vulnerability evaluation of classes of buildings,’’ Journal of Earthquake Engineering, 3(3), 411-438.

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.

Carballo, J.E. (2000), “Probabilistic seismic demand analysis spectrum matching and design,” PhD Thesis, Stanford University, CA, USA.

CEN (1994), “Eurocode 6: Design of masonry structures- Part 1-1: General rules for buildings. Rules for reinforced and unreinforced masonry,” ENV 1996-1-1, Comité Européen de Normalisation, CEN, Brussels.

55

CEN (2004), “Design of structures for earthquake resistance. part-1: general rules, seismic actions and rules for buildings,” EN 1998-1-3, Comite Europeen de Normalisation, Brussels, Belgium.

Chandra, U. (1992), “Seismotectonics of Himalaya,” Current Science, 62(1-2), 40-71.

Coburn, A. and Spence, R. (2002), “Earthquake Protection,” John Wiley and Sons Ltd., West Sussex, England.

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.

Crisafulli, F. (2008), “Seismic behavior of reinforced concrete structures with masonry infills,” PhD Thesis, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.

Crowley, H. and Pinho, R. (2010), “Revisiting Eurocode 8 formulae for periods of vibration and their employment in linear seismic analysis,” Earthquake Engineering and Structural Dynamics, 39(2), 223-235.

Crowley, H. and Pinho, R. (2008), “Using basic principles of mechanics of materials to assess the seismic risk of entire countries,” Environmental Semeiotics, 1(1), 1-s19.

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.

CSI (1999), “SAP2000: Three dimensional static and dynamic finite element analysis and design of structures,” Computers and Structures Inc. (CSI), Berkeley, CA, USA.

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.

Doherty, K., Griffith, M.C., Lam, N., and Wilson, J. (2002), “Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls,” Earthquake Engineering and Structural Dynamics, 31(4), 833-850.

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.

Elms, D.G. (2004), “Structural safety-issues and progress,” Progress in Structural Engineering and Materials, 6(2), 116-126.

Elnashai, A.S. and Di Sarno, L. (2008), “Fundamentals of earthquake engineering,” John Wiley and Sons Ltd., West Sussex, UK.

Erdik, M., Sesetyan, K., Demircioglu, M.B., Hancilar, U., and C., Z. (2010), “Rapid earthquake loss assessment after damaging earthquakes,” In Garevski, M. and Ansal, A. (eds.), Earthquake Engineering in Europe, 17(6), 523-547.

Erdik, M., Fahjan, Y., Ozel, O., Alcik, H., Mert, A., and Gul, M. (2003), “Istanbul earthquake rapid

56

response and early warning system,” Bulletin of Earthquake Engineering, 1(1), 157-163.

ERRA (2006a), “Earthquake reconstruction and rehabilitation in earthquake affected areas,” Web Report, Earthquake Reconstruction and Rehabilitation Authority (ERRA), Islamabad, Pakistan.

ERRA (2006b), “No. of houses destroyed by Tehsil: progress up to 5 June 2006,” Technical Report, Earthquake Reconstruction and Rehabilitation Authority (ERRA), Islamabad, Pakistan.

Faccioli, E., Paolucci, R., and Rey, J. (2004), “Displacement spectra for long periods,” Earthquake Spectra, 20(2), 347-276.

Fardis, M. and Calvi, G. (1994), “Effects of infill on the global response of reinforced concrete frames,” Proceedings of the Tenth European Conference on Earthquake Engineering, Vienna, Austria.

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.

Galasco, A., Lagomarsino, S. and Penna, A. (2002), “TREMURI Program: seismic analyses of 3D masonry buildings,” University of Genoa, Genoa, Italy.

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

Glaister, S. and Pinho, R. (2003), “Development of a simplified deformation-based method for seismic vulnerability assessment,” Journal of Earthquake Engineering, 7(S1), 107-140.

Goel, R.K. and Chopra, A.K. (1998), “Period formulas for concrete shear wall buildings,” Journal of Structural Engineering, ASCE, 124(11), 426-433.

Griffith, M.C., Magenes, G., Melis, G., and Picchi, L. (2003), “Evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitations,” Journal of Earthquake Engineering, 7(1), 141-169.

Gregor, N. and Bolt, B. (1997), “Peak strong motion attenuation relations for horizontal and vertical ground displacement,” Journal of Earthquake Engineering, 1(2), 275-292.

Javed M. (2008), “Seismic risk assessment of unreinforced brick masonry buildings of northern Pakistan,” PhD Thesis, University of Engineering & Technology, Peshawar, KP Pakistan.

Javed M., Naeem, A. and Magenes G. (2008), “Performance of masonry structures during earthquake-2005 in Kashmir,” Mehran University Research Journal of Engineering & Technology, 27(3), 271-282.

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.

Kadysiewski, S. and Mosalam, K. (2009), “Modeling of unreinforced masonry infill walls considering in-plane and out-of-plane interaction,” Technical Report, Pacific Earthquake Engineering Research Center (PEER), Berkeley, CA, USA.

Kappos, A., Penelis, G., and Drakopoulos, C. (2002), “Evaluation of simplified models for lateral load analysis of unreinforced masonry buildings,” Journal of Structural Engineering, 128(7), 890-897.

Kappos, A., Stylianidis, K., and Pitilakis, K. (1998), “Development of seismic risk scenarios based on a hybrid method of vulnerability assessment,” Natural Hazards, 17(2), 177-192.

57

Khan, M.A. (2007), “disaster preparedness for natural hazards: current status in Pakistan,” Technical Report, International Centre for Integrated Mountain Development, Kathmandu, Nepal.

Kircher, C.A., Nassar, A.A., Kustu, O., and Holmes, W.T. (1997), “Development of building damage functions for earthquake loss estimation,” Earthquake Spectra, 13(4), 663-682.

Kouris, L.A.S. and Kappos, A.J. (2012), “Detailed and simplified non-linear models for timber-framed masonry structures,” Journal of Culture Heritage, 13(1), 47-58.

Lam, N. and Chandler, A. (2005), “Peak displacement demand of small to moderate magnitude earthquakes in stable continental regions,” Earthquake Engineering and Structural Dynamics, 34(9), 1047-1072.

Langenbach, R. (2010), “Rescuing the baby from the bathwater: Traditional masonry as earthquake-resistant construction,” Proceedings of the Eight International Masonry Society, Dresden, Germany.

Langenbach, R. (2009), “Don’t Tear it Down: preserving the earthquake resistant vernacular architecture of Kashmir,” Oinfroin Media, Oakland, CA, USA.

Lobo, N.V. (2010), “Regional modeling beyond insurance,” Proceedings from the 2010 UR Forum, Washington, DC, USA.

Lodhi, S. (2010), “Working Plan 4: city scenarios,” Presentation at the Coordination Meeting of Earthquake Model of the Middle East Region (EMME).

Magenes, G. (2006), “Masonry building design in seismic areas: recent experiences and prospects from a European standpoint,” In Proceedings of the first European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, Paper No. K9.

Magenes, G. (2000), “A method for pushover analysis in seismic assessment of masonry buildings,” Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand.

Magenes, G. and Calvi, G.M. (1997), “In-plane seismic response of brick masonry walls,” Earthquake Engineering and Structural Dynamics, 26(11), 1091-1112.

Magenes, G. and Fontana, D. (1998), “Simplified non-linear seismic analysis of masonry buildings,” Proceedings of the 5th British Masonry Society, London, UK.

Magenes, G., Bolognini, D., and Braggio, C. (2000), “Metodi Semplificati per l’Analisi Sismica Non Linear di Edifici in Muratura,” Technical Report, CNR-Gruppo Nazionale per al Difesa dai Terremoti (GNDT), Roma, Italy.

Mahul, O. (2010), “Promoting disaster risk financing in developing countries-The role of catastrophe risk modeling,” Proceedings from the 2010 UR Forum. Washington, DC, USA.

McGuire, R.K. (2004), “Seismic hazard and risk analysis,” Earthquake Engineering Research Institute, Oakland, CA, USA.

Meireless, H.A., Bento, R., Cattari, S., and Lagomarsino, S. (2012), “A hysteretic model for “frontal” walls in Pombalino buildings,” Bulletin of Earthquake Engineering, 10(5), 1481-1502.

Menon, A. and Magenes, G. (2011), “Definition of seismic input for out-of-plane response of masonry walls: I. Parametric study,” Journal of Earthquake Engineering, 15(2), 165-194.

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.

Mumtaz, H., Mughal, S.H., Stephenson, M., and Bothara, J.K. (2008), “The challenges of reconstruction after the October 2005 Kashmir earthquake,” In Proceedings of the New Zealand Society for Earthquake Engineering, Wairakei, New Zealand, Paper No. 34.

Naeim, F. and Lew, M. (1995), “On the use of design spectrum compatible time histories,”

58

Earthquake Spectra, 11(1), 111-127.

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.

NDMA (2007), “National disaster risk management framework Pakistan,” Technical Report, National Disaster Management Authority (NDMA), Islamabad, Pakistan.

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

Phillips, E., Grubisich, T., and Lyon, B. (2010), “Understanding risk: Innovation in disaster risk assessment,” In Proceedings from the 2010 UR Forum, Washington, DC, USA.

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.

Pinho, R., Bommer, J., and Glaister, S. (2002), “A simplified approach to displacement-based earthquake loss estimation analysis,” Proceedings of the Twelfth European Conference on Earthquake Engineering. London, UK.

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.

Priestley, M.J.N. (1985), “Seismic behavior of unreinforced masonry walls,” Bulletin of the New Zealand National Society for Earthquake Engineering, 18(2), 191-205.

Priestley, M.J.N. (1997), “Displacement-based seismic assessment of reinforced concrete buildings,” Journal of Earthquake Engineering, 1(1), 157-192.

Priestley, M., Calvi, G., and Kowalski, M. (2007), “Displacement-based seismic design of structures,” IUSS Press, Pavia, Italy.

Rafi, Z., Lindholm, C., Bungum, H., Laghari, A. and Ahmed, N. (2012), “Probabilistic seismic hazard of Pakistan, Azad-Jammu and Kashmir,” Natural Hazards, 61(3),1317-1354.

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

Restrepo-Velez, L.F., and Magenes, G., (2009), “Static tests on dry stone masonry and evaluation of static collapse multiplier,” Technical Report, IUSS Press, Pavia, Italy.

Restrepo-Velez, L. and Magenes, G. (2004), “Simplified procedure for the seismic risk assessment of unreinforced masonry buildings,” Proceedings of the Thirteenth World Conference on Earthquake Engineering. Vancouver, Canada.

Rose, A.Z. et al. (2007), “Benefit-cost analysis of FEMA hazard mitigation grants,” Natural Hazards Review, 8(4), 97-111.

Rossetto, T. and Peiris, N. (2009), “Observations of damage due to the Kashmir earthquake of October 8, 2005 and study of current seismic provisions for buildings in Pakistan,” Bulletin of Earthquake Engineering, 7(3), 681-699.

Rossetto, T. and Elnashai, A. (2003), “Derivation of vulnerability functions for European-type rc structures based on observational data,” Engineering Structures, 25(10), 1241-1263.

Sacchi, M. and Riccioni, R. (1982), “Comportamento Statico e Sismico Delle Strutture Murarie (in Italian).” , CLUP Editore, Milano, Italy.

Schacher, T. (2005), “Observations on the situation in the Kagan Valley, Pakistan hit by the 8 October

59

2005 earthquake,” Technical Report, Swiss Agency for Development and Cooperation-Swiss Humanitarian Aid Unit, Berne, Switzerland.

Schacher, T. and Ali, Q. (2008), “Timber reinforced stone masonry in northern Pakistan in the context of the post earthquake reconstruction efforts,” In International Seminar on Seismic Risk and Rehabilitation, Azores, Portugal.

Scott, M. and Fenves, G. (2006), “Plastic hinge integration methods for force–based beam-column elements,” Journal of Structural Engineering, 132(2), 244-252.

Shah, H.C. (2010), “Catastrophe micro-insurance for those at the bottom of the pyramid: Bridging the last mile,” In Garevski, M. and Ansal, A. (eds.), Earthquake Engineering in Europe, 17(6), 549-561.

Shah, H.C. (2009), “Catastrophe risk management in developing countries and the last mile,” In Mendes-Victor, L. A. and Oliveira, C. S. and Azevedo, J. and Ribeiro A. (eds.), The 1755 Lisbon earthquake: Revisited, 7(3), 111-120.

Shahzada, K., Naeem, A., Elnashai, A.S. Ashraf, M., Javed, M., Naseer, A. and Alam, B. (2012), “Experimental seismic performance evaluation of unreinforced brick masonry buildings,” Earthquake Spectra, 28(3), 1269-1290.

Shibata, A. and Sozen, M.A. (1976), “Substitute-structure method for seismic design in r/c,” Journal of the Structural Division - ASCE, 102(1), 1-18.

Smyrou, E., Blandon, C., Antoniou, S., Pinho, R., and Crisafulli, F. (2011), “Implementation and verification of a masonry panel model for nonlinear dynamic analysis of infilled rc frames,” Bulletin of Earthquake Engineering, 9(5), 1519-1534.

Stafford, P.J. (2007), “Basics of seismology and seismic hazard assessment: probabilistic seismic hazard analysis (PSHA),” Graduate Coursework, ROSE School-IUSS Pavia, Pavia, Italy.

Stephenson, M. (2008), “Notes from experience in post-earthquake rural housing reconstruction in Pakistan,” In Proceedings of the Building Back Better Workshop, Beijing, China.

Spence, R. (2007), “Earthquake disaster scenario predictions and loss modelling for urban areas,” LESSLOSS Report, IUSS Press, Pavia, Italy.

Tarque, N., Crowley, H., Pinho, R. and Varum, H. (2012), “Displacement-based fragility curves for seismic assessment of adobe buildings in Cusco, Peru,” Earthquake Spectra, 28(2), 759-794.

Tomazevic, M. (2000), “Earthquake resistant design of masonry buildings, innovation in structures and construction, Vol. 1,” Imperial College Press, London, UK.

Turnsek, V. and Sheppard, P. (1980), “The shear and flexure resistance of masonry walls,” Proceedings of the International Research Conference on Earthquake Engineering. Skopje, Macedonia.

UN-HABITAT (2008), “Balochistan earthquake initial assessment report October 2008,” Technical Report, UN-HABITAT, Islamabad, Pakistan.

Vacareanu, R., Lungu, D., Arion, C., and Aldea, A. (2004), “WP7-Seismic risk scenarios handbook,” Technical Report, Risk-UE Project: An advanced approach to earthquake risk scenarios with applications to different European towns.

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

Vasconcelos, G. and Lourenco, P.B. (2009), “In-plane experimental behavior of stone masonry walls under cyclic loading,” Journal of Structural Engineering, 135(10), 1269-1277.

Villaverde, R. (1997), “Seismic design of secondary structures: state of the art,” Journal of Structural Engineering ASCE, 123(8), 1011-1019.

Villaverde, R. (2004), “Seismic analysis and design of non-structural elements,” In Bozorgnia, Y.,

60

and Bertero, V.V. (eds.), Earthquake Engineering: from engineering seismology to performance-based design, CRC Press pp. 19-48.

Wyss, M. (2005), “Human losses expected in Himalayan earthquakes,” Natural Hazards, 34(3), 305-314.

Wyss, M. and Trendafiloski (2009), “Trend in the casualties ratio of injured to fatalities in earthquakes,” In Proceedings of the Second International Workshop on Disaster Casualties, University of Cambridge, Cambridge, UK.

Youngs, R.R., Abrahamson, N., Makdisi, F.I., and Sadigh, K. (1995), “Magnitude-dependent variance of peak ground acceleration,” Bulletin of the Seismological Society of America, 85(4), 1161-1176.

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