International Journal of Engineering Research ISSN:2319-6890(online),2347-5013(print) Volume No.5 Issue: Special 3, pp: 591-594 27-28 Feb. 2016

NCASE@2016 doi : 10.17950/ijer/v5i3/016 Page 591

Development of Fragility Curves for RC Buildings

Vazurkar U. Y., Chaudhari, D. J. Department of Applied Mechanics, Government College of Engineering, Amravati, Maharashtra,

India-444604 E-mail: umeshvazurkar@gmail.com, dilipbhanu.chaudhari@gmail.com

Abstract: The damage to the buildings during recent earthquakes has demonstrated the need of seismic evaluation which is used to predict the probability of damage to the building. This paper describes the vulnerability assessment of reinforced concrete buildings using fragility curves. Fragility curves are used to describe the probability of damage being exceeded a particular damage state. For the development of fragility curves, guidelines given by HAZUS technical manual have been used. For the analysis, the RC buildings were modelled in SAP2000 v14. Non-linear static analysis procedure is used for the analysis of RC buildings. The pushover analysis is carried out as per the ATC40 guidelines. Capacity curve is generated as a result of pushover analysis. Results from pushover analysis are used for plotting fragility curves. The Fragility Curves are plotted considering Spectral Displacement as a ground motion parameter. Various ‘damages states’ are used to describe the damage level of the buildinggiven in HAZUS technical manual. Finally, using constructed fragility curves the spectral displacement values that satisfy the ‘slight’, ‘moderate’, ‘extensive’, ‘complete’ performance level requirements were estimated. The fragility curves developed from the analysis were used to study the seismic performance of building models.

Keywords: Fragility Curves, HAZUS, Damage States, Ground Motion Parameters

I. Introduction

Seismic vulnerability assessment is a method used for quantification of risk involved due to expected earthquake in a region. The vulnerability is usually represented in terms of either Damage Probability Matrices (DPM) or Vulnerability (Fragility) curves. The seismic vulnerability of structures is commonly expressed through probabilistic fragility functions representing the conditional probability of reaching or exceeding a predefined damage state given the measure of earthquake shaking. Fragility curves are the conditional probability of exceedance of response of a structure for a given ground motion intensity. Fragility curves are used commonly for the estimation of probability of structural damage due to earthquakes as a function of ground motion indices or other design parameters. The most basic inelastic method of seismic analysis is complete non-linear time history analysis. But this method is complex and requires much time for completion. Therefore, Non-linear static procedures are used in this paper for the generation of fragility curves as per the HAZUS [1] manual.

Three building frame models were considered in this paper for the development of fragility curves. Spectral displacement is used as a ground motion parameter. SAP200

v14 is used for the modeling of building and pushover analysis. Results from pushover analysis are used for development of fragility curves. The infill walls are not considered in modeling of RC buildings

II. Literature review

The researchers have recognized that the need of vulnerability assessment for seismic evaluation of buildings. They have identified Fragility curves is one of the tool for vulnerability assessment. The literature has been referred from various research papers is illustrated.

Murat and Zekeriya (2006) presented a study on Fragility analysis of mid-rise RC buildings. They had performed incremental dynamic analysis on 3, 5, 7 storey RC buildings using 12 artificial earthquake records.Yielding and collapse capacity of the buildings was determined from the analysis. They used PGA and elastic spectral displacement as ground motion parameters. Also they used inter-storey drift and spectral displacement values as a damage measurement parameter.

Farsi, et.al. (2015) presented a work to estimate the seismic vulnerability of existing buildings in Algeria. For this purpose, capacity curves were developed for the reinforced concrete buildings using push-over method. In the modeling of nonlinearity three types of plastic hinges were considered which are Flexural plastic hinges (M2, M3), Compound compression and bending plastic hinges (PMM), and shear plastic hinges (V2, V3). The analysis was performed using ETABS software.Four performance levels, corresponding to the expected damage after an earthquake OL, IO, LS and CP were considered in the vulnerability assessment of buildings in Algeria. Elastic response spectra, plotted for each soil type in acceleration vs. period coordinates are based on estimates of seismic coefficients CA and CV presented in ATC-40(4)report.

Raipure P. (2015) presented a study on development of fragility curves for open ground storey buildings. She had used probabilistic seismic demand model (PSDM) as per power law for the generation of fragility curves. a typical ten storied OGS framed building was considered and the building considered is located in Seismic Zone-V. The design forces for the ground storey columns were evaluated based on various codes such as Indian, Euro, Israel, and Bulgarian suggested approach. She designed various OGS frames considering MF as 1.0, 2.1 (Israel), 2.5 (Indian), 3.0 (Bulgarian), and 4.68 (Euro). The performance of each building was studied using the fragility analysis method introduced by Cornell et. al (2002). Twenty computational models were developed in the program ETABs for nonlinear dynamics analysis for each case. For the analysis, a set of twenty natural time histories was selected.

International Journal of Engineering Research ISSN:2319-6890(online),2347-5013(print) Volume No.5 Issue: Special 3, pp: 591-594 27-28 Feb. 2016

NCASE@2016 doi : 10.17950/ijer/v5i3/016 Page 592

III. System Development In this paper the methodology used for development of

fragility curve is divided into two parts. Firstly pushover analysis is performed on building models in SAP2000 v14. The results from pushover analysis are used for generation of fragility curves as per HAZUS manual.

3.1 Pushover Analysis Displacement based pushover analysis is performed in

SAP2000 v14 as per the guidelines given in FEMA 356 and ATC40. As per the FEMA 356 target displacement is necessary to perform displacement based pushover analysis. This target displacement is given by equation (1)

Δt= C0C1C2C3SaTe2g / 4π2 (1)

Where, C0,C1,C2,C3 are modification factors. The values of the modification factors are available in section 3.3.3.3.2 of FEMA 356.

After the analysis in SAP, Capacity curve in the form of Base shear vs Roof displacement will be obtained from display menu. This capacity curve is converted into ADRS (Acceleration Displacement Response Spectra) format. Performance point is obtained as intersection of capacity spectra and elastic demand spectra.

3.2 HAZUS methodology There has been numerous works in the literature for the

evaluation of the fragility curves of the structures. However For the development of fragility curves, guidelines given by HAZUS technical manual have been used. HAZUS methodology was developed for FEMA by National Institute of Building Science (NIBS) to reduce seismic hazard in United States. HAZUS technical manual provides the procedure for deriving the fragility curves for different types of structures. Building fragility curves are lognormal functions that describe the probability of reaching, or exceeding, structural and non-structural damage states, given median estimates of spectral response, for example spectral displacement. These curves take into account the variability and uncertainty associated with capacity curve properties, damage states and ground shaking. 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

P[ ds | Sd ] = Φ[ ln( )] (2) Where is Sd,ds the threshold spectral displacement,βds

is the standard deviation of the natural logarithm of this spectral displacement, Φ is the standard normal cumulative distribution function and Sd is the spectral displacement of the structure. Table (1) shows how the thresholds obtain from capacity spectrum.

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.

Table 1: Damage state thresholds defines with the

agreement of capacity spectrum (1)

Damage States Spectral Displacements (Sd,ds)

Slight 0.7Dy Moderate Dy Extensive Dy + 0.25(Du – Dy) Complete Du 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 So now in the formula of cumulative normal

distributive probability, value of Sd was found from pushover analysis result and the value of� is taken from HAZAUS Technical manual (table 5.11- 5.11d). Figure (1) shows Example damage state medians of saw-tooth pushover curve.

Figure 1: Example damage state medians of saw tooth pushover curve (1)

IV. Results and Discussion

In this paper three building models are considered for the development of fragility curves. Fragility curves are generated for four damage states as per HAZUS. Results of one of the building model are validated. No infill walls were considered in the modeling of all the buildings. Spectral displacement is used as ground motion parameter.

4.1 Building Model 1: A Three dimensional model of G+3 RCC frame is

considered. The model specification and the loading data isgiven in Table (2). This frame is designed for gravity loads in SAP 2000 v14. Pushover analysis is performed for the gravity load designed frame. The given G+3 building frame is considered as validation case for the study of intrest. The probability of damage for a particular damage state is worked out. Then comparison of values corresponding to probability of damage with the validation paper [6] is done.

International Journal of Engineering Research ISSN:2319-6890(online),2347-5013(print) Volume No.5 Issue: Special 3, pp: 591-594 27-28 Feb. 2016

NCASE@2016 doi : 10.17950/ijer/v5i3/016 Page 593

Table 2: Description of Building Model 1 Description Value Number of Stories 4 Height of Storey 3.5 m Grade of steel Fe 415 Grade of Concrete M25 Density of RC members 25 kN/m3

Live load on floors 3.5 kN/m2

Slab thickness 120 mm The fragility curve obtained considering four damage

states is shown in figure (2).

Figure 2: Fragility Curve for Building Model 1 The probability of damage or the probability of

exceedancefor the four damage states i.e. Slight, Moderate, Extensive and Collapse can be read from the fragility curve. The table 3 shows the probability of exceedanceof particular damage state for the spectral displacement value of 0.15 m.

Table 3: Comparison of Probability of Damage State Damage

State Reference

Paper SAP

analysis Probability

of damage Probability

of Damage Slight 0.98 0.99 Moderate 0.82 0.90 Extensive 0.65 0.79 Complete 0.48 0.47 4.2 Building Model 2: A typical 4-storey 2-bay RC frame that represents a

symmetric building in plan is considered in the building model 2[7]. Grades of concrete and steel are taken as M25 and Fe415 respectively. Typical bay width and column height are selected as 5m and 3m respectively. A live load of 2 kN/m2 is considered at all floor levels. The total width of building is of 10.0 m having 2 bays, width of each bay is 5.0 m. The total height of the building is 12.0 m, having 4 storeys, height of each storey being 3 m. The size of typical columns and beams

considered are 3000mm x 300mm and 300mm x 500mm respectively [7]. All the columns have four reinforcement bars with diameter equal to 16 mm, 14 mm and 12 mm at I, II and III-IV floor levels, respectively. Percentage values of the reinforcements are in the 0.50–0.68% range. Transverse reinforcement is made up of 6 mm hoops with constant spacing equal to 0.15 m. Beam reinforcement is constant along the height with percentages equal to about 0.5%.

Figure 3: Pushover Curve for Building Model 2

Figure 4: Fragility Curve for Building Model 2 Plot of Capacity of capacity spectrum curve obtained is

shown in figure 3. This figure represents the capacity and response spectrum plots. The graph obtained of pushover curve is converted into ADRS(Acceleration Displacement \Response Spectra) format. The co-ordinates of performance point valueisshown in figure 3. Performance point is estimated using ATC 40 method. SAP2000v14 will directly give the value of spectral acceleration and spectral displacement corresponding to performance point..

The value of spectral displacement corresponding to performance point is used to plot fragility curve.

International Journal of Engineering Research ISSN:2319-6890(online),2347-5013(print) Volume No.5 Issue: Special 3, pp: 591-594 27-28 Feb. 2016

NCASE@2016 doi : 10.17950/ijer/v5i3/016 Page 594

The spectral displacement value corresponding to performance point is 0.022 m. The fragility curve for building model 2 is shown in figure 4.

4.3 Building Model 3: A two dimensional, 3 storey reinforced concrete frame

isanalysed [8]. The frame has 2 openings of 4.85 m and 3.25 m, respectively, and a ground floor of 5 m high and two others of 2.55 m. The properties of the used materials are presented in Table 4. The columns cross-section dimensions are 60 × 60 cm for the ground floor, 55 × 55 cm for the first floor and 50x50 cm for the second one. The longitudinal steel rebars have diameters of 20 mm, and the transversal reinforcement is made of stirrups of 8 mm, spaced at 12 cm in the potentially plastic areas and in the beam–column connections of the column. The beam cross-section dimensions are 30 × 60 cm for level +4.95 m and 30 × 45 cm for levels +7.50 m and +10.05 m, respectively. The reinforcement consists of bars with diameters of, respectively, 16 mm, 18 mm and 20 mm in the longitudinal direction, and stirrups of 8 mm spaced at 10 cm in the support areas and at 15 cm in the field.

Table 4: Material Properties of Building Model 3

Materials

Pa c y u

Concrete 0 .2 0.5

Longitudinal Reinforcement

10 .3 55 70

Shear Reinforcement 10 .3 55 60

The pushover curve is obtained in SAP2000 v14. Based

on the spectral displacement values that satisfies the damage level as per HAZUS manual, the fragility curve is plotted.

Figure 5: Fragility Curve for Building Model 3

5 Summary and Conclusions In this study, HAZUS methodology for the generation

of fragility curves is discussed and the fragility curves are generated for low-rise RC building structures without considering infill walls. From the results generated, it is concluded that this methodology gives an idea to predict the damage level of the building corresponding to particular value of spectral displacement. The damage state of the building is also identified from the above analysis.

As HAZUS method works on non-linear static procedures, it is also concluded that the results from this paper need to be compared with another method, such as time-history, which is expected as future scope for this paper.

REFERENCES

i. FEMA, HAZUS technical manual MH MR1, Earthquake loss estimation methodology, Department of homeland security, Washington DC, USA, 2003.

ii. Murat S. K., “Fragility analysis of mid-rise R/C frame buildings”, Engineering Structures, 28, 2006, 1335-1345.

iii. Farsi M. et. al., “Seismic Vulnerability of Reinforced Concrete Structures in Tizi-Ouzou City (Algeria)”, 1st International Conference on Structural Integrity, science direct, 2015, 838 – 845.

iv. ATC40, seismic evaluation and retrofit of concrete buildings-volume I, Report no. SSC 96-01, Redwood city, Applied Technology Council, 1996.

v. Raipure P., seismic vulnerability assessment of open ground storey RC buildings by using fragility curves, Government College of Engineering, Amravati, M-Tech thesis, 2013-14.

vi. Borele. S, Damage assessment of structural systems using fragility curves, Journal of civil engineering and environmental technology, volume 2, june 2015, pp 72-76.

vii. Angelo Masi, Seismic vulnerability saaessment of gravity load designed RC frames, Bulletin of earthquake engineering, 2003, 371-395.

viii. IoanaOlteanuet. al., Vulnerability and risk evaluation for a reinforced concrete frame, Bulletin of earthquake engineering, April 2011

ix. FEMA 356, Pre-standard and commentary for seismic rehabilitation of buildings, Federal Emergency Management Agency, Washington DC, USA, 2000.