Download Vulnerability Functions - National Disaster Management Authority

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