Proceedings of IOE Graduate Conference, 2019-SummerPeer Reviewed

Year: 2019 Month: May Volume: 6ISSN: 2350-8914 (Online), 2350-8906 (Print)

Seismic Risk Assessment of Vertically Irregular Buildings

Latip Kumar Sharma a, Kamal Bahadur Thapa b

a, b Department of Civil Engineering, Pulchowk Campus, IOE, Tribhuvan University, NepalCorresponding Email: a 073msst110@ioe.edu.np, b kamal.thapa@ioe.edu.np

AbstractThe construction of the vertically irregular buildings are almost inevitable due to the functional as well asaesthetic requirements. However, Post-Earthquake damage assessment shows that the structural irregularityplays vital role in the seismic performance of the buildings. Sudden change in the strength, stiffness as well asload path discontinuity increase the seismic demand of the building which increase the vulnerability of thebuildings. Seismic risk assessment in certain geographical area requires the fragility model of the differentarchetype of the buildings. In this research, a humble effort is made to comprehend the analytic seismicfragility estimate of the existing types of the vertically irregular reinforced concrete buildings in Nepal.

KeywordsVerical Irregularity, Seismic risk, Reinforced Concrete, Pushover Curve, IDA curves, Fragility curves

1. Introduction

On 25th April 2015, a strong earthquake of momentmagnitude Mw 7.8 hit central part of Nepal causingover 8000 casualties and nearly 23000 injuries. About7 lakhs plus residential buildings, 4000 governmentoffices and 8200 schools were damaged due to thisearthquake. 14 districts were severely affected by this2015 Gorkha Earthquake followed by severalaftershocks[1].Various post damage assessmentstudies were made to assess the seismic performanceof the existing buildings in Nepal so as to providevaluable insight to the seismic risk and futureopportunities for retrofit and mitigation.

Reinforced concrete (RC) buildings construction hasincreased drastically over the last few decades in thecapital as well as other major urban centers of Nepal.According to the National census of 2011, about 10%of the buildings construction in Nepal is RC type,with more than 40% of the total RC construction areconcentrated in the Kathmandu valley[2] . Recentfield investigation shows that majority of the RCconstruction does not comply with the building codeprovisions.Majority of the buildings lacks gradualreduction of the stiffness as well strength reductiondue to the absence of the infill at the ground story aswell as load path discontinuity. These structuraldeficiencies increase the seismic vulnerability of thebuildings[3].

In this context, present study focuses on the seismicfragility estimate of the existing RC verticallyirregular buildings which helps to develop thevulnerability model for these type of the buildings.The demand estimate of the buildings has been doneby the static pushover analysis of the buildings at theevery floor level. Using the modal analysis results andpushover curves, fragility curves at the different limitstates are evaluated using MATLAB code based toolSPO2FRAG[4]. To be structure-specific estimate ofthe fragility, the intensity measures are spectralacceleration Sa (T1) at the fundamental time-period ofthe buildings and the structural demand asEngineering demand parameter (EDP) which isinter-storey drift capacities at any story level.

2. Development of Analytical fragilityestimate

The next generation seismic design and assessmentprocedure for buildings within the performance basedframework are radical departure from the traditionalseismic design practice and performanceassessment[5]. The performance bases seismic designand assessment approach, in which the building isexpected to satisfy certain performance requirementsin its lifetime, make a paradigm shift from traditionaldesign and assessment procedure.The uncertainty andrandomness in the building performance and seismic

Pages: 589 – 594

Seismic Risk Assessment of Vertically Irregular Buildings

hazard will be captured and quantified in each steps indesign and assessment procedure.Finally theperformance will be measured in terms of direct andindirect economic losses and causalities [6].

Perhaps the most notable example is the problem ofthe estimating the rate of the earthquakes leading thestructure to exceed the different limit states which canbe computed using total probability theorem[4]

The methods used to derive the fragility function canbe classified as empirical, analytical or hybrid[7]. Inrecent years, a considerable effort has been made tocompute the analytical fragility which is based on thenumerical model, especially for the structure specificfragility function. Analytical method rely on theadvanced numerical model of the structure subjectedto nonlinear dynamic analysis.These nonlineardynamic analysis (NDA) can be used to build therelationship between the demand and the spectralacceleration or Peak ground acceleration (PGA),which are type of IMs. Some of the widely used NDAare cloud analysis [8], multiple stripe analysis(MSA)[9], Incremental dynamic analysis (IDA)[10].IDA seeks to map the seismic structural responsestatistically, from the first sign of nonlinear inelasticbehavior up to eventual collapse. However the maindisadvantage of this method (including CA and MSA)is the computational burden and the amount of theeffort that has to go into the modelling of the highlynonlinear behavior. Combination of the selection ofadequate ground motion history, numerical modelcomplexity, required number of the runs and theelaborate post processing motivates the engineers toseek the simplified, approximate procedures.Simplified procedure which is based on nonlinearpushover analysis and MATLAB code based tool(SPO2FRAG) to convert pushover curves to fragilitycurves are used in this research work.

3. Fragility functions for consideredNepalese RC buildings

The seismic risk assessment can be described usingvulnerability or fragility functions. Fragility functionsprovide the probability of exceeding different damagestates for a set of levels of ground shaking whereas thevulnerability functions are related to the probability ofloss given a level of shaking.

In this research study, two typical types of the verticalirregularity along with their regular counterpart areconsidered, first type is Open ground storey (OGS)

and second type is load path discontinuity (floatingcolumns) which are faulty RC construction prevalentin the urban centers.

Analytical fragility curves are derived based on theresults of the static pushover curves and SPO2FRAGsoftware.SPO2FRAG (Static Pushover to Fragility), aMATLAB coded software tool for estimating structurespecific seismic fragility curves of buildings, using theresults of static pushover analysis.

The SPO2FRAG tool helps to avoid the computationaldemanding dynamic analyses by simulating theresults of the incremental dynamic analysis viaSPO2IDA algorithm[11] and an equivalentsingle-degree-of-freedom approximation of thestructure.

The step by step process of constructing the fragilityfunctions are as follows

Step 1: Appropriate numerical modelling of theselected buildings for nonlinear analysis.Thecomputer software SeismoStruct[12] was used todefine the numerical models where use is made of theso-called fiber approach to represent the cross-sectionbehavior.Each fiber is associated with a uniaxialstress-strain relationship; the sectional stress-strainstate of beam-column elements is then obtainedthrough the integration of the nonlinear uniaxialstress-strain response of the individual fibers(typically 100-150).

Nonlinear material model ( Menegotto-Pinto andMander model) defined in Seismostuct are used todefine the nonlinear behavior of the material. Infilledmasonry walls are modelled,which takes into accountof the stiffness and strength degradations in eachcycle, which is implemented in SeismoStruct(2018).

The reinforcement details of the Beam (230*355) andColumns (300*300) are as per Ready to use guidelinesfor detailing of low rise reinforced buildings NBC205:2012.Slab thickness and details are also based onsame document for all selected buildings

Step 2: Derive the Static Pushover (SPO) curves atdifferent floor levels which relates the inelastic seismicresponse of the structures to that of some equivalentSDOF system.

Step 3: Define the SDOF backbone of the equivalentSDOF system using piece-wise linear idealization ofthe SPO curve. In this case bilinear fit in the spirit ofFEMA 356 displacement coefficient method[13].

590

Proceedings of IOE Graduate Conference, 2019-Summer

Figure 1: Bare frame Building(BF)

Figure 2: Infilled frame Building(FF)

Figure 3: Open ground story Building(OGS)

Figure 4: Open at one side building(OGS1)

Figure 5: Open at two side Building(OGS2)

Figure 6: floating columns Building(FC)

Figure 7: SPO-BF

Figure 8: SPO-FF

Figure 9: SPO-OGS

Figure 10: SPO-OGS1

Figure 11: SPO-OGS2

Figure 12: SPO-FC591

Seismic Risk Assessment of Vertically Irregular Buildings

Figure 13: Limit state thresholds

Step 4: Input the dynamic characteristics whichincludes the no of storey, floor masses and modalcharacteristics. In this study, multistory pushover areperformed which helps to calculate the modalproperties automatically by treating the displacementvector at the elastic limit as the first mode eigenvector.

Step 5: Using the SPO2IDA algorithm, generate ananalytical prediction of the 16%, 50%, and 84% IDAfractile curves. In this study, IM is 5% dampedspectral acceleration at the period of the equivalentSDOF and the engineering demand parameter (EDP)is automatically set to inter-storey drift ratio (IDR)when multistory SPO curves are available.

Step 6: Define the limit state thresholds as per FEMA356 or other similar documents in terms of the EDP.In this case, for the fully operational level (FO),immediate occupancy (IO), Life safety (LS), collapsePrevention (CP), the IDR thresholds are 0.5%, 1%,2%, 4% respectively.

Step 7: Up to this step, the sufficient parametersrequired to generate the fragility curves are alreadygenerated. One can update the IDA curves usingadditional variability at the nominal yields andmodelling uncertainity. However in this researchstudy, no such modifications are made.

4. Analysis and Results

The pushover curves of the buildings at every storeylevel is obtained so as to obtain model characteristicsof the buildings. The equivalent SDOF backbonecurve along with pushover curves for each types ofbuildings are as shown for each types of buildings areas shown in figure as SPOs.The generated16%,50%,84% fractile curves for each types ofbuildings are shown in figure as IDAs.

Figure 14: IDA-BF

Figure 15: IDA-FF

Figure 16: IDA-OGS

Figure 17: IDA-OGS1

Figure 18: IDA-OGS2

Figure 19: IDA-FC592

Proceedings of IOE Graduate Conference, 2019-Summer

Finally the fragility curves for each defined limit statesare plotted

Figure 20: Fragility-Bare frame Building

Figure 21: Fragility-Infilled frame Building

Figure 22: Fragility-OGS Building

Figure 23: Fragility-OGS at one side Building

Figure 24: Fragility-OGS at two side Building

Figure 25: Fragility-Floating Column Building

5. Conclusions and Recommendations

In order to study the performance of selectedvertically irregular buildings, the fragility curves aredeveloped for all the buildings for each performancelimit states (FO,IO, LS, and CP as per FEMA356).The fragility curves shows that the effect of theinfill helps to reduce the vulnerability of the buildingsin some extent. However sudden change in stiffnessand strength due to open ground storey suggest that

593

Seismic Risk Assessment of Vertically Irregular Buildings

the performance of the building is also worse thanfully infilled case.Also the discontinuity in load pathof the column increases the vulnerability of thebuildings than its regular counterpart.From thefragility curves above,the Open ground storey buildigand load path discontinous type buildings arevulnerable than their regular counterpart.

The zero slope of the IDA fractile curve shows thatopen ground building as well as floating columnbuildings reaches the dynamic instability relatively atlower intensity measures than their regularcounterpart.

Fragility functions obtained from this study can beintegrated with probabilistic seismic hazard analysisto compute the mean annual rate of exceedance ofdifferent limit states.

Loss analysis can be performed after the formulation ofthe fragility functions, which are more meaningful tothe stakeholders to know about the decision variablessuch as fatalities,economic losses and repair duration.

Acknowledgments

This research has been performed under the assistanceof Department of Civil Engineering, PulchowkCampus.I would like to thank my family,colleaguesfor supporting and encouraging me in all of mypursuits and inspiring me during the research work.

References

[1] Dipendra Gautam, Hugo Rodrigues, Krishna KumarBhetwal, Pramod Neupane, and Yashusi Sanada.Common structural and construction deficienciesof nepalese buildings. Innovative InfrastructureSolutions, 1(1):1, 2016.

[2] Humberto Varum, Rakesh Dumaru, Andre Furtado,Andre R Barbosa, Dipendra Gautam, and HugoRodrigues. Seismic performance of buildings in nepalafter the gorkha earthquake. In Impacts and insightsof the Gorkha earthquake, pages 47–63. Elsevier,2018.

[3] Avadhoot Bhosale, Robin Davis, and Pradip Sarkar.New seismic vulnerability index for verticallyirregular buildings. ASCE-ASME Journal of Risk andUncertainty in Engineering Systems, Part A: CivilEngineering, 4(3):04018022, 2018.

[4] Georgios Baltzopoulos, Roberto Baraschino, IunioIervolino, and Dimitrios Vamvatsikos. Spo2frag:software for seismic fragility assessment based onstatic pushover. Bulletin of Earthquake Engineering,15(10):4399–4425, 2017.

[5] P Rajeev. Probabilistic performance-based earthquakeengineering: A review. 2015.

[6] Selim Gunay and Khalid M Mosalam. Peerperformance-based earthquake engineeringmethodology, revisited. Journal of EarthquakeEngineering, 17(6):829–858, 2013.

[7] G Michele Calvi, Rui Pinho, Guido Magenes, Julian JBommer, L Fernando Restrepo-Velez, and HelenCrowley. Development of seismic vulnerabilityassessment methodologies over the past 30 years.ISET journal of Earthquake Technology, 43(3):75–104, 2006.

[8] F Jalayer, P Franchin, and PE Pinto. A scalardamage measure for seismic reliability analysis ofrc frames. Earthquake Engineering & StructuralDynamics, 36(13):2059–2079, 2007.

[9] Jack W Baker. Efficient analytical fragility functionfitting using dynamic structural analysis. EarthquakeSpectra, 31(1):579–599, 2015.

[10] Dimitrios Vamvatsikos and C Allin Cornell.Incremental dynamic analysis. EarthquakeEngineering & Structural Dynamics, 31(3):491–514,2002.

[11] M Fragiadakis and D Vamvatsikos. Approximateseismic performance uncertainty estimation usingstatic pushover methods. In Proceedings of the 14thWorld Conference in Earthquake Engineering, 2008.

[12] SeismoStruct SeismoSoft. A computer programfor static and dynamic nonlinear analysis of framedstructures. Disponıvel online em: http://www.seismosoft. com, 2006.

[13] F De Luca, D Vamvatsikos, and I Iervolino. Near-optimal piecewise linear fits of static pushovercapacity curves for equivalent sdof analysis.Earthquake Engineering & Structural Dynamics,42(4):523–543, 2013.

594