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Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 www.nat-hazards-earth-syst-sci.net/12/3441/2012/ doi:10.5194/nhess-12-3441-2012 © Author(s) 2012. CC Attribution 3.0 License. Natural Hazards and Earth System Sciences Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures, experimental and analytical studies N. Ahmad1,2 , Q. Ali2 , M. Ashraf3 , B. Alam3 , and A. Naeem3 1 ROSE School-IUSS Pavia, Pavia, Italy Engineering Center, University of Engineering & Technology (UET), Peshawar, Pakistan 3 Civil Engineering Department, University of Engineering & Technology (UET), Peshawar, Pakistan 2 Earthquake Correspondence to: N. Ahmad ([email protected]) Received: 27 April 2012 – Revised: 10 July 2012 – Accepted: 9 October 2012 – Published: 21 November 2012 Abstract. Half-Dressed rubble stone (DS) masonry structures as found in the Himalayan region are investigated using experimental and analytical studies. The experimental study included a shake table test on a one-third scaled structural model, a representative of DS masonry structure employed for public critical facilities, e.g. school buildings, offices, health care units, etc. The aim of the experimental study was to understand the damage mechanism of the model, develop damage scale towards deformation-based assessment and retrieve the lateral force-deformation response of the model besides its elastic dynamic properties, i.e. fundamental vibration period and elastic damping. The analytical study included fragility analysis of building prototypes using a fully probabilistic nonlinear dynamic method. The prototypes are designed as SDOF systems assigned with lateral, force-deformation constitutive law (obtained experimentally). Uncertainties in the constitutive law, i.e. lateral stiffness, strength and deformation limits, are considered through random Monte Carlo simulation. Fifty prototype buildings are analyzed using a suite of ten natural accelerograms and an incremental dynamic analysis technique. Fragility and vulnerability functions are derived for the damageability assessment of structures, economic loss and casualty estimation during an earthquake given the ground shaking intensity, essential within the context of risk assessment of existing stock aiming towards risk mitigation and disaster risk reduction. 1 Introduction Mountainous regions in the Himalayan largely employ stone masonry in building constructions, either as load-bearing walls or as an infill in timber framing structures. For example, in Pakistan stone masonry is used in construction in 40 to 80 percent of sub-administrative units (Tehsil) of the state of Khyber Pakhtoonkhwa and Punjab (Maqsood and Schwarz, 2008). This is due to the fact that stone material is abundantly available in northern parts of Pakistan. Low-cost and lowskilled labour may be employed for construction work that consequently results in overall economical schemes. Stone masonry buildings in the Himalayan region consist of two-wythe, load-bearing walls (Fig. 1). The void between the wythes is left empty or filled with small stones. For rural constructions, i.e. residential buildings, bearing walls are built in rubble stone masonry in which undressed stone units are laid randomly in mud mortar or simply placed in dry form, whereas half-dressed stone units laid in cement mortar are employed for urban constructions, i.e. public buildings. The buildings are provided with wooden floors in case of rural constructions, whereas reinforced concrete slab floors and roofs are used in the case of urban constructions (Ali and Mohammad, 2006; Gupta et al., 2008). The public buildings are also provided with a lightly reinforced roof band (ring beam) at the top of the walls. Stone masonry buildings, having thick walls provided with heavy roofing, perform excellently in protecting the inside of the building from the extremity of the outside temperature and humidity, a characteristic essential in most of the Himalayan region. However, due to the low quality of construction, this structure type has performed very poorly in recent Published by Copernicus Publications on behalf of the European Geosciences Union. 2008). The public buildings are provided that represent critical facilities like sch also roof band offices, healthstructures care units, e 3442 with aN.lightly Ahmad et reinforced al.: Seismic vulnerability of the Himalayanbuildings, half-dressed rubble stone masonry are constructed of load bearing walls b (ring beam) at the top of the walls. in the Governor’s estate in Darjeeling were damaged during in half-dressed stone masonry in cem the recent 2011 Sikkim earthquake in India. Typical damages with reinforced concr observed inmortar Darjeelingprovided public buildings included separation at wall junctions and in-plane shear failure (EERI, 2012). slab floors and roofing. In the recent 20 The complex seismic behavior of this construction type renKashmir ab ders its modeling timid forearthquake analytical studies.unfortunately Thus, experimental investigations essential to calibrate 19,000 arechildren died engineering because of tools and help develop simplified hypotheses for seismic collapse of school buildings of analysis and vulnerability assessment of the considered construction type. mentioned characteristics (EERI, 200 This study presents research carried out on the seismic state of geodynamic assessmentThe of DScurrent masonry structures employed for public setting buildings (schools, offices, health units, etc.). the region hascareshown toIt isbepartcapable of the research program focusing on the seismic vulnerabilFigure 1 Cross-section of the typical stone masonry Fig. 1. Cross-section of the typical stone masonry load-bearing trigger further future large earthquakes load practiced Himalayan. From ity assessment of typical building types in the Himalayan rewalls bearing practiced in walls the Himalayan region.in From left to right: halftowards mitigation and disaster risk reducor risk even greater than magnitude dressed wall employed for publicmasonry buildings (in-wall gion aimingto left to coursed right:masonry half-dressed coursed tion in the region (Ali et al., 2012). Fragility and vulnerabilvestigated in the present study) and undressed random masonry wall (Avouac et by al.,means2006; Bilham, 200 employed for public buildings (investigated in the ity functions are derived herein of analytical and employed for rural residential buildings. present study) and undressed random masonry wall experimental investigations. The presentessential study provides eswhich makes to asse sential input for risk assessment of the considered DS maemployed for rural residential buildings. communicate and consequently mitig sonry structures aiming towards risk mitigation (pre-event and past earthquakes (e.g., Ali and Mohammad, 2006; Bothphase) andthe disaster riskof reduction (post-eventvulnerable phase) in the stock. risk the existing ara and Brzev, 2011; Guptabuildings et al., 2008; Kaushik et al., 2006; Stone masonry having thick Himalayan region in general and northern Pakistan in particMurty, 2003; Naseer et al., 2010; Rai and Murthy, 2006,). walls provided with heavy roofing perform ular. Figure 2 reports an office building The poor performance of stone masonry buildings have also been observedin in other parts of thethe worldinside (Adanur, 2010; excellent protecting of the Mansehra City of Pakistan that w 2 Experimental investigation of half-dressed stone Akkar et al., 2011; Gulkan et al., 1992; Ingham and Griffith, building from the extremity of the outside masonry model by means of dynamic shake table test moderately damaged in 2005 Kashmir M 2011; Spence, 2007a). temperature and humidity, characteristic Earthquakes observations may provide a significant qualita7.6objective earthquake. Typical 2.1 Aim and of the dynamic test damages observ tive information on the earthquake resistance and vulneraessential in most of the Himalayan region. in the building are also described. This c bility of stone masonry buildings common in the Himalayan Earthquake observations in the Himalayan region have However, due to the low quality of region. However, there is very limited quantitative informareported with of VII-VIII shown verywas complex behavior of ruble intensity masonry structures, tion available to help this derive analytical fragility and vulnera-has including in-plane shear cracking, damage to walls from roof construction structure type MMI scale (Javed et al., 2008). Sim bility functions for half-dressed stone DS masonry in urban thrust, delamination of stone units, damage to building corperformed very poorly in recent and past structures found in the Himalayan region. It is very essential type bulging, of collapse dressed stone maso ners, out-of-plane of walls and totalDS colto investigate this construction type, as most of the public earthquakes (Ali and Mohammad, 2006; lapse of structures (EERI,found 2012; Javed al.,Governor’s 2008; Naseer buildings in etthe estate buildings that represent critical facilities like school buildet al., 2010). This fact makes the analytical modeling of rubBothara and Brzev, 2011; Gupta et al., ings, offices, health care units, etc., are constructed of loadDarjeeling damaged during ble stone masonry structureswere less confident for seismic anal- the rec bearing walls built in half-dressed stone masonry in cement 2008; Kaushik et al., 2006; Murty, 2003; ysis, which2011 makes the experimental investigation in essential. Sikkim earthquake India. Typi mortar and are provided with reinforced concrete slab floors The aim of the dynamic test was to retrieve the elastic dyNaseer et Inal., Rai and earthquake, Murthy,about 2006, namic properties and roofing. the 2010; recent 2005 Kashmir damages observed Darjeeling pub (i.e. fundamental vibrationin period and elas19 000 children unfortunately because of the collapse of tic viscous damping) of the building, understand the damage among others). The died poor performance buildings included separation at w of school buildings of the mentioned characteristics (EERI, mechanism of the model, obtain lateral force-deformation restone buildings been 2006). Themasonry current state of geodynamic settingshave in the region and limits in-plane shear failure (EE sponse and junctions deduce performance for deformation-based has shown to also be capable of triggering further observed in other parts of future the large world assessment2012). of the building model. These properties will be The complex seismic behavior earthquakes up to or even greater than a magnitude 8 (Avouac employed later for analytical modeling and fragility analysis (Adanur, 2010; Akkar et al., 2011; Gulkan et al., 2006; Bilham, 2004), which makes it essential to asthisengineering construction using simplified tools. type renders its modell communicate consequently mitigate the risk of2011; the etsess,al., 1992; and Ingham and Griffith, timid for analytical studies. Th existing vulnerable stock. 2.2 Model description Spence, 2007a). experimental investigations are essentia Figure 2 reports an office building in Mansehra City of Pakistan that was moderately damaged in the 2005 KashThe DS masonry structure investigated herein is a represencalibrate engineering tools and h mir Mw = 7.6 earthquake. Typical damages observed in the tative model of public buildings, e.g. school buildings, ofEarthquakes observations may provide develop simplified hypotheses building are also described. This city was reported with an fice buildings, health care units, etc., common in the north-for seism significant qualitative on the ern areas ofanalysis intensity of VII–VIII on the MMI information scale (Javed et al., 2008). Pakistan. Theand modelvulnerability is designed respecting the assessment Similar types of dressed stone DS masonry buildings found similitude requirements for a reduced scaled Simple Model earthquake resistance and vulnerability of the considered construction type. stone masonry buildings common in the Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Himalayan. However, there is very limited This study presents research carried out quantitative information available to help the seismic assessment of DS maso 375 OUT SIDE 375 IN SID E THE ROOM N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures 3443 Page 1/1 Minor diagonal shear cracks observed in load-bearing walls. Horizontal large cracks developed between the floor and walls. Separation of paint coating is observed in slab and walls. Delamination of wall is observed whereby stone units fell out of walls. Description: A two-story office building situated in Mansehra City, Pakistan. It was subjected to the 2005 Kashmir earthquake Mw 7.6 at a distance of about 40 km from seismic source. Fig. 2. A moderately damaged half-dressed stone DS masonry structure. From left to right: view of the building and description of the observed main damages in the building. (Tomazevic, 2000; Ali et al., 2012). A scale factor of 3 is used to reduce the dimensions of the model, whereas a scale factor of 1 is used for scaling the mechanical properties (stressstrain constitutive law) of materials (stone units, mortar, masonry, concrete, steel). Table 1 reports the characteristics of the simple model and similitude requirements for model-to-prototype conversion of quantities. Figure 3 shows details of the building model tested at the Earthquake Engineering Center of UET Peshawar. 2.3 2.3.1 Testing program the model. Figure 4 provides details on the instrumentation of building model. 2.3.2 Characteristics of input excitation The North–South component of the Kobe 1995 record is used for the dynamic excitation of the model. The acceleration record is modified to respect the prototype to model similitude requirements (Tomazevic, 2000). The time duration and predominant period of the record was reduced by 3. It resulted in a compressed acceleration time history with peak ground acceleration (PGA) of 0.83 g, predominant period of 0.12 s and total duration of 10 s. Model setup and instrumentation 2.3.3 The structure model was built on a strong concrete pad which was firmly connected to the shake table by means of bolts. The model was tested in the weaker direction. Three accelerometers were installed on the model: two at the base to record the input excitation and one at the roof level to record the response acceleration of the model. Four displacement transducers were installed to record the displacement time history of the model: two at the base of the model and two at the roof level. The difference of the top and bottom transducers will provide an estimate of the relative lateral deformation of the model. All the gauges were connected to a data acquisition system where the data (acceleration and displacement time history) were recorded at a time step of 0.005 s. Cameras were installed to continuously monitor the behavior of Testing scheme The model was subjected to dynamic excitation in three phases. The input excitations were designed accordingly to push the structure from elastic to inelastic to collapse state, thereby enabling the monitoring of the complete response of the model. The first phase included a low amplitude, 5 percent scaled record excitation of the model, having a PGA of 0.04 g. This phase was mainly included to retrieve the dynamic characteristics, i.e. fundamental vibration period and viscous damping, of the model. For the second and third run, the record was scaled up in 5 percent increments in the excitation amplitude resulting in a PGA of 0.083 g and 0.20 g, respectively. The model was completely collapsed in the last run. The test video can be viewed online at the Copernicus Publications Contact Bahnhofsallee 1e [email protected] www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Nat. Hazards 37081 Göttingen http://publications.copernicus.org Germany Phone +49-551-900339-50 Fax +49-551-900339-70 Martin Rasmussen (Managing Director) Legal Body Copernicus Gesellschaft mbH Earth Syst. Sci., 12, 3441–3454, Based in Göttingen Registered in HRB 131 298 County Court Göttingen Tax Office FA Göttingen 2012 Table 1. Characteristics of the simple test model and similitude requirements for quantities conversion of The Tested Model of the HimalayanSimilitude Requirements formasonry Simple Model N. Characteristics Ahmad et al.: Seismic vulnerability half-dressed rubble stone structures 3444 Physical Quantity Prototype Building Model Building for quantities Table 1. Characteristics of the simple test model1/3 andScaled similitude requirements conversion. Scale Factor 3.00 Length Load bearing walls: 450mm thick Load bearing walls: 150mm thick Characteristics of The Tested Model Similitude Requirements two wythes coursed half-dressed two wythes coursed half-dressed Stress, Strengthfor Simple Model1.00 stone masonry. stone masonry. 1.00 Strain 1/3Cement-sand Scaled modelmortar building Prototype building mortar with Mortar: Physical quantity Scale factor Mortar: Cement-sand with 4 Load-bearing walls: 150 mm thick Load-bearing walls: 450 mm thick 4 MPa compressive strength. MPa compressive strength. 1.00 Specific Mass Length 3.00 two wythes half-dressed two wythes coursed half-dressed Concrete: Normal concrete with stone Concrete: Normalcoursed concrete with stone Stress, Strength 1.00 3.00 Displacement masonry. masonry. strength of 17 MPa. compressive compressive strength of 17 MPa. 1.00 Mortar: Cement-sand mortar with Mortar: Cement-sand mortar with Strain Force Horizontal Band: 150mm thick Horizontal Band: 50mm thick beam Specific Mass 1.00 9.00 4 MPa compressive strength. 4 MPa compressive strength. beam lightly reinforced with 4 10 lightly reinforced with 4 3 Displacement 3.00 3.00 Concrete: Normal concrete with com- Concrete: Normal concrete with Time longitudinal bars tied with 1 3 longitudinal bars tied with 1 1 Force 9.00 strength of 17 MPa. pressive strength of 17 MPa. stirrup provided at 150mm center- stirrupcompressive provided at 50mm center-toFrequency Time 3.00 0.33 Horizontal Band: 50 mm thick beam Horizontal Band: 150 mm thick beam to-center distance. center distance. Frequency 0.33 1.00 lightly reinforced with 4–10 longitudi- lightly reinforced with 4–3 longitudinal Velocity Roof: 150mm thick reinforced Roof: 50mm thick reinforced Velocity 1.00 nal bars tied with 1–3 stirrup provided bars tied with 1–1 stirrup provided at concrete slab. concrete slab. Acceleration 0.33 0.33 Acceleration 50 mm center-to-center distance. at 150 mm center-to-center distance. Roof: 150 mm thick reinforced concrete slab. Roof: 50 mm thick reinforced concrete slab. 5" [127.00mm] 5' [1524.00mm] 6" [152.40mm] 3' [914.40] W SINGLE ROOM STONE MESONARY MODEL W 6" [152.40mm] D 5" [127.00mm] 4' [1219.20mm] 4" [101.60mm] 6" [152.40mm] 6" [152.40mm] 4" [101.60mm] (1/3 Scaled DS Masonry Structures Model) (Plan View) 2" [50.80mm] 1' [304.80] WINDOW 1' [304.80] 1'-212" [368.30] Concrete Pad 1'-6" [457.20] 3' [914.40mm] 1'-6" [457.20] 3' [914.40mm] 4" [101.60mm] 3" [76.20] WINDOW 1'-6" [457.20] 1'-6" [457.20] 3" [76.20] 2" [50.80mm] Concrete Pad 4" [101.60mm] (Front and Back Elevation View) Fig. 3. Geometric details of the structural model tested at the Earthquake Engineering Center of UET Peshawar. Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 www.nat-hazards-earth-syst-sci.net/12/3441/2012/ N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures YouTube videos database maintained by EERI Institute of USA (http://www.youtube.com/watch?v=r8JDj-DFzJs). 2.4 2.4.1 Observed behavior and damage mechanism Global performance under input excitation The first test run at PGA of 0.04 g did not cause any appreciable damage in the model. The building behaved primarily in a boxlike manner. A horizontal crack was developed between the walls and ring beam during the second test run at PGA of 0.08 g. Slight cracks were also developed in the inplane and out-of-plane walls. The building collapsed during the third test run at PGA of 0.20 g. 2.4.2 Observed main damages During the last test cracks developed in the in-plane and out-of-plane walls, which widened largely with increased shaking intensity. Damage in the in-plane walls included diagonal, horizontal and inclined pattern cracks. Horizontal and inclined cracks developed in the out-of-plane walls. The widening of cracks and separation of roof from walls upon increased shaking intensity led to extensive damage in the in-plane walls, delamination of stone units from the out-ofplane walls, damage to corners and consequent stone falling, out-of-plane collapse of walls and complete collapse of the building model. The observed behavior of the model in the initial stages were comparable with the observed damages in the recent 2005 Kashmir earthquake for public buildings (see Fig. 2). 2.4.3 Observed global damage mechanism and comparison with EMS-98 scale The behavior of the model was closely monitored during the last run to deduce damage states of the buildings and develop a damage scale towards performance-based assessment of the building for future applications. Figure 5 reports the global damage states of the building observed during the test with increased shaking level. The observed damage states are also compared with the EMS-98: European Macroseismic Scale (Grunthal et al., 1998) for masonry buildings. It is a standard scale adopted in Europe for masonry building damage rating within the context of post-earthquake screening, vulnerability and fragility analysis. It is observed that the two scales are comparable for DS1 and DS2 damage states. However, the EMS-98 damage scale seems more conservative for DS3 and DS4 limit states, i.e. the extent of building damage specified by the EMS-98 scale is more than the observed damages in the considered building. The observed damage, particularly of the floor, is different than the EMS-98 specified damage pattern. The floor for the considered building failed in an abrupt manner upon the complete damage and spalling of load-bearing walls, which is due to the rigid nature of the floor and its monolithic connection with the walls. This type www.nat-hazards-earth-syst-sci.net/12/3441/2012/ 3445 of roof collapse was also observed during the 2005 Kashmir earthquake for block masonry buildings with monolithic RCC roof slab (Bothara and Brzev, 2011). Generally, the typical roof used for European masonry buildings is composed of timber, roof trusses braced with timber, covered with an iron sheet (in some cases) and roof tiles. For these types of buildings, the tiles from the roof detach in a progressing manner during earthquakes, unlike the rigid RCC slab employed for the considered buildings. 2.4.4 Damage mechanism of component walls The behavior of individual component walls, i.e. in-plane walls and out-of-plane walls, were also closely monitored with increased shaking level, in order to fully understand the seismic response of each component wall. Figure 6 reports the damage mechanism and cracking propagation for each component wall. It can be observed that the response of rubble masonry structure is very complex, which is due to the random nature of rubble masonry and rough construction work. For example, one of the piers (with similar characteristics) of the in-plane wall developed diagonal shear mechanism, whereas the other pier developed sliding and rocking mechanism, with progressing disintegration of piers. Such complex behavior, which is due to the random nature of masonry, cannot be simulated with available numerical tools and thus presents a challenge for computing tools for seismic behavior assessment of rubble stone masonry buildings. This fact also point to the importance of experimental investigation of rubble masonry buildings for understanding the seismic behavior and evaluating the seismic performance. 2.4.5 Dynamic characteristics of the building model: walls The low amplitude input excitation (PGA 0.04 g) was primarily meant to help retrieve the elastic dynamic properties of the model, including fundamental vibration period T0 and damping coefficient ζ . Both the vibration period T0 and damping were obtained from the response acceleration time history (Fig. 7). The period is obtained using the basic definition of period of an oscillating body (i.e. the time required for a complete oscillation). An average value of 0.07 s is obtained for the vibration period. The decay function for the time history of the response acceleration as proposed by Chopra (2003) is used to calculate the model damping A1 1 Ln , (1) ζ= 2nπ An where ζ represents elastic damping coefficient; A1 represents the peak amplitude of response acceleration at reference point 1; An represents the peak amplitude of response acceleration at reference point after n cycles; and n represents the number of cycles between the peaks. The model Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 3446 online at the YouTube videos database Characteristics of Input Excitation: The maintained by EERI Institute of USA north-south component of the Kobe 1995 (http://www.youtube.com/watch?v=r8JDjrecord is used for the dynamic excitation DFzJs&feature=plcp&context=C45c7e56VDvjVQa1PpcFMfBU of theN.model. acceleration record isof the Himalayan 0O_Ox2aFLz4o5w8JWsi84jR0y4ZEw%3D). AhmadThe et al.: Seismic vulnerability half-dressed rubble stone masonry structures D4,D2 W A3 SINGLE ROOM STONE MESONARY MODEL A1 A2 W D Instrument Type Designation D3,D1 Accelerometer A1 A2 Displacement Transducer A3 D1 D2 D3 D4 Figure 4 Testing setup and instrumentation details of the building model tested on shake table at the Earthquake Engineering Center of Peshawar. Fig. 4. Testing setup and instrumentation details of the building model tested on shake table at the Earthquake Engineering Center of Peshawar. gives an estimate of 4.008 % for damping using the positive peaks and 5.404 % using the negative peaks. On average a damping value of 4.71 % is computed, which may be approximated as 5 % for the building model. 3 3.1 Fragility assessment of half-dressed stone DS masonry structures Seismic assessment framework Many available techniques may be employed to derive the fragility functions of structures (Borzi et al., 2008; Calvi et al., 2006; Crowley, 2004; Coburn and Spence, 2002; D’Ayala et al., 1997; Erberik, 2008; Kappos and Panagopoulos, 2010; Porter et al., 2007; Rota et al., 2010, among others). The present study included a fully probabilistic, nonlinear, dynamic reliability-based method (NDRM) recently developed by Ahmad (2011) for the seismic performance evaluation and fragility analysis of considered structure, as employed recently for other structure types (Ahmad et al., 2012a, b). This method is found to provide reasonable estimates of building damageability when compared with earthquake observations in Pakistan (Ahmad et al., 2012c). The NDRM is a probabilistic method for calculating the damage exceedance probability of structures for a specified ground motion. The method of incremental dynamic analysis (IDA) proposed by Vamvatsikos and Cornell (2002) was used to derive the structure response curve that correlates the shaking intensity with the drift demand. The method incorporates total uncertainties in the drift demand. The drift demand on structure is convolved then with the structure drift capacity for a specified limit state to obtain the exceedance probability of target limit state at a given shaking level. It is Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 carried out for all the intensity levels to allow the derivation of fragility functions. 3.2 Mathematical modeling Other available, more or less sophisticated modeling techniques may be calibrated for global seismic analysis of masonry buildings (Magenes and Fontana, 1998; Galasco et al., 2002; Kappos et al., 2002). However, these methods cannot be confidently extended for seismic response evaluation of rubble masonry buildings due to its complex behavior as observed during the experimental investigation. The present study included single degree of freedom (SDOF) mathematical model for seismic analysis. The SDOF system is assigned with observing the global lateral force-deformation response of the building simulating the lateral stiffness, strength and deformation capacity of the tested building model. Thus, fully respecting the fundamental response parameters importance for global dynamic seismic analysis and response evaluation of buildings (Elnashai and Di-Sarno, 2008). The SDOF system is assigned with lateral forcedeformation constitutive law, which is derived from the observed response of the model, i.e. the peak drift and the corresponding base shear observed during each test run. The model is assigned with the mass of the building model, which is adjusted to achieve the fundamental vibration period (T0 0.07 s) of the model as observed during the test. The model is assigned with 5 % elastic viscous damping, as observed during the low amplitude test. For dynamic seismic analysis, the Rayleigh damping model with tangent stiffness proportionality is used in the present study. The system of nonlinear equations in the analysis is solved using the KrylovNewton algorithm (Scott and Fenves, 2010) and the average acceleration Newmark time-stepping method www.nat-hazards-earth-syst-sci.net/12/3441/2012/ N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures 3447 Damage Description and Comparison with EMS Damage Scale Present Study EMS-98 Damage States Grade–1: DS1 Slight diagonal cracks are initiated in walls parallel to excitation direction. Horizontal cracks initiated at the opening base corner of walls parallel to excitation, likely to forming short pier. Horizontal cracks initiated between walls and roof. Vertical cracks initiated at the end of walls parallel to excitation direction, likely to form failure plane for detachment of walls perpendicular to excitations i.e. face loaded walls. Horizontal cracks initiated in the face loaded walls at mid-height and top of wall. Inclined cracks initiated in the face loaded walls, likely to form a wedge for out-of-plane failure. Grade–2: DS2 Diagonal cracking increased in walls parallel to excitation direction. Horizontal cracks developed at the opening base and top corners of walls parallel to excitation, short pier is formed. Horizontal cracks fully developed between walls and roof. Inclined cracks developed at the end of walls parallel to excitation direction, failure plane for detachment of face loaded wall is developed. Horizontal cracks fully developed in the face loaded walls at mid-height and top of wall. Inclined cracks developed in the face loaded walls, a wedge for out-of-plane failure is formed. Grade–3: DS3 Diagonal cracking widened significantly in walls parallel to excitation direction. Horizontal cracks developed at the opening base and top corners of walls parallel to excitation, short pier is formed to slide and rock. Horizontal cracks fully developed between walls and roof. Inclined cracks fully developed at the end of walls parallel to excitation direction, detachment of face loaded wall is likely to occur. Horizontal cracks fully developed in the face loaded walls at mid-height and top of wall. Top wall portion is likely to rock. Inclined and horizontal cracks developed in the face loaded walls, a wedge is likely to separate. Grade–4: DS4 Diagonal cracking widened extensively in walls parallel to excitation direction. Horizontal cracks fully formed at the opening base and top corners of walls parallel to excitation, short pier is responding through inplane sliding and rocking. The face loaded wall fully detached from walls parallel to excitation direction, separating a wing from transverse walls. The face loaded wall fully developed horizontal crack at the top, base and mid-height, forming three pivot points for rocking. A wedge like portion started falling in out-ofplane direction from the face loaded walls. The structure is at the verge of total collapse. Negligible to slight damage, No structural damage, slight nonstructural damage. Hair-line cracks in very few walls. Fall of small pieces of plaster only. Fall of loose stones from upper parts of buildings in very few cases. Remarks: comparable damage state. Moderate damage, Slight structural damage, moderate non-structural damage. Cracks in many walls. Fall of fairly large pieces of plaster. Partial collapse of chimneys. Remarks: comparable damage state. Substantial to heavy damage, Moderate structural damage, heavy non-structural damage. Large and extensive cracks in most walls. Roof tiles detach. Chimneys fracture at the roof line; failure of individual non-structural elements (Partitions, Gable Walls) Remarks: conservative damage state. Very heavy damage, Heavy structural damage, Very heavy non-structural damage. Serious failure of walls; partial structural failure of roofs and floors. Remarks: conservative damage state. Figure 5. Global damage mechanism of half-dressed stone DS masonry building model retrieved through shake tableof test and comparison withmasonry the EMS-98 (Grunthal et al., 1998) damage scale.shake Fromtable left test to and comparFig. 5. Global dynamic damage mechanism half-dressed stone DS building model retrieved through dynamic right: observed damage label andleft description observed and EMS damage scale. ison with the EMS-98 (Grunthal et al.,state, 1998)damage damagestate scale. From to right: of observed damage state, damage state label and description of observed and EMS damage scale. www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 3448 N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures 0.06 0.02 Response Acceleration(g) Response Acceleration(g) Response Acceleration(g) Right Pier (Diagonal Shear Damages) Transverse Wall (Out-of-Plane Delamination and Collapse) Left Pier (Shear Sliding and Rocking) Response Acceleration(g) For example, one of the piers (with similar 0.015 Building Model 0.04 Free Vibration characteristics) of in-plane wall developed 0.01 diagonal shear 0.02 mechanism whereas the 0.005 other pier developed sliding and rocking 0 mechanism, 0 with progressing disintegration of piers. Such complex -0.005 -0.02 behavior, which is due to the random -0.01 nature of masonry, cannot be simulated -0.04 -0.015 with available numerical tools and thus 3 Cy -0.06 -0.02 presents a challenge for computing tools 40 42 44 46 48 50 47 for seismic behavior assessment of rubble Time(sec) (Response stone masonry buildings. This Acceleration) fact also 0.06 7. Dynamic characterization of building model under 0.04g inp point toFigure the0.02 importance of experimental 3 Cycles in and 0.21 Secs response acceleration freebuildings vibration time history processed for the 0.015 Building Model investigation of rubble masonry 0.04 (47.05,0.0078g) and elastic damping coefficient. Free Vibration for understanding the seismic behavior and 0.01 (47.26,0.0037g) evaluating the seismic performance. 0.02 drift dem 3 Fragility Assessment of Half0.005 total unce Dressed Stone DS Masonry 0 0 DynamicStructures Characteristics of The Building drift dem Model: Walls: -0.005 The low amplitude input then with -0.02 excitation 0.04g) was primarily (47.23,0.0036g) specified -0.01 3.1 (PGA Seismic Assessment Framework meant to help retrieve the elastic dynamic (47.015,0.01g) -0.04 exceedanc -0.015 properties includingmay be 3the Cycles inmodel 0.215 Secs at a given Manyof available techniques -0.06 -0.02vibration period T0 and fundamental 40 42 44 46 48 50 47 47.1 47.2 47.3 47.4 47.5 for all th employed to derive the fragility functions damping coefficient ζ. Both Time(sec) the vibration Time(sec) derivation of structures (Borzi et al., 2008; Calvi et period T0 and damping were Model obtained (Response Acceleration) (Building Freefrom Vibration) al., 2006; Crowley, 2004; Coburn and Figure 7. Dynamic characterization of building model under 0.04gacceleration input excitation. From left to right: model the response time history 2002; D’Ayala et model al., 1997; Fig. 7.Spence, Dynamic of building under 0.04 g in- 3.2 Math response acceleration and free vibration time history processed for characterization the estimation of building vibration period (Figure 7). The period is obtained using put excitation. From top to bottom: model response acceleration and Erberik, 2008; Kappos and Panagopoulos, and elastic damping coefficient. the free basic definition ofprocessed periodforof an vibration time history the estimation of building 2010; Porter et 2007; Rota et Other ava oscillating body (i.e.elastic theal., time required foral., 2010, periodothers). and damping coefficient. drift demand. The method incorporates 3 Fragility Assessment of Half- vibration among The present study included modelling a complete oscillation). An average value total uncertainties in nonlinear the drift demand. The Dressed Stone DS Masonry a fully probabilistic dynamic for globa of 0.07 sec is obtained for vibration period. drift demand on structure is convolved Structures reliability-based method (NDRM) recently The(Chopra, decay function forγ the time ofA time step equal buildings 2003) with = 0.5 and history β = 0.25. then with the structure drift capacity for a developed by Ahmad (2011) for the the toresponse acceleration proposed by record the sampling size of theasground motion is consid- Galasco e specified limit state to obtain 3.1 Seismic Assessment Framework seismic evaluation and the However, Chopra (2003) isperformance used to calculate the ered in the analysis. exceedance probability of target limit state fragility analysis of considered structure, modelUncertainties damping: that may be observed when considering a confidentl recently for other evaluation a given shaking level. It is structure carried out Many available techniques may be groupasofatemployed buildings the characteristics are incorpo⎞ same ⎛of 1 A Ln ⎜⎜ 1et⎟⎟ al., 2012a, 2012b). ζ = (Ahmad (1) This for all the intensity levels to allow the employed to derive the fragility functions ratedtypes in the 2constitutive nπ ⎝ A n ⎠ law through Monte Carlo simula- due to its method is found to provide reasonable tions. In this regard, SDOF systems were generated, during the of fifty fragility functions. of structures (Borzi et al., 2008; Calvi where et ζ derivation represents elastic damping which are assigned with random constitutive Uncertain- present s estimate building damageability when al., 2006; Crowley, 2004; Coburn and the peak law. coefficient; A1 ofrepresents ties in the lateral stiffness, strength and deformation compared with earthquake observations in limits freedom ( Spence, 2002; D’Ayala et al., 1997; 3.2 Modelling amplitude of Mathematical response acceleration at are modeled considering lognormal distribution. The exper- seismic a Pakistan (Ahmad et al., 2012c). Erberik, 2008; Kappos and Panagopoulos, reference point 1; A represents the peak imentally obtained nmechanical properties are considered as assigned 2010; Porter et al., 2007; Rota et al., 2010, available acceleration less or more atsophisticated amplitude Other of response the median estimate. A logarithmic standard deviation of force-defo The NDRM istechniques a probabilistic for among others). The present study included modelling may method be calibrated reference point after n cycles; n represents 0.25 calculating is considered tothe modeldamage variability in the peak strength, exceedance simulating the whereas number ofglobal cycles between the peaks. a fully probabilistic nonlinear dynamic for seismic analysis of is masonry 0.50 logarithmic standard deviation considered probability of structures for a specified and defo The model gives estimate of 4.008% for reliability-based method (NDRM) recently to model buildings and Fontana, variability(Magenes in the deformation limits. The1998; ratios of ground motion. The method of incremental damping using the positive peaks and developed by Ahmad (2011) for the the lateral Galasco et al., 2002; 2002). lat- building m force (i.e., limit stateKappos force to et theal., maximum dynamic analysis (IDA) proposed by be to fundamen 5.404% using negative peaks. Figure 6.seismic Local damage mechanism of half-dressed performance evaluation and However, these limits methods cannot eral force) andthe deformation (i.e.,On limit state drift Vamvatsikos and Cornell (2002) was used stone damage DSfragility masonry wallsofobserved during average damping of 4.71% Fig. 6. Local mechanism half-dressed stoneshake DS masonry analysis of considered structure, extended for seismic response as importanc the firstaconfidently drift limit) ofvalue the constitutive lawisare considered table test. From top to bottom: damages observed to evaluation derive the structure response curve that computed which may be approximated as walls observed during shake table test. From topfor to bottom: observed experimentally. The uncertainty in the stiffnesses analysis asand employed recently otherdamages structure of rubble masonry buildings in in in-plane out-of-plane walls. observed in-plane and out-of-plane walls. correlates the shaking intensity with the 5% for the building model. are considered then accordingly. Figure 8 reports the lateral buildings types (Ahmad et al., 2012a, 2012b). This due to its complex behavior as observed Damage Pattern with Increasing Shaking Intensity law obtained experimentally. method is found to provide reasonable force-deformation during theconstitutive experimental investigation. The estimate of building damageability when present study included single degree of earthquake observations in freedom (SDOF) mathematical model for Nat. Hazards compared Earth Syst. with Sci., 12, 3441–3454, 2012 www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Pakistan (Ahmad et al., 2012c). seismic analysis. The SDOF system is assigned with the observed global lateral The NDRM is a probabilistic method for force-deformation response of the building Base Shear Coefficient Normalized when f the ed in variability that in the Uncertainties maydeformation be observedlimits. whenThe assigned to each of the fifty SDOF systems ratios of athe lateral (i.e. limit considering group of force buildings of thestate are also shown in Figure 8. force to the maximum lateral force)in and same characteristics, are incorporated N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures 3449 deformation limits (i.e. limit state drift to 2 the0.2first drift limit) of the constitutive law Table 2. Damage scale considered for fragility Medianfunctions derivation. BSC = BSCmax Random Simulation are considered as observed experimentally. θ(%) = 0.50 Limit States (LS) versus Damage State (DS) Drift Limits 1.5 The 0.15 uncertainty in the stiffnesses are LS1: Damage level Grade-1 DS1 will be attained. θ1 = 0.7θy consideredBSC then accordingly. Figure 8 LS2: Damage level Grade-2 DS2 will be attained. θ2 = 1.5θy = 0.80BSCmax θ(%) = 0.16 Damage1 level Grade-3 DS3 will be attained. θ3 = 0.5 θy + θu reports the lateral force-deformation LS3: 0.1 LS4: Damage level Grade-4 DS4 will be attained. θ4 = θu constitutive law obtained experimentally. where θi represents the mean target drift limit states; θy represents the idealized yield The simulated constitutive laws drift limit derived 0.5 from the possible bi-linearization of lateral force-deformation 0.05 randomly BSC = 0.33BSCmax response of model; θu represents the ultimate drift limits. A mean value of 0.16 % is θ(%) = 0.02 assigned to each of the fifty SDOF systems considered for θy and 0.60 % for θu . A logarithmic standard deviation of 0.20 is considered for each of the drift limit sates. are also shown in Figure 8. 0 0 Base Shear Coefficient n the inear using and erage pping and β pling rd is 0.03ki -0.10ki 0.16ki ki 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 Peak Normalized Drift(%) 3.4 Fragility functions (Randomly Generated, Fifty Simulations) 2 Figure 8 Lateral force-deformation constitutive law of DS masonry structures. From using left totheright: constitutive Each SDOF system is analyzed selected ground Median motions scaled to multiple PGA levels. The drift demand law obtained experimentally and randomly generated for SDOF mechanical model. The lateral force in thefor later Random Simulation each record and target PGA is obtained for all the SDOF syscase is normalized by the peak lateral strength. 1.5 tems. The drift demand is correlated with the corresponding ground motion intensity to derive response curves for each natural accelerograms are record. obtained from 3.3 Selection and Scaling of SDOF system under each ground motion The mean 1 thespectral PEER NGA strong motions database. elastic acceleration, considering all the records for a Accelerograms target PGA, at 0.30 s is considered as the intensity measure The acceleration response spectrum of the 0.5 in the present study. Figure 10 shows the response curves obThe NDRM method requires selected accelerograms is The compatible tained for the considered structure class. drift demand with for accelerograms to perform the nonlinear the building code specified a specified shaking level takes into account allspectrum the uncertain-for 0 ties, type material and record-to-record variability. 0 0.5 1 1.5 2 1 dynamic time history analysis as2.5 part3 of D uncertainties soil of NEHRP classification (BCP, Peak Normalized Drift(%) For the fragility functions derivation, the NDRM method the IDA of structures. A suite of ten 2007). The accelerograms were also computes the limit state probability of exceedance for a spec(Randomly Generated, Fifty Simulations) ve law of DS masonry structures. From left to right: constitutive ified ground motion through the integration of the joint probFig. 8. Lateral force-deformation constitutive law of DS masonry enerated forstructures. SDOF mechanical model.constitutive The lateral in experthe later ability density function of the drift demand and drift capacFrom top to bottom: law force obtained ity. The First Order Reliability Method, FORM, approximah. imentally and randomly generated for SDOF mechanical model. tions (Der Kiureghian, 2005; Pinto et al., 2004) are employed The lateral force in the later case is normalized by the peak lateral to obtain the limit state exceedance probability. A damage strength. natural accelerograms are obtained from scale was developed as per recommended of FEMA (2003) of the PEER NGA strong motions database. for the derivation of fragility functions (see Table 2). The idealized yield drift limit θy was selected such that the damThe randomly simulated constitutive lawsspectrum assigned to each The acceleration response of the age state between 0.7θy and 1.5θy is a slight damage, as of the fifty SDOF systems are also shown in Fig. 8. quires selected accelerograms is compatible with per FEMA (2003) recommendation, which is roughly simSelection and scaling of accelerograms inear 3.3 the building code specified spectrum for ulated compared to the observed behavior. The ultimate drift limits θu corresponds to the lateral deformation when the art of The NDRM type Dmethod soil of NEHRP classification requires accelerograms to perform(BCP, the lateral force drops by 20 %, as proposed by Magenes and f ten nonlinear 2007). The accelerograms also Calvi (1997), which corresponds to the near collapse limit dynamic time history analysis as part were of the IDA of structures. A suite of ten natural accelerograms are obstate. This limit state in our study approximately corresponds tained from the PEER NGA strong motions database. The acto the near collapse limit state as the strength drops very celeration response spectrum of the selected accelerograms rapidly after the ultimate limit state (see Fig. 8). is compatible with the building code specified spectrum for The FORM approximation is used to obtain the limit state type D soil of NEHRP classification (BCP, 2007). The acprobability of exceedance for various target ground motions. celerograms were also selected and used elsewhere (Ahmad A lognormal cumulative distribution function is assumed, et al., 2012a, b, c; Menon and Magenes, 2011). The acceleroas employed elsewhere (Kircher et al., 1997; Porter et al., grams are normalized, anchored to common PGA, and lin2007), and fitted to the observed points. The median and logearly scaled to multiple shaking levels for IDA of each SDOF arithmic standard deviation of each limit state are obtained, system. which can be used for fragility derivation (see Fig. 11): Base Shear Coefficient Normalized Drift (%) (Experimentally Derived) www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 N. Ahmad et al.: Seismic vulnerability of the Himalayan half-dressed rubble stone masonry structures 2 1.5 BCP-2007, D Soil Mean Spectrum 4.5 Individual Record 4 3.5 BCP-2007, D Soil Mean Spectrum Individual Record 2 BCP-2007, D Soil Mean Spectrum Individual Record Spectral Displacement (1/PGD) 3450 Spectral Acceleration (1/PGA) 7, D Soil ctrum Record scaled to multiple shaking levels for IDA of each SDOF system. Spectral Displacement (1/PGD) genes, lized, 1.5 employed elsewhere (Kircher et al., 1997; approximations (Der Kiureghian, 2005; 3 Porter et al., 2007), and fitted to the 1 Pinto et al., 2004) is employed to obtain 2.5 the limit state exceedance probability. A points. The median and 1 observed 2 damage scale was developed as per logarithmic standard deviation of each 0.5 1.5 limit state are obtained which can be used recommended of FEMA (2003) for the 0.5 1 derivation of fragility functions (see Table for fragility derivation (see Figure 11): 0.5 2). The idealized yield drift limit θ was ⎛ 1 ⎛ SA ⎞ ⎞ y 0 ⎟⎟ ⎟ P[D ≥ d LS / SA = sa ] = Φ ⎜⎜ Ln ⎜⎜ 0 1 2 3 4 5 (2) 5 0 ⎟ selected such that the3 damage state 0 0 1 2 3 ⎝β 4⎝ sa LS ⎠ ⎠5 0 1 Period (sec) 2 4 5 Period (sec) between and 1.5θy isSpectrum) a slight (EC8 Specified PGD at 0.7θy Target PGA 0.4g-Normalized Period (sec) where P represents the Spectrum) limit state (EC8 Specified PGD at Target PGA 0.4g-Normalized (PGA-Normalized damage, as per Spectrum) FEMA (2003) probability of exceedance; represents recommendation, which is roughly the standard normal cumulative simulated compared to the observed distribution function; β represents the behavior. The ultimate drift limits θu logarithmic standard deviation of fragility corresponds to the lateral deformation function; SA represents the seismic when the lateral force drops by 20%, as intensity; sa LS represents the median proposed by Magenes and Calvi (1997), estimate of the distribution. The values of which corresponds to the near collapse β and sa LS are also provided in Figure 11. limit state. This limit states in our study The functions can be employed in future approximately corresponds to(Detailsnear of Individual Record) Details of Individual Record) applications for the damageability collapse limit state as the strength drops Fig. 9. Characteristics of the accelerograms used in the present study. From left to right and top to acceleration response spectrum, assessment ofbottom: considered DS masonry s used in the present vary study.rapidly From left to right and top tolimit bottom: after the ultimate states displacement response spectrum and details of the individual record. t response spectrum and details of the structures during earthquake induced (see Figure 8).individual record. ground motions. 3.4 Fragility Functions 0.8 2 Damage scale considered for fragility function; β represents the logarithmic standard deviation Order Reliability Method FORMof fragility function; SA represents the seismic intensity; The FORM approximation is usedandto obtain the limit state probability of exceedance various target Nat. Hazards Earth Syst. for Sci., 12, 3441–3454, 2012ground motions. A lognormal cumulative distribution function is assumed, as Probability of Exceedance 0.7 SA(g)@0.30sec functions derivation Each SDOF system is analyzed using the 0.7 Limit States (LS)motions versus scaled to multiple selected ground Drift Limits 0.6 Damage State (DS) PGA levels. The drift demand for each LS1: Damage level PGA Grade-1 0.5 record and target is obtained θ 1 = 0for .7 θ yall DS1 will be attained. the SDOF systems. The drift demand is 0.4 LS2: Damage level Grade-2 θ = 1 . 5 θ correlated with the corresponding ground 2 y 0.3 DS2 will be attained. LS3: Damage level motion intensity to Grade-3 derive response curves θ = 0 .5 (θ y + θ u ) 0.2 DS3 will be attained. for each SDOF system under 3each ground LS4: Damage level Grade-4 0.1 motion record. The mean elastic θ 4 spectral = θu DS4 will be attained. acceleration, considering all the records 0 0 0.1 0.2 0.3 0.4 0.5 0.6 for a target PGA, at (%) 0.30sec is considered Drift where θi represents the mean target drift as 10 the Structure intensity response in the obtained present Figure curves limit states; θy measure represents the idealized Fig. 10. Structure response curves obtained through IDA of SDOF study. Figure 10 shows the response through IDA of SDOF systems. yield drift limit derived from the possible systems. curves obtained for the considered bi-linearization of lateral forceclass.functions The driftderivation, demand forthea For structure the fragility deformation specified shakingresponse level takesofintomodel; account θu NDRM methodthecomputes the limits. limit A state represents ultimate drift mean all the uncertainties, material uncertainties 1 is SA probability of exceedance for a specified value of 0.16% considered for θ y and and record-to-record P [D ≥ dLS /SA = sa] 8 Ln variability. , (2) ground motion of 0.60% for through θβu. Asathe logarithmic standard LS integration deviation 0.20 isprobability considered forofeach theP joint probability density function the of where represents theof limit state of exceedance; driftstandard limit drift the demand and sates. drift First 8 represents the normalcapacity. cumulativeThe distribution SA(g)@0.30sec g the ultiple each or all nd is round urves round ectral cords dered resent ponse dered for a count inties 0.8Table 1 0.6 0.5 0.8 0.4 0.3 0.2 0.6 0.4 0.1 0 0.2 0 0.1 0.2 0.3 0.4 LS1(0.15,0.31) LS2(0.25,0.31) LS3(0.33,0.31) 0.5 0.6 LS4(0.45,0.31) NDRM Drift (%) Figure 10 Structure response curves obtained 0 0 0.2 0.4 0.6 0.8 through IDA of SDOF systems. SA(g)(0.30sec,5%) 1 Figure 11 Fragility functions for Himalayan DS Fig. 11. Fragility functions for Himalayan DS NDRM. masonry For the fragility functions derivation, the structures masonry structures obtained through obtained through NDRM. NDRM method computes the limit state probability of exceedance for a specified 3.5 Vulnerability Functions ground motion through the integration of the The joint impact probability density functiononofthe the built of an earthquake driftenvironment demand andisdrift capacity. The First computed in terms of the Reliability Method saOrder represents the median estimate of casualties. the FORM distribution. LS monetary losses and human TheThe valuesmonetary of β and sa LSlosses are also provided in Fig. 11. The funccorrespond to the tions economic can be employed in future applications for the damlosses the authority has to bear ageability assessment of considered DS masonry structures to bring the devastated society to habitable during earthquake induced ground motions. condition. It includes the direct losses due to building damage and indirect losses www.nat-hazards-earth-syst-sci.net/12/3441/2012/ including business downtime and loss of means of income besides the response and relief expenditure. The direct economic Economic Loss Ratio (%) The impact of an ELR(0.38,0.37) earthquake on the built environment is computed in terms of monetary losses and human casualties. The 80 monetary losses correspond to the economic losses the authority has to bear to bring the devastated society to habit60 able condition. It includes the direct losses due to building damage and indirect losses, EL including business downtime and = (ELR/100)xNxC 40 loss of means of income besides the response and relief exwhere penditure. The direct economic losses Losses related to the buildEl = Economic 20 ELR = Economic Loss Ratio ing damage represent the amount required to pay for the reN = Number of Buildings pair, demolishment and replacement of structures C = Replacement Cost of Buildingdamaged 0 in earthquakes (Bal0.2et al., 2008; FEMA, 2003). 0 0.4 0.6 0.8 Only1 the direct economic losses are considered in the present research SA(g)(0.30sec,5%) study. The human casualties include the number of people injured and trapped in the collapsed buildings which are essential for rescue operation soon after the earthquake (Erdik et al., 2011; Hancilar et al., 2010). The casualties may be further classified into minor, moderate and serious injuries and deaths (Spence, 2007b). Vulnerability function for economic losses is derived from the building fragility functions. It included the estimation of probability of building damages at a specified shaking intensity, which are convolved with the economic consequence factor ECF (Ahmad, 2012c), where ECF refers to the scale relating building damage with the monetary losses. The FEMA model which assigns a cost ratio (the ratio of damaged building repair to replacement cost) of 0.02 for DS1, 0.10 for DS2, 0.50 for DS3 and 1.0 for DS4, is employed herein to derive vulnerability curve for the considered DS masonry building. Figure 12 reports the vulnerability curve for the considered DS masonry structures where the losses are represented in terms of the economic loss ratio. The function can be used to compute the economic losses for the structures during earthquake given the shaking intensity (SA @ 0.30 s). www.nat-hazards-earth-syst-sci.net/12/3441/2012/ Human Loss Ratio (%) Economic Loss Ratio (%) functions. It included the estimation of Figure 13 Vulnerability functions for Himalayan Human loss ratio which can provide economic loss ratio. The function can be DS masonry structures obtained using the Spence probability of building damages at a used to compute the economic losses for estimates of human casualties (2007b) human consequence factor. in collapsed specified shaking intensity which are the structures during earthquake given the buildings during earthquake given 3451 the N. Ahmad et al.: Seismic vulnerability the Himalayan half-dressed rubble stone masonry structures convolved with the economicofconsequence shaking intensity ([email protected]). shaking intensity ([email protected]). 4 Seismic Risk of DS Masonry factor ECF (Ahmad 2012c), where ECF Structures in Scenario Earthquakes 100 50 refers to theELR(0.38,0.37) scale relating building damage Slight Injuries HL = (HLR/100)xNxO with the monitory losses. The FEMA 80 40 The present studywherealso included case model which assigns a cost ratio (the ratio Hl = Human Injuries studies for risk assessment ofRatioconsidered HLR = Human Loss of damaged building repair to replacement 60 N = Number of Buildings 30 DS masonry structures in large scenario O = Occupants Per Building cost) of 0.02 for DS1, 0.10 for DS2, 0.50 earthquakes. Three scenario earthquakes = (ELR/100)xNxC Moderate Injuries 40 for DS3 and 1.0 ELfor DS4, is employed 20 Critical Injuries with Mw 7.0, 7.5 and 8.0Injuries are &considered where Serious Fatalities herein to derive vulnerability curve for the El = Economic Losses 20 for which building damageability is ELR = Economic Loss Ratio 10 considered DS masonry Figure N = Numberbuilding. of Buildings assessed at various source-to-site C = Replacement Cost of Building 12 reports the vulnerability curve for the 0 distances. Each of the1 scenario earthquake 0 0.2 0.4 0.8 1 0 considered DSSA(g)(0.30sec,5%) masonry0.6structures where 0 0.5 1.5 2 ground motions is simulated with 1000 SA(g)(0.30sec,5%) the losses are represented in terms of the different motion fields,for considering Figure 13 ground Vulnerability functions Himalayan Fig. economic 12. Vulnerability function for The Himalayan DS masonry loss ratio. function canstrucbe Fig. 13. Vulnerability functions for Himalayan DS masonry strucDS masonry structures obtained using the Spence tures obtained using the FEMA (2003) economic consequence factures obtained using the Spence (2007b) human consequence factor. used to compute the economic losses for (2007b) human consequence factor. tor. the structures during earthquake given the shaking intensity ([email protected]). 4 Seismic Risk of casualties DS Masonry Vulnerability functions for human are derived 3.5 Vulnerability functions from the collapse fragility function of the buildings. For this Structures in Scenario Earthquakes 100 purpose the human consequence factor (HCF) developed by Spence (2007b) is employed in the present study. It includes present case the The convolution of the study collapse also fragilityincluded function with the forSpence risk model. assessment of assigns considered lossstudies ratio of the This model ratio of slight with 0.50, moderate injuries withscenario 0.12, seriDSinjuries masonry structures in large ous earthquakes. injuries with 0.08Three and critical injuries and deaths with scenario earthquakes 0.064 in collapsed buildings. Figure 13 reports the vulnerawith Mwderived 7.0, 7.5 and 8.0 are considered bility functions for the casualty estimation in earthfor which building damageability is quakes. The losses are represented in terms of the Human lossassessed ratio, which canatprovide estimates ofsource-to-site human casualties various in collapsed buildings during earthquake given the shaking distances. Each of the scenario earthquake intensity (SA @ 0.30 s). ground motions is simulated with 1000 different ground motion fields, considering 4 Seismic risk of DS masonry structures in scenario earthquakes The present study also included case studies for risk assessment of considered DS masonry structures in large scenario earthquakes. Three scenario earthquakes with Mw = 7.0, 7.5 and 8.0 are considered, for which building damageability is assessed at various source-to-site distances. Each of the scenario earthquake ground motions is simulated with 1000 different ground motion fields, considering uncertainties in the ground motions estimate. Empirical ground motion prediction equations (GMPEs) are used to estimate ground motions (Abrahamson and Silva, 2008; Boore and Atkinson, 2008; Campbell and Bozorgnia, 2008). Damageability of structures is assessed using the previously derived fragility function. For a given earthquake and specified source-to-site distance, the corresponding seismic intensity is obtained using the GMPEs. The associated limit state probability of exceedance is obtained to compute the percentage of structures in various damage states. Figure 14 reports the damage probability matrix, showing the mean Nat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 Campbell and Bozorgnia, 2008). various damage states. Figure 14 reports the damage probability matrix, showing Damageability of structures is assessed the mean estimate of the percentage of 3452using the N.previously Ahmad et al.:derived Seismic vulnerability of the Himalayan with half-dressed stone masonry structures fragility structures variousrubble damage levels. function. For a given earthquake and Rjb = 0 – 10km Rjb = 10 – 20km Rjb = 20 – 30km Rjb = 30 – 40km Rjb = 40 – 50km DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 DS1 DS2 DS3 DS4 100 Mw = 7.0 80 60 40 20 0 100 Mw = 7.5 80 60 40 20 0 100 Mw = 8.0 80 60 40 20 0 Figure 14 Damageability (percentage of total stock) of DS masonry structures in scenario earthquakes. DS1 Fig. 14. Damageability (percentage of total stock) of DS masonry structures in scenario earthquakes. From top to bottom: Damageability represents slight damages; DS2 represents moderate damages; DS3 represents heavy damages; DS4 represents for Mw = 7.0, Damageability for Mw = 7.5 and Damageability for Mw = 8.0. DS1 represents slight damages; DS2 represents moderate near-collapse/collapse limit state. damages; DS3 represents heavy damages. The observed damageability of the estimate of the percentage of type structures withvery various damage considered structure seems high. levels. It can be observed that more than 40 The observed damageability of the considered structure percent of the stock may collapse during type seems very high. It can be observed that more than earthquake withmay Mwcollapse equal during or greater thanwith 40 percent of the stock earthquake buildings located in the nearinand Mw7.0, equalfor or greater than 7.0, for buildings located the near field. The percentage and intermediate intermediate field. The percentage of collapsedof structurescollapsed can even rise to 70–80 during large earthquakes structures can rise even up to 70- and for buildings located in close source-to-site and distance. 80 during large earthquakes forThis huge percentage of damageability will consequently result in buildings located in close source-to-site highly associated socio-economic losses. This high vulneradistance. This huge percentage of bility of the considered building type gives merit to the use damageability will consequently resultbyinAli et of simple retrofitting interventions, as investigated high toassociated losses. al. (2012), mitigate the socio-economic risk of vulnerable stone masonry buildings the future expected large This inhigh vulnerability of earthquake. the considered building type gives merit to the use of simple retrofitting interventions, as 5 Conclusions investigated by Ali et al. (2012), to the a risk vulnerable The mitigate paper presents study of carried out as part stone of the research aiming buildings towards riskinmitigation and disaster risk remasonry future expected large duction in the Himalayan region, which could be subjected earthquakes. to very large earthquakes in the future. Half-dressed masonry structures representing public critical facilities in the region are considered for investigation, a very common type in the region. Fragility functions are derived for the considered construction type using experimental and numerical investigations. Furthermore, vulnerability functions are derived for economic loss estimation and human casualty estimation. The derived fragility and vulnerability functions are employed for earthquake scenario risk assessment considNat. Hazards Earth Syst. Sci., 12, 3441–3454, 2012 moderate and large magnitude earthquakes. The con5ering Conclusions sidered construction type exhibits high vulnerability against earthquakes. Up to 40 percent of building stock can collapse The paper presents a study carried out as in large earthquakes, where the percentage of collapse can part the research aiming towards rise asof high as 70–80 for large earthquakes with risk close sourcemitigation and riskcan reduction in for comto-site distance. Thedisaster present study be employed the Himalayan region, could authorities be municating the expected risk which level to public to take measures aiming towards risk mitigation and disaster subjected to very large earthquakes in the risk reduction. This can in turn result in the mitigation of ecofuture. Half-dressed masonry structures nomic losses from future earthquakes. The findings from the representing public critical facilities in the present study can also be employed for rapid earthquake loss region are considered for investigation, a estimation within the context of prompt response to disaster very common inoperation the region. Fragilityplanning sites, essential fortype rescue and emergency functions arehuman derived for the considered that can reduce casualties in earthquakes. construction using experimental and Supplementarytype material related to this article is numerical investigations. Furthermore, available online at: vulnerability functions are derived for http://www.nat-hazards-earth-syst-sci.net/12/3441/2012/ nhess-12-3441-2012-supplement.zip. economic loss estimation and human casualty estimation. The derived fragility and vulnerability Acknowledgements. Thefunctions reviewers’ are effortemployed in evaluating the for earthquake risk assessment manuscript and kindlyscenario providing encouraging remarks is highly appreciated. The experimental study presented herein is financially supported by the Board of Advanced Studies and Research (BOASAR) of the University of Engineering & Technology (UET) Peshawar and the Higher Education Commission (HEC) of Pakistan, which are gratefully acknowledged. Edited by: M. E. Contadakis Reviewed by: J. M. Dulinska, T. Makarios, and one anonymous referee www.nat-hazards-earth-syst-sci.net/12/3441/2012/ N. 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