ESTIMATION OF EARTHQUAKE VULNERABILITY OF A

STRUCTRUE

by

MD. Ziya Ur Rahman Siddiqui, Ranjeet Joshi, Pradeep Kumar Ramancharla

in

International Conference on Natural Hazards and Disaster Management

Report No: IIIT/TR/2007/-1

Centre for Earthquake EngineeringInternational Institute of Information Technology

Hyderabad - 500 032, INDIADecember 2007

ESTIMATION OF EARTHQUAKE VULNERABILITY OF A STRUCTRUE

Md. Ziya ur Rahman Siddiqui, Ranjeet Joshi Graduate Student, Computer Aided Structural Engineering

IIIT Hyderabad

And

Ramancharla Pradeep Kumar Earthquake Engineering Research Centre

IIIT Hyderabad ramancharla@iiit.ac.in

ABSTRACT

This paper describes the procedure of vulnerability assessment of structures for site specific peak ground acceleration. The objective of this paper is to define the building classification and development of damage probability matrix which represent the vulnerability of structure. The organization of this paper is as follows. First, the types of the structures are reviewed and a classification of structure based on the available data with Vulnerability Atlas of India is done. Second, the description of methodologies developed under various organizations is studied, adopted and summarized. Third, the theoretical methodology of the vulnerability analysis using fragility curve parameters given by HAZUS and capacity curve generated using SAP2000 for typical structure are presented and performance of structure is calculated by using capacity spectrum method.

Key words: HAZUS methodology, capacity curve, demand curve, damage probability matrix

INTRODUCTION

India is always vulnerable to multiple hazards. Whether they are earthquakes, floods, cyclones or droughts, every year significant losses can be observed in either of the forms. India shares the 7th largest area in the world and 60% of this area is earthquake prone to earthquake of intensity MSK VII or more as per Bureau of Indian d Standard. In last 2 decades, India has witnessed several moderate earthquakes (Bihar-Nepal border (M6.4) in 1988, Uttarkashi, Uttaranchal (M6.6) in 1991, Latur, Maharashtra (M6.3) in 1993, Jabalpur, Madhya Pradesh (M6.0) in 1997, Chamoli, Uttaranchal (M6.8) in 1999, Bhuj, Gujarat (M6.9) in 2001 and Muzafarrabad in 2005) causing over 1 lakh casualties due to collapse of structures.

These earthquakes were not regionalized to particular locations rather their influence was felt throughout the nation. Andhra Pradesh lies in central part of the peninsular Indian shield and long considered to be a seismically passive area, But after the Jabalpur (1997), Latur (1993), and Koyna (1967) earthquakes now its seismicity is questionable and few zones with reactivated faults in the crustal layers of this region have been detected.

Earthquake risk

Earthquake Risk gives an estimate of damage and loss due to earthquakes. Earthquake risk can be defined in terms of three prime factors as given below:

Earthquake Risk = Vulnerability x Hazard x Exposure time (1)

Vulnerability is one of the main factor in defining risk and it is defined as the degree to which a system is susceptible or unable to cope with adverse effect of climate change. It is more important to study and evaluate vulnerability of areas occupied by weak infrastructure system in a highly seismically active area and find out expected structural damage losses during earthquake. Vulnerability assessment of such seismically active area helps local authorities in proper disaster management.

METHODOLOGY

There are several risk assessment tools proposed by different countries and organizations like HAZUS (USA), TELES (Taiwan), RADIUS (UN) based on inventory data and inputs through GIS engine to produce result for different disaster. One of the major components of the methodology is extensive database. An inventory is made up of general building stock and groups of building with specific characteristics. The main aim of making inventory of building is for classification of building in different group with similar characteristics. The classification of building based on the construction type, material type, and structural type, buildings are classified into five categories such as wood framing, steel framing, concrete framing, reinforced concrete framing, and unreinforced concrete framing. These structure frames are further classified to different structural classes based on their material used and structural design. Figure 1 shows the methodology of earthquake loss estimation adopted by HAZUS. This methodology is divided in seven steps from input requirement to the development of Damage Probability Matrix.

1. Model building type 2. Ground motion & seismic data

3. Response spectra at period of 0.1 and 0.3 sec

6. Calculation of

cumulative propabilities of all damage state

5. Peak response of model building

4. Capacity curve, yield and ultimate capacity

7. Discreet damage probabilities of all

damage states

8. Damage probability matrix

Figure 1: Flow diagram of HAZUS methodology

BUILDING CLASSIFICATION

Based on the available data with Vulnerability Atlas of India (VAI, BMTPC Govt. of India) classification is developed and used in the development of Damage probability Matrix for a particular model type. The classification is available with VAI is as follows:

Category-A: Buildings in fieldstone, rural structures, un-burnt brick houses, clay houses Category-B: ordinary brick buildings, building of the large block and prefabricated type, half-timbered structures, building in natural hewn stone. Category-C: reinforced building, well built wooden structures Category-X: other types not covered in A, B, C. these are generally light

Buildings are classified based on structural characteristics like number of stories, low-rise (1-3 stories), Mid-rise (4-7 stories) and High-rise (8+ stories) and material type: steel frame, concrete frame, brick masonry burned and unburned, stone masonry and mud wall. Figure 2 shows tow types of buildings.

A total of 10 classes of buildings are defined in Table 1 below.

Table 1: classification based on material and storey height (Wen-I L, Chin-hsiung L 2006, HAZUS-MH 2003)

Figure 2: (a) Example of RM (Mid-Rise) and (b) is an example of URM (Low-Rise)

RESPONSE CURVE AND CAPACITY CURVE

The building performance (peak response) for particular ground motion is determined by intersection of capacity curve of building and seismic response spectrum, the standardized response spectrum shape as given in IBC 2006 (SELENA V2.0, 2007), which consist of four parts, peak ground acceleration, region of constant spectral acceleration at period of zero second to TAV, a region of constant spectral velocity between period TAV to TVD and region of constant spectral displacement for period of TVD and beyond. The region of constant acceleration is defined by Sa at 0.3 sec (Sa@0.3). The region of constant spectral velocity is defined by Sa is proportional to 1/T and Sa at 1 sec (Sa@1).

In general, the elastic design spectrum is defined by following equations: Sa (T) = Sa@0.3 (0.4+0.6 T/TA) if 0 < T < TA (2) Sa (T) = Sa@0.3 if TA < T< TAV (3) Sa (T) = Sa@1.0/T if TAV < T < TVD (4) Sa (T) = Sa@1.0/T*T if TVD < T < 10 s (5)

The value of TAV is based on intersection of spectral acceleration and velocity:

TAV = Sa@1.0 / Sa@0.3 (6) TA=0.2 TAV =0.2 (Sa@1.0 / Sa@0.3) (7)

The period TVD is based on the reciprocal of corner frequency (fc) this frequency is estimated by using Joyner and Boore relationship (SELENA v2.0, 2007) as a function of Moment magnitude:

TVD = 1/fc = (8)

In order to be able to describe the elastic design spectra (for rock: site class B) in that case only PGA is give the following expression have to be used:

Sa@0.3 = SAS= 2.5 PGA (9) Sa@1.0 = SAL = PGA (10)

In account of amplification of ground shaking multiply amplification factor to PGA:

PGAi = PGA FAi (11)

The construction of demand spectra including soil effect can be calculated by using following expression:

SASi = SAS · FAi for short period amplification factor (FAi) for site class i. SAli = SAl · FVi for long period amplification factor (FVi) for site class i.

While the period TAV, which defines the transition period from constant spectral acceleration to constant spectral velocity is a function of the site class. It can be determined by the following equation:

TAVi = { SAl / SAS } { FVi / FAi } (12)

Capacity curve

The building capacity curve is also known as push-over curve based on engineering designed parameter and nonlinear elastic analysis method which gives accurate estimation of building displacement. The capacity curve of building construct under three control points the design capacity, the yield capacity and ultimate capacity. The design capacity represent nominal building strength, the yield capacity represent lateral strength and the ultimate capacity represent maximum strength of the building. The capacity curve represents characteristics of the structure, which is a plot of lateral resistance of building to the lateral displacement. For this study development of building capacity curve for a model of concrete structure is created by using SAP 2000 analysis program.

Figure 3: (a): Standard shape of response spectrum (b) example of capacity curve for concrete structure.

DEFINATION OF DAMAGE STATES

The peak building response is taken from the interaction of capacity curve and demand curve at the building location. The peak building response either spectral displacement or spectral acceleration at the point of interaction is used as parameter with fragility curve to estimate the damage state probabilities. The method adopted by HAZUS and in this study, damage states are divided in four classes as shown in Table 2.

Table 2: damage states thresholds defines with the agreement of capacity spectrum

Where,

Sd is spectral displacement and suffix 1, 2, 3, 4 show slight damage, moderate damage, extensive damage, and complete collapse respectively.

Ay = yield spectral acceleration

Au = ultimate spectral acceleration.

Dy = yield spectral displacement

Du = ultimate spectral displacement.

CUMULATIVE DAMAGE PROBABILITIES

For a given damage state, P [S | Sd ], P [M| Sd], P [E | Sd], P [C | Sd] a fragility curve is well described by the following lognormal probability density function Barbat et al, (2002), HAZUS (2003 ).

(13)

Where is the threshold spectral displacement, is the standard deviation of the natural logarithm of this spectral displacement Table2 shows how the threshold obtain from capacity spectrum, Φ is the standard normal cumulative distribution function and Sd is the spectral displacement of the structure.

Where, P [S | Sd] = probability of being in or exceeding a slight damage state, S. P [M | Sd] = probability of being in or exceeding a moderate damage state, M. P [E | Sd] = probability of being in or exceeding an extensive damage state, E. P [C | Sd] = probability of being in or exceeding a complete damage state, C.

Fragility curve Figure 4 which shows the probability of exceeding or being in for expected spectral displacement (obtain from performance point) for all damage states.

Figure 4: shows example of fragility curves

Discrete damage probabilities can be calculated as follows:

Probability of complete damage, P [C] = P [C | Sd] Probability of extensive damage, P [E] = P [E | Sd] - P [C | Sd] Probability of moderate damage, P [M] = P [M | Sd] - P [E | Sd] Probability of slight damage, P [S] = P [S | Sd] - P [M | Sd] Probability of no damage, P [None] = 1 - P [S | Sd]

……………… (14)

EXAMPLE PROBLEM OF RM (LOW-RISE) AND SL (MID-RISE) STRUCTURE

Generation of elastic demand spectra (SELENA v2.0, 2007):

Demand spectra for NEHRP site classes B (rock site), PGA for rock site conditions PGAB = 0.2 g

Step1) calculation of spectral acceleration at T= 0.3s and T= 1.0s, According to equations (9) & (10):

Sa@0.3 = SAS = 0.5g Sa@1.0 = SAl = 0.2g

Step2) site amplification factor for site given by IBC-2006 (SELENA V2.0, 2007)

Table 3: site amplification factor Site amplification factor = SAS = 0.5g, SAl = 0.2g

Site class B

FA 1.0 FV 1.0

Step3) calculation of short period and long period spectral accelerations as well as Transition period

Table 4: show calculated value of short and long period acceleration

Parameter Class B PGAi = PGA FAi 0.2 SASi = SAS · FAi 0.5 SAli = SAl · FVi 0.2 TAVi = { SAl / SAS } { FVi / FAi } 0.4 TA=0.2 TAV 0.08

Step4) Generation of elastic demand spectrum (damping ξ= 5%)

For the evaluation of structural damage it is more convenient to plot the acceleration response spectrum as a function of the spectral displacement. This could be achieved due to the relation between the different spectral parameters:

Sd = Sa *g*T*T / 4 * (15)

Figure 5 (a) shows demand spectrum and Figure (b) shows demand spectrum as a function of spectral displacement, values along abscissa of spectral displacement is calculated by using equation (14), these curve are plotted by using MS-Excel software.

Figure 5: (a) demand spectrum (b) demand spectrum as a function of the spectral displacement

Generation of capacity curve using SAP2000:

For a low-rise reinforced concrete structure (RM) and a mid-rise steel (SL) structure pushover analysis is carried out. Following are the details of the both structure.

Concrete structure

• Grade of Concrete is 25 Mpa

• Grade of steel is 415 Mpa

• Slab thickness 100mm

• Column 450 X 300mm, Beam 350X250mm

• Live load 4kN/m2, storey height 3m

Steel structure

• 5 storey building, Storey height 3m

• E=29000 ksi, poisons ratio=0.3

• Beam w24x55, column w14x90

• Load on roof: DL=75 psf, LL=20 psf

• Load on floor: DL-125psf, LL=100psf

Figure 6(a), (a1) shows result of pushover analysis using SAP2000 for a structure in the form of capacity curve. The values of yield acceleration, ultimate acceleration, yield spectral displacement and ultimate spectral displacement are given in the Table 5 which can be read directly from capacity curve. Figure7 is a plot describes intersection of capacity curve and demand spectrum, the corresponding value of spectral displacement at the intersection point is a performance point (peak response) of the structure and peak responses for structures is given in Table 6.

Figure 6: (a), (a1) capacity curve (b), (b1) concrete and steel models generated in SAP2000

Table 5: yield and ultimate values from capacity curve

Yield capacity Ultimate capacity Building type Dy cm Ay (g) Du cm Au (g) RM(Low-

Rise) 2.9 0.42 8.18 0.53

SL(Mid-Rise) 5.708 0.408 12.741 0.462

Figure 7: Intersection of capacity curve and demand curve

Table 6: peak building response from intersection of demand and capacity curve

Calculation for cumulative damage probability:

According to equation 13 For a given damage state, P [S | Sd ], P [M| Sd], P [E | Sd], P [C | Sd] is the threshold spectral displacement, Table 2 shows how the threshold obtain from capacity spectrum (Barbat et al 2002) and is the lognormal standard deviation parameter that describes the total variability of damage state (HAZUS 2003), Table 7 show the values of and for each damage state, values of taken from HAZUS in this study.

Peak building response in cm

Building type Sd (cm) RM (Low-Rise) 3 cm

3.5cm SL(Mid-Rise)

Table7: Parameter for fragility curve defined by HAZUS for RM and SL type model buildings Slight Moderate Extensive Complete

Type βS βM βCβE

RM(low-Rise) 0.812 1.05 1.16 1.07 1.688 1.09 3.272 0.91

SL(Mid-Rise) 1.596 0.68 2.283 0.78 2.986 0.85 5.0964 0.98

Table 8 shows calculation of probability of being in or exceeding damage states by using equation 13, and the discreet damage probabilities is calculated by using equations (14) and it is represented in Table 9

Table 8: calculation of cumulative probabilities

RM (Low-Rise) X y

Damage state Sd βds Sd/ ln(x) ln(x)/

βdsΦ[y]

Slight 1.2 0.812 1.05 1.477 0.3900 0.37 0.6443 Moderate 1.2 1.16 1.07 1.034 0.033 0.030 0.5120 Extensiv

e 1.2 1.688 1.09 0.710 -0.342 -0.313 0.3783

Complete 1.2 3.272 0.91 0.360 -1.005 -1.104 0.1357

SL (Mid-Rise) X y

Damage state Sd βds Sd/ ln(x) ln(x)/

βdsΦ[y]

Slight 1.4 1.596 0.68 0.877 -0.131 - 0.1929 0.4247 Moderate 1.4 2.283 0.78 0.613 -0.489 -0.6269 0.2676 Extensiv

e 1.4 2.986 0.85 0.468 -0.757 -0.8911 0.1867

Complete 1.4 5.096 0.98 0.274 -1.292 -1.3183 0.0951

Table 9: damage probability matrix Damage probability Matrix

Model type Slight P[S] Moderate P[M]

Extensive P[E]

Complete P[C]

RM(Low-Rise) 0.1323 0.1337 0.2426 0.1357

SL(Mid-Rise) 0.1571 0.0809 0.0916 0.0951

Figure 8: damage probabilities for (a) SL (Mid-Rise) (b) RM (L0w-Rise) building type

The Figure 8 represents the discrete damage probabilities of building type RM (Low-rise) and SL(Mid-Rise) for all damage states, calculated by method explained above and graph shows concrete Structure is more vulnerable to Extensive damage and steel structure is more vulnerable to slight damage for a generated response spectrum of PGA= 0.2g for site class B (rock site).

CONCLUSIONS

A computer based program which provides assessment of risk due to earthquake is proposed in this paper. This program computes the Damage Probability Matrix for a given building type.

REFERENCES

1. Wen-I L, Chin-hsiung L 2006. Study on the fragility of building structures in Taiwan, Natural Hazards (2006) 37:55-69, National university of Kaohsiung.

2. Ggulati. B 2006. Earthquake assessment of buildings: applicability of HAZUS in Dehradun, India. Unpublished report, Indian institute of remote sensing, Dehradun, India.

3. Barbat A. H, Lagomarsino S, Pujades L.G. 2002. Vulnerability assessment of dwelling buildings. projects: REN 2001-2418-C04-01 and REN2002-03365/RIES Universitat Politdecnica de Catalunya, Barcelona, Spain, University of Genoa,Genoa, Italy.

4. HAZUS-MH 2003. Advance engineering building module. Report by: Department of Homeland Security Emergency Preparedness and Response Directorate FEMA Mitigation Division Washington, D.C.

5. SELENA v2.0 2007. seimic loss Estimation using a logic tree approach. prepared by Sergio Molina-Palacios, Dominik H. Lang, and Conrad D. Lindholm at NORSAR Kjeller, Norway.

6. Vulnerability Atlas of India (2007), Building Materials & Technology Promotion council Govt. of India.

7. International Code Council (2006). International Building Code (IBC-2006). United States, January 2006, 664 pp.

8. Joyner, W.B. and Boore, D.M. (1988). Measurement Characterization and Prediction of Strong Ground Motion. Proc. of Earthquake Engineering and Soil Dynamics II, 43–102. Park City, Utah, 27 June 1988. New York: Geotechnical Division of the American Society of Civil Engineers.