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SeismicVulnerabilityAssessmentof BuildingTypesinIndia TechnicalDocument(Tech‐Doc) onSeismicVulnerabilityFunctions ofBuildingTypologies by Seismic Vulnerability Assessment Project Group of IIT Bombay IIT Guwahati IIT Kharagpur IIT Madras IIT Roorkee Submitted to National Disaster Management Authority Government of India September 15, 2013 TechnicalDocument(Tech‐Doc)on SeismicVulnerabilityFunctionsof BuildingTypologies Seismic Vulnerability Assessment Project Group, consisting of the following authors, has contributed to the Tech-Doc: IIT Bombay IIT Madras Mahendra Meena Arun Menon Rohan Shinde A Meher Prasad Ashish Sapre Devdas Menon Ravi Sinha CVR Murty Alok Goyal Deepti R Krrishnan N Uma IIT Guwahati IIT Roorkee SK Deb Yogendra Singh Kaustubh Dasgupta DK Paul Hemant B Kaushik Putul Haldar Aditya Rahul Ankita Sood IIT Kharagpur Nirjhar Dhang Sushanta Chakrabarty Arghya Deb ii Table of Contents Table of Contents ......................................................................................................... iii List of Figures .............................................................................................................. iv List of Tables .................................................................................................................v Abstract ........................................................................................................................ vi Chapter 1 Introduction ................................................................................................1 1.1 1.2 1.3 GENERAL ..................................................................................................................................... 1 VULNERABILITY FUNCTIONS ............................................................................................................. 2 SCOPE OF THE TECHNICAL DOCUMENT .............................................................................................. 2 Chapter 2 Vulnerability Functions for Indian Building Typologies ...........................3 2.1 INTRODUCTION ............................................................................................................................. 3 2.2 COMMON VULNERABILITY FUNCTIONS FOR VARIOUS BUILDING TYPOLOGIES ............................................ 3 2.3 ANALYTICAL DERIVATION OF VULNERABILITY FUNCTIONS ...................................................................... 8 2.3.1 Non-engineered buildings ................................................................................................... 8 2.3.2 RCC Buildings ................................................................................................................... 11 2.4 VULNERABILITY FUNCTIONS ........................................................................................................... 13 Chapter 3 Conclusions ..............................................................................................16 References ....................................................................................................................17 iii List of Figures Figure 1: Modelling of URM piers using two sets of interacting P-M hinges: (a) plastic hinges for simulating rocking and shear behaviour (b) P-M interaction curves corresponding to rocking and shear ............................................................................... 9 Figure 2: Modelling of Spandrel: (a) typical spandrel (b) shear hinge (c) brittle elastic behaviour of the spandrel in shear.................................................................................. 9 Figure 3: Example moment-rotation curve and its bi-linear representation for beam and column.............................................................................................................................. 12 Figure 4: Typical nonlinear modelling of RCC frame ....................................................... 12 Figure 5: Vulnerability functions for various building typologies .................................... 14 Figure 6: Scatter of Expert Opinion and Proposed Vulnerability Curve for RC buildings .......................................................................................................................... 14 iv List of Tables Table 1: Seismic vulnerability functions for Indian building typologies ............................ 4 Table 1(a): Seismic vulnerability functions for Indian building typologies ....................... 5 Table 1(b): Seismic vulnerability functions for Indian building typologies ....................... 6 Table 1(c): Seismic vulnerability functions for Indian building typologies ....................... 7 Table 2: Material properties of brick masonry with different mortars (ISET, 2001; Krishna and Chandra, 1965) ......................................................................................... 10 Table 3: Fragility curve parameters for non-engineered buildings .................................. 11 Table 4: Interstory drift ratio and standard deviation of natural logarithm of spectral displacement at threshold of damage state................................................................... 13 Table 5: Parameters of vulnerability functions................................................................... 13 v Abstract The past few decades have witnessed an increase in the number of damaging earthquakes in India, with nine damaging earthquakes occurring during the last two decades itself. The vast extent of damage and the consequent loss of life associated with these events reflect the poor construction practice in India. Before the 2001 Bhuj earthquake, constructions with poor seismic resistance were assumed to be a feature of non-urban areas, with urban structures considered safer due to the use of engineering knowledge and modern construction materials. However, this earthquake shattered the myth of urban seismic safety through widespread damage to modern buildings. The low awareness among the general public towards structural safety and the inability of regulatory bodies and technical professionals in maintaining quality standards in constructions has created an urgent need to educate the leaders, public, city planners, architects and the engineering professional about the consequences of earthquakes. As a step in understanding the seismic risk in our country, there is a need to determine the vulnerability of prevalent construction types in India, against earthquakes. When various types of buildings are considered for risk assessment, the vulnerability can be established in terms of the structural characteristics, and suitable modifiers to the vulnerability function can be established in terms of the geometrical characteristics. Since the construction practices vary in different parts of the country even when using the same construction material, the vulnerability function of different buildings in the typology catalogue will need to be developed for each region separately. This report presents a summary of the building typologies used or proposed in different parts of the world. The report presents an analysis of these typologies to assess their suitability for India. Based on this assessment, the building typology for use in India has been presented in the report. The proposed building typology is hierarchical, and considers material of construction, structural system, structural irregularities, building height, code compliance and level of maintenance. The building typology catalogue is also developed in a format that is amenable to database management and use of portable computing devices for field data collection. vi Chapter 1 Introduction 1.1 General India faces threats from a large number of natural hazards such as earthquakes, floods, droughts, landslides, cyclones and tsunamis. During the period 1990 to 2010, India experienced 9 damaging earthquakes that have resulted in over 30,000 deaths and caused enormous damage to property, assets and infrastructure. In many cases buildings and structures have proven inadequate to resist earthquake forces and the failure of these can be held responsible for most of the resulting human fatalities. It is also evident from past fatal earthquakes around the world that the existence of vulnerable buildings in high intensity areas has in most cases contributed the total human losses (Jaiswal and Wald, 2008). Understanding the causes of such damage and means to reduce risk demands effective participation of the scientific and engineering community. The detailed assessment of damage after past earthquakes in our country shows that both non-engineered and engineered buildings suffer extensive structural damage (for example, Sinha et al., 2001). It is also found that even the non-engineered constructions sometimes possess the required resistance to earthquake ground motions (for example, the Assam-type traditional housing in NorthEastern states and the Dhajji-Diwari buildings in Kashmir have good earthquake resistance). Recent earthquakes, such as the 2001 Bhuj earthquake that had followed the damaging Anjar earthquake in 1957 in the same area, have shown that the vulnerability of the constructions were not reduced due to the experiences from the 1957 earthquake. As a result, the same tragic lessons had to be re-learnt in 2001 as during 1957 (Sinha et al., 2001). In order to predict the likely impact of an earthquake on the built environment in any part of the country, it is essential to know the seismic vulnerability of the built environment on the affected areas. This information depends on the structural systems of the buildings to resist vertical and lateral loads, performance of similar buildings in past earthquakes, and engineering standards adopted during construction. The assessment of likely impact also depends on the location and distribution of vulnerable building stock in the affected areas. Very limited data currently exists in our country to quantify the building stock and their seismic vulnerability in different parts of the country. The Housing Census data collected every decade compiles information on the construction materials used for walls, floor and ceiling of dwellings. However, this information is technically very difficult to relate to the construction materials used for buildings as a whole due to the nature of data collection that separates out information regarding walls, floor and ceiling so that their combination for buildings is not reported. Even where such information is available based on detailed field surveys, the use of construction materials has not been related to the seismic vulnerability of the buildings. As a result, the technical information on building constructions cannot be fully used for earthquake risk management strategies and programs. 1 1.2 Vulnerability Functions Buildings of any region can be divided into different categories based on construction material, buildings height, building age, code compliances etc. Such categorisation is called building typology. Buildings in a particular typology are expected to behave in similar fashion for same earthquake. Yet, buildings damage from a large pool of buildings show large variations in damage within same types of buildings. This is caused by variations in construction practices, quality control during construction, building age and maintenance and several other factors. Due to large variations in building response analysis results are presented in probabilistic domain. Such presentation helps in identifying distribution of damage state of various buildings at city/regional level. These functions are called fragility or vulnerability functions. Fragility functions are plotted for various damage states and it shows relationship between probability of damage more than or equal to the damage state with respect to chosen earthquake intensity parameter. Vulnerability functions are derived from fragility functions and represent mean damage state for earthquake intensity. A single vulnerability function is generated from set of fragility functions. Details of fragility and vulnerability functions can be found in Chapters 2 and 3 of technical document on "Seismic Vulnerability Assessment Methods for Buildings". 1.3 Scope of the Technical Document This report presents vulnerability functions for Indian typologies. About 50 typologies are defined for Indian buildings in the technical document on "Typology of Buildings in India". Out of these many are combined together to be represented using single vulnerability function. Final functions have been proposed for reinforced concrete buildings, steel buildings, masonry buildings, non-engineered buildings (weak) and non-engineered buildings (strong). 2 Chapter 2 Vulnerability Functions for Indian Building Typologies 2.1 Introduction Vulnerability functions are developed for a particular building type. This function helps to identify mean damage of a building population for given earthquake excitation. Vulnerability functions are generated with the help of fragility functions. Usually probabilistic damage of building is defined by fragility functions, which are as many in number as damage states. A vulnerability function is a single function by combining all fragility functions for chosen building typology. 2.2 Common Vulnerability Functions for Various Building Typologies Vulnerability functions are generated for a particular building type. In the current procedure many building typologies are represented by a single vulnerability functions. This is because the seismic behaviour of many building typologies IS very close to each other and they can be represented by a single curve. Thus all RCC buildings by a single vulnerability function. All typologies of steel buildings are represented by another curve which represents all such buildings. Similarly all masonry buildings have a single representative vulnerability function. Non-engineered buildings have two functions, one for weak buildings and another for strong buildings. These five vulnerability functions can represent the entire population of building typologies throughout the country. These vulnerability functions are derived from analytical model and expert opinion. Next section gives details of analytical method used to generate vulnerability functions. Table 1 gives compatible seismic vulnerability functions for proposed Indian building typologies. Last two columns of Table 1 show the colours of their corresponding vulnerability curves in Figure 5. 3 Table 1: Seismic vulnerability functions for Indian building typologies Material Sub- Types Load Resisting System(Lateral/ Vertical) Rubble stone (field stone) in mud/lime mortar or without mortar (usually with timber roof) Building Category Recommended Seismic Vulnerability Function MASTXXXXXXXX Non-Engineered (weak) MBSTXXXXXXXX Non-Engineered (strong) MCSTXXXXXXXX Non-Engineered (strong) MDEWXXXXXXXX Non-Engineered (weak) MEEWXXXXXXXX Non-Engineered (weak) MFEWXXXXXXXX Non-Engineered (weak) MGEWXXXXXXXX Non-Engineered (weak) MHBWXXXXXXXX Non-Engineered (weak) MIBWXXXXXXXX Non-Engineered (strong) MJBWXXXXXXXX Non-Engineered (strong) MKBWXXXXXXXX Masonry (A) Massive stone masonry (in lime/cement mortar) Stone Masonry Walls (ST) (B) Dressed stone (regular shape) masonry (in lime/cement mortar) (C) Mud walls (D) Mud walls with horizontal wood elements (E) Masonry (M) Earthen/Mud/ Adobe/Rammed Earthen Walls Adobe block walls (EW) (F) Rammed earth/Pise construction (G) Unreinforced brick masonry in mud/lime mortar (H) Unreinforced brick masonry in mud mortar with vertical posts (I) Unreinforced brick masonry in cement mortar Burnt clay brick/block masonry walls (BW) (J) Unreinforced brick masonry in cement mortar with reinforced concrete floor/roof slabs (K) 4 Table 1(a): Seismic vulnerability functions for Indian building typologies Material Sub- Types Unreinforced brick masonry in cement mortar with lintel bands (various floor/roof systems) (L) Confined brick/block masonry with concrete posts/tie columns and beams Load Resisting System(Lateral/ Vertical) Building Category Recommended Seismic Vulnerability Function MLBWXXXXXXXX Masonry MMBWXXXXXXXX Masonry MNCBXXXXXXXX Masonry MOCBXXXXXXXX Masonry MPMSXXXXXXXX Masonry MQMSXXXXXXXX Masonry MRMSXXXXXXXX Masonry CAMFXXXXXXXX RCC CBMFXXXXXXXX RCC CCMFXXXXXXXX RCC CDMFXXXXXXXX RCC CEMFXXXXXXXX RCC Burnt clay brick/block masonry walls (BW) (M) Masonry (M) Unreinforced lime/cement (various floor/roof) (N) Reinforced, in cement mortar (various floor/roof systems) Concrete block masonry (CB) (O) With reinforced concrete (P) With composite steel (Q) Mixed Structure (MS) With timber, bamboo or others (R) Designed for gravity loads only (predating seismic codes i.e. no seismic features) (A) Designed with seismic features (various ages) Structural Concrete (C) (B) Frame with unreinforced masonry infill walls Moment Resisting Frame (MF) (C) Flat slab structure (D) Precast frame structure (E) 5 Table 1(b): Seismic vulnerability functions for Indian building typologies Material Load Resisting System(Lateral/ Vertical) Building Category Recommended Seismic Vulnerability Function CFMFXXXXXXXX RCC CGMFXXXXXXXX RCC CHSWXXXXXXXX RCC CISWXXXXXXXX RCC CJMSXXXXXXXX RCC CKMSXXXXXXXX RCC CLMSXXXXXXXX RCC SAMFXXXXXXXX Steel SBMFXXXXXXX Steel SCMFXXXXXXX Steel SDBFXXXXXXXX Steel SELFXXXXXXX Steel With load-bearing masonry (F) SFMSXXXXXXX Masonry With Reinforced Concrete (G) SGMSXXXXXXX RCC SHMSXXXXXXX RCC SIMSXXXXXXX Steel Sub- Types Frame with concrete shear walls (dual system) Moment Resisting Frame (F) (MF) Open ground storey structure (G) Walls cast in-situ (H) Structural Concrete (C) Precast wall panel structure Shear Wall Structure (SW) (I) With load bearing masonry (J) With composite steel (K) Mixed Structure (MS) With timber, bamboo or others (L) With brick masonry partitions (A) With cast in-situ concrete walls (B) Moment Resisting Frame (MF) With lightweight partitions (C) With various floor/roof systems Steel (S) (D) Single storey LM frame structure (E) With composite steel and concrete vertical members (H) Braced Frame (BF) Light Metal Frame (LF) Mixed Structure (MS) With Timber, Bamboo or others(I) Wooden Structures (W) Thatch roof (A) Load Bearing Timber Frame WATFXXXXXXXX Masonry Post and beam frame (B) (TF) WBTFXXXXXXXX Steel 6 Table 1(c): Seismic vulnerability functions for Indian building typologies Material Building Category Recommended Seismic Vulnerability Function WCTFXXXXXXX Masonry WDTFXXXXXXXX Masonry WETFXXXXXXX Steel WFTFXXXXXXXX Steel Dhajji-Diwari with light weight sloping roof (G) WGTFXXXXXXXX Steel Dhajji-Diwari with heavy/stone sloping roof (H) WHTFXXXXXXXX Masonry WITFXXXXXXXX Steel Sub- Types Load Resisting System(Lateral/ Vertical) Walls with bamboo/reed mesh and post (Wattle and Daub) (C) Frame with (stone/brick) masonry infill (D) Frame with plywood/gypsum board sheathing (E) Frame with stud walls (F) Wooden Structures (W) Thatra with timber plank partitions with light weight sloping roof (I) Load Bearing Timber Frame (TF) Thatra with timber plank partitions with heavy/stone sloping roof (J) Bamboo (B) WJTFXXXXXXXX Masonry Thatra with Dhajji-Diwari partitions with light weight sloping roof (K) WKTFXXXXXXXX Steel Thatra with Dhajji-Diwari partitions with heavy/stone sloping roof (L) WLTFXXXXXXXX Masonry Kath-Kunni walls with stone packing with light weight sloping roof (M) WMTFXXXXXXXX Masonry Kath-Kunni walls with stone packing with heavy/stone sloping roof (N) WNTFXXXXXXXX Non-engineered (strong) BABFXXXXXXXX Steel Thatch roof (A) Bamboo frames with Bamboo/Ekra/ straw partitions ‘Bunga’ (BF) 7 2.3 Analytical Derivation of Vulnerability Functions Vulnerability functions are generated based on nonlinear static analysis. Mathematical models of buildings are generated with nonlinear moment and shear hinges and pushover curve of it is obtained. Then Using HAZUS methodology fragility functions are obtained for four damage states: slight, moderate, extensive and complete. These fragility functions are combined to get vulnerability functions. 2.3.1 Non-engineered buildings Unreinforced masonry walls have three primary mode of in-plane failure: Sliding shear failure, diagonal shear failure and rocking failure. All these failure modes are considered in the analytical model. In this study an equivalent frame model has been used for simulation of the effect of varying axial stress in piers. This has been accomplished by using different sets of plastic hinges and nonlinear link elements available in SAP2000 Nonlinear software. Interacting P-M plastic hinges have been used to simulate the effect of varying axial stress on rocking strength of piers. In equivalent frame model, a masonry pier is modelled by a linear frame element with a set of two ‘interacting P-M’ hinges to simulate rocking and another set of ‘interacting P-M’ hinges to simulate shear behaviour, as shown in Figure 1(a). However, the sliding and diagonal shear capacities are to be represented in terms of equivalent moments at the location of the P-M hinges assigned in the model. Figure 1(b) shows the equivalent moment-axial force interaction curves corresponding to diagonal and sliding shear for a typical pier. It can be noted that the shear failure mode is governed by diagonal or sliding shear in different ranges of axial force. Considering the governing shear mode, a convex P-M interaction curve as shown in the Figure can be developed and assigned to the P-M hinges simulating shear behaviour. Rocking P-M hinge Shear P-M hinge Normalised Axial Force 1.2 1 0.8 Rocking 0.6 Sliding Shear Diagonal Shear 0.4 Governing Shear 0.2 0 0.0 0.5 1.0 Normalised Moment (a) (b) 8 1.5 Figure 1: Modelling of URM piers using two sets of interacting P-M hinges: (a) plastic hinges for simulating rocking and shear behaviour (b) P-M interaction curves corresponding to rocking and shear Similarly the shear behaviour of spandrel is also modelled as a nonlinear hinge. The elasto-brittle behaviour of spandrels failing in shear as proposed by Pasticier et al. (2008) is shown in Figure 3. It is assumed that the residual strength after yielding of the spandrel beam element is equal to one-fourth of the ultimate strength, with no limit on ultimate deformation. The proposed models have been validated by applying them to two multi-storey walls of the ‘Catania Project’ (Liberatore, 2000) presented by Pasticier et al., (2008). Shear hinge (a) (b) V δ (c) Figure 2: Modelling of Spandrel: (a) typical spandrel (b) shear hinge (c) brittle elastic behaviour of the spandrel in shear Selection of representative building plans The main parameters expected to influence the resistance of masonry buildings are: (i) amount of wall area per floor area in each direction, â and (ii) eccentricity (distance between centre of mass and centre of rigidity), as a ratio of the dimension of the building, ê in the direction of earthquake (Giovinazzi, 2005; Erberick, 2007). The parameters â and ê depend upon, (i) spacing and distribution of structural walls in the building, and (ii) openings in walls due to presence of doors and windows. These parameters have been evaluated for all the 32 randomly selected existing buildings, in both the orthogonal (X and Y) directions and five representative cases which are close to following criteria have been selected: Case 1: Plan with â and ê close to the mean values 9 Case 2: Plan with â close to mean and ê close to mean + standard deviation Case 3: Plan with â close to mean and ê close to mean - standard deviation Case 4: Plan with ê close to mean and â close to mean + standard deviation Case 5: Plan with ê close to mean of ê and â close to mean - standard deviation Material properties of masonry The mechanical properties of brick masonry are governed by the characteristics of brick units and type of mortar. A variety of bricks are available in India, commonly used are hand moulded burnt clay solid bricks. Soil available at site of kiln is normally used for making the bricks and due to significant variation in soil properties, the characteristics of bricks vary significantly across the country. The type of mortar used in masonry also influences the strength of masonry, significantly. The shear strength of masonry walls depends primarily on the type of mortar. Different kinds of mortars are used in India. In older constructions and rural areas, mud mortar is commonly used in construction of masonry buildings. In urban areas also, sometimes, small size buildings of low income people are in mud mortar. The use of Lime-surkhi mortar is commonly observed in historical and old buildings. Now-a-days, use of cement-sand mortar is the most common in urban areas. In the present study, the material properties for burnt clay brick masonry with cementsand mortar have been considered from the manual of Indian Society for Earthquake Technology (ISET, 2001) and for masonry with lime-surkhi and mud mortars have been taken from Krishna and Chandra (1965). The material properties adopted for the analysis are shown in Table 2. All these material properties are based on experimental studies carried out at IIT Roorkee. Table 2: Material properties of brick masonry with different mortars (ISET, 2001; Krishna and Chandra, 1965) Mortar type 1:6 cement-sand mortar 1:2 lime-surkhi Clay mud Compressive strength (MPa) Shear strength (MPa) Elastic modulus (MPa) 6.0 0.39 2000 5.87 4.75 0.25 0.08 990 420 Fragility functions Based on the above mentioned parameters and modelling methodology, pushover curves are generated for six types of structures: one and two story structures with cement mortar, lime-surkhi mortar and mud-mortar. Fragility functions are generated for these buildings with the help of HAZUS formulation. For a given damage grade, Fragility Curve represents the probability of reaching or exceeding the damage grade, as a function of severity of seismic ground motion to which the building is subjected. This formulation is given by equation-1 and the estimated fragility curve parameters - median and beta values for the different damage grades of the six building types are shown in Table 3. 10 1 S P[ds | Sd ] ln d ................................................................................... (1) ds S d ,ds Where: Sd Given spectral displacement S d ,ds is the median value of spectral displacement at which the building reaches the threshold of damage state, ds ds is the standard deviation of the natural logarithm of special displacement of damage state, ds (given in Table-3) is the standard normal cumulative distribution function Table 3: Fragility curve parameters for non-engineered buildings Mortar Type No. of storeys Spectral Displacement Gr2 Gr3 Gr1 Gr4 S d ,ds (mm) ds S d ,ds (mm) ds S d ,ds (mm) ds S d ,ds (mm) ds 1 1.07 0.8 1.90 0.95 3.89 1.05 7.5 1.05 2 2.09 0.8 3.69 0.95 7.53 1.05 14.5 1.05 1 1.36 0.8 2.4 0.95 4.5 1.05 8.3 1.05 2 2.13 0.8 3.75 0.95 7.64 1.05 14.6 1.05 Mud 1 1.31 0.8 2.31 0.95 4.35 1.05 8.0 1.05 Mud 2 2.80 0.8 4.95 0.95 8.31 1.05 14.3 1.05 Cementsand CementSand LimeSurkhi LimeSurkhi 2.3.2 RCC Buildings RCC frame building is very common construction in urban and semi-urban India. Affect of earthquake on such buildings can be seen in terms of failure of beams or columns at joints. In the present study nonlinear static procedure is used to find out the seismic behaviour of RCC frame buildings. Nonlinear model of such frame structures is constructed using nonlinear moment-curvature hinges at beams and columns. Moment-curvature relationship for beams and columns is function cross section dimension, location and area of reinforcement bar and material strength of cement and concrete. Stress-strain behaviour of cement and concrete are assumed as per IS-456 (2000). Figure-3 shows sample moment-curvature relationship for beam and columns. SAP2000 v14 software is used to build nonlinear static model of RCC frames. 2D frame of buildings are analysed using static pushover analysis. Figure 4 shows typical modelling of nonlinear RCC frame. 11 250 250 Column section 200 Column (axial load 325kN) 500 150 200 150 54 Moment (kN-m) 100 300 8-25 Beam Beam section 50 100 50 3-20 0 -50 0 400 -50 48 300 2-20 -100 -100 -150 -150 -200 -200 -250 -0.02 -0.01 0.00 0.01 -250 0.02 Rotation (radians) Figure 3: Example moment-rotation curve and its bi-linear representation for beam and column Nonlinear hinge Elastic beam Rigid support Figure 4: Typical nonlinear modelling of RCC frame 12 Nonlinear analysis is carried out in SAP2000 to generate pushover curve for the sample RCC frames. These curves are then used to convert fragility functions to vulnerability functions. Process of generating fragility functions is same as described in section 2.3.1. In case of RCC buildings S d ,ds is defined as product of drift ratio (R,Sds) at the threshold of structural damage state, fraction of building (roof) height at the location of pushover mode displacement (2) and story height (h). Parameters to generate fragility functions for RCC buildings are based on HAZUS and given in Table 4. Table 4: Interstory drift ratio and standard deviation of natural logarithm of spectral displacement at threshold of damage state Building Type Low-rise Mid-rise High-rise Slight R , Sds 0.0050 0.0033 0.0025 Moderate ds 0.89 0.70 0.66 R , Sds 0.0087 0.0058 0.0043 Extensive R , Sds ds ds 0.90 0.70 0.66 0.0233 0.0156 0.0117 Complete 0.90 0.70 0.76 R , Sds 0.0600 0.0400 0.0300 ds 0.89 0.89 0.91 2.4 Vulnerability Functions Vulnerability functions for all building typologies follow lognormal distributions. Damage to a building is described as given in equation-2. ln( MMI ) Damage A B ......................................................................... (2) where is cumulative normal distribution, and are lognormal distribution constants and A and B are regression coefficients. Vulnerability functions are given in Table 5. Table 5: Parameters of vulnerability functions Building Typology Non-engineered (weak) Non-engineered (strong) Masonry RCC Steel Mean ( Std. dev. ( A B 1.3386 0.31659 -0.26018 1.2681 1.5799 0.24673 0.09946 0.9106 1.835 1.9018 2.0463 0.27605 0.30349 0.26156 0.1766 0.07209 0.09678 0.95774 1.03098 0.92843 The vulnerability functions have been proposed on the basis of analytical investigations for non-engineered (weak) buildings and non-engineered (strong) buildings. For masonry, RCC and Steel buildings, they are based on a combination of expert opinion and analytical investigations. Analytical simulation for RC buildings and steel buildings, 13 masonry buildings, and non-engineered buildings (strong and weak) were done at IIT Bombay, IIT Madras and IIT Roorkee respectively. The final vulnerability functions for various building typologies based on the above equation are given in Figure 5. 1 Structural Damage 0.8 0.6 0.4 Non-engineered (weak) Non-engineered (strong) Masonry RCC Steel 0.2 0 V VI VII VIII IX X MSK Intensity Figure 5: Vulnerability functions for various building typologies All proposed vulnerability curves have also been validated by observed data of the damaged buildings from past earthquakes. The comparison between the proposed vulnerability curve and the scatter of expert opinion on the seismic vulnerability of reinforced concrete buildings is shown in Fig. 6. Expert Opinion Proposed Vulnerability Curve Structural Damage 1 0.8 0.6 0.4 0.2 0 VI VII VIII MSK Intensity IX Total No. of Experts = 16 Figure 6: Scatter of Expert Opinion and Proposed Vulnerability Curve for RC buildings 14 From Fig. 6, it can be observed that there is a variation between proposed curve and the scatter from experts' opinion. It may be because of experts' wide opinion and also they have given their opinion based on their limited experience of damaged buildings only in their particular region. And also, there is a lot of variation in the structural characteristics of the buildings such as stiffness, soft storey, plan irregularity etc. which have been considered in the analytical model, unlike the experts' opinion, to propose a uniform vulnerability curve for buildings across India. Due to inadequacy of expert opinion data on Masonry, Steel and Non-Engineered buildings, the comparison between the proposed vulnerability curve and the scatter of expert opinion on the seismic vulnerability of these building types is not shown. The proposed vulnerability curves for these building types, as shown in Fig. 7, are based on a combination of observed damage data of past earthquakes with the project team and analytical investigations. Very few earthquake engineering experts in India have the necessary expertise in both aspects, and most such experts were already a part of the project team from various IITs or did not participate in the NDMA workshop. The issue of limited experience of the experts in India is not surprising since an expert would need both expertise in analytical methods for vulnerability assessment and field experience through post-earthquake reconnaissance in order to validate the expected sequence of analytically-assessed damage through post earthquake observations. The project team would like to reiterate that several structural engineers in various institutions work on the topic of analytical vulnerability assessment. However, there is no systematic opportunity for them to participate in post-earthquake damage surveys either in India or in other countries of the world. As a result of this systemic deficiency, our country will not be able to develop such experts in required numbers. The NDMA may wish to address this through suitable programs so that at least 50-100 structural engineers (faculty members, practicing engineers and post-graduate students) with experience in analytical vulnerability assessment are able to visit sites of earthquake damage to validate their analytical research and thus develop into vulnerability assessment experts. 15 Chapter 3 Conclusions This report presents the vulnerability functions for building typologies in India. This can serve as a very useful tool in assessing seismic risk of country. Proposed vulnerability functions are based on combination of analytical simulation and expert opinion. However, these functions provide just the starting point in the absence of reliable post-earthquake damage data. In future as the reliable studies will collect more and more damage pattern for various earthquakes these functions should further improved, if required. 16 References Erberick, M.A., 2007. Generation of fragility curves for Turkish masonry buildings considering in-plane failure modes, Earthquake Engineering and Structural Dynamics, 37(3), 387-405. Giovinazzi, S. 2005. The Vulnerability Assessment and the Damage Scenario in Seismic Risk Analysis, PhD thesis, Technical University Carolo-Wilhelmina at Braunschweig, Germany and University of Florence, Florence, Italy. IS 456 (2000). “Plain and reinforced concrete – Code of practice (Fourth revision)”, Bureau of Indian Standards, New Delhi. ISET, 2001. A manual of earthquake resistant Non-engineered construction, Indian Society of Earthquake Technology, Indian Institute of Technology, Roorkee. Krishna J., and Chandra, B., 1965. Strengthening of brick buildings against earthquake forces, Proc., of the Third World Conference on Earthquake Engineering, New Zealand. Liberatore, D. 2000. Catania Project: Investigation on the Seismic Response of Two Masonry Buildings. CNR-National Group for Seismic Protection: Rome, 275 (in Italian). Pasticier, L., Amadio, C., and Fragiacomo, M., 2008. Non-linear seismic analysis and vulnerability evaluation of a masonry building by means of the SAP2000 V.10 code, Earthquake Engineering and Structural Dynamics, 37(3), 467-485. 17