Citation:
Adhikari, P., T. Azuhata (2019), Fragility evaluation of RC buildings designed by Nepal
Building Code considering deformation capacity, Synopsis of IISEE-GRIPS master report.

FRAGILITY EVALUATION OF RC BUILDINGSDESIGNED BY NEPAL BUILDING CODECONSIDERING DEFORMATION CAPACITY
Praveen Pratap Adhikari1,2Supervisor:

Tatsuya AZUHATA3

ABSTRACT
Fragility evaluation assessed for RC moment-resisting frame structures designed by the Nepal Building
Code considering deformation capacity. The site soil type, the number of stories, and seismic protection
intensity were supposed to be design variables. Also, the limit state (global seismic damage index) andmaximum inter-story drift ratio had employed as the damage identifiers. The non-linear static push-overanalysis determined the limit state of the structure. The probability of exceeding each damage level ineach scaled earthquake intensities of applied 40 ground motions is determining by incremental dynamicanalysis (IDA) with the aid of dynamic response time history analysis. The fragility curves of the target
building and revised model building derived by the statistics analysis are considering lognormal
accumulative distribution function. The fragility evaluation of the target structure and revised model
against earthquakes motion were examined using the developed fragility curves. The results indicatethat target RC frame structures designed by the Nepal Building Code (NBC 105:1994 and NBC
110:1994) can be achieved satisfactorily with some modification in the limit state of shear design.
Keywords: Limit state, maximum inter-story drift ratio, incremental dynamic analysis, fragility curve.

1. INTRODUCTION
Nepal lies on the Main Himalayan Thrust (MHT) fault line that divides the Indian and Eurasian tectonicplates. The movement of the Indian Plate towards north collided with the Eurasian Plate. Due to interplate crustal shortening activity, the probability of the occurrence of an earthquake is very high in theHimalaya Range. Therefore, Nepal is one of the world's most earthquake-prone countries. The recent
big earthquake occurred in Nepal was the Gorkha Earthquake in 2015 (Mw 7.8) resulted in huge lossesof lives and physical infrastructures. To overcome these types of earthquake fatalities, we needearthquake-resistant resilient structures based on a seismic performance design. The purpose of thisstudy is to evaluate the seismic performance of a target RC structure designed by Nepal Building Code(NBC105:1994, Seismic Design of Buildings in Nepal and NBC 110:1994, Plain and Reinforced
Concrete) and to know the size of an earthquake the buildings can sustain.
2. DATAIn this study, a set of 40 ground motions data are applying to the analytical model for the dynamic
response time history analysis which recorded in various earthquakes in California. These data are1

Department of Urban Development and Building Construction (DUDBC), Kathmandu, Nepal.
IISEE-GRIPS master course student
3International Institute of Seismology and Earthquake Engineering (IISEE), Building Research Institute (BRI).
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attained from the web-based PEERground motion database and theCenter for Engineering Strong
2.0
Motion Data (CESMD). The ground1.8
motions data consists of Type D site
1.6of NEHRP (National Earthquake
1.4
Hazards Reduction Program) having
1.2
earthquake magnitude ranges from
1.0
6.5 to 6.9 Mw, and source-to-site
distance ranges from 13 to 40 km.
0.8Each ground motion systematically0.6
scaled to increasing earthquake
0.4
intensities from 0.1 g to 1.5 g.
0.2
Altogether 600 (40 x 15) numbers of0.0
the earthquake intensities are applied
0.01
0.1
1
10
for the dynamic response time
Period (s)history analysis in the incremental
Figure 1. Acceleration response spectra of ground motions used dynamic analysis (IDA). The
for dynamic response analyses.
acceleration response spectra of theselected 40 ground motions, scales at
PGA of 0.4 g, are shown in Figure 1.

Sa (g)

Acceleration response spectra (h=5%)
Ground motions scaled at PGA of 0.4 g

3. METHODOLOGY
3.1. Target building structure

Figure 2. An analytical model of the target building by
the STERA 3D computer program.

In this study, a 7-story special momentresisting framed RC structure selected as atarget structure. It consists of size 27.94 mx 17.33 m having standing height 23.1 m
in medium soil site condition. The size ofthe column is 600 mm x 600 mm. The
analytical model constructed with the aidof the STERA 3D (Version 10.1, Saito T.,2019) computer program, which shown inFigure 2. The only bare frame structure is
carried out for the model analysis. The
compressive strength of concrete of 20
N/mm2 and tensile yield strength of steel
rebar of 500 N/mm2 is used in the target
building and also in the analytical model.

3.2. Research Procedure
The research procedure for this study follows mainly in three steps. They are:
Step 1: Evaluate the limit state of the building by non-linear static pushover analysis,
Step 2: Execute incremental dynamic analysis proposed by Vamvatsikos and Cornell (2002), andStep 3: Statistics analysis for the fragility evaluation by the lognormal cumulative distribution function.
3.2.1. Estimation of limit state
The evaluation of the limit state was carried out by non-linear static pushover analysis. The static pushover analysis is a technique in which the model of the structure subjected to predetermined lateral forces.

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The lateral forces represent the relative inertia forces, which is equivalent to the seismic forces inducedby earthquake ground motion. In the static pushover analysis, applied forces gradually increased, andthe sequences of cracks, yielding plastic hinge formations, and the load at which the failure of the various
structural components occur recorded. This incremental process continued until the structural model
reaches a collapse or target global structural drift limit achieved.
3.2.2. Incremental Dynamic Analysis
The Incremental Dynamic Analysis (IDA) proposed by Vamvatsikos D. and Cornell C.A. (2002) andused to the collapse evaluation. To develop the analytical fragility curve, it is required to carry out theincremental dynamic analysis. IDA is executed to estimate the limit-state capacity and the seismic
demand for a specified structure by performing a series of non-linear dynamic response time history
analysis under a suite of multiple scaled ground motions records. For evaluating the seismic capacity,
the selected ground motion intensity increased incrementally until the intended structural capacity
reaches the global collapse achieved.
3.2.3. Statistics analysis for fragility evaluation
The conditional probability that the maximum inter-story drift ratio (IDRmax) exceeds IDR at given PGA
is calculated (for example, Nagae T. et al., 2006, Jiang H. et al., 2012 etc.) by the Eq. (1) moreover,consequently it applied in the fragility evaluation.
P[IDRmax > IDR] = 1- P[IDRmax ≤ IDR]
= 1- ϕ(ln(𝑥)−ln(𝜇))𝛿(1)where ϕ is the function of the normal cumulative distribution function,
x is the limit state of the target structure, i.e. IDR,
μ is the mean of the statistical data, computed by 50th percentile data, andδ is the standard deviation of the statistical data, which is the equivalent dispersion of the 16th percentile
and 84th percentile data of maximum IDR in the normal distribution, computed by Eq. (2).
δ=𝑙𝑛(𝐼𝐷𝑅𝑚𝑎𝑥)84%−𝑙𝑛(𝐼𝐷𝑅𝑚𝑎𝑥)16%2(2)where (IDRmax)84% is the 84th percentile and (IDRmax)16% is the 16th percentile statistics data of themaximum inert-story drift ratio for specified scaled ground intensities.
A fragility curve is developed from the behavior model of a structure, capacity and a suiteof ground motions. Fragility curves is a cumulative distribution function that describes the probabilityof collapse or failure. The maximum inter-story drift ratio (IDRmax) of the structure is adopted as anengineering demand parameter (EDP) to represent the degree of seismic response in the incremental
dynamic analysis and applied for the fragility evaluation.

4. RESULTS AND DISCUSSION
4.1. Results of the target building structure
The limit state of the structure evaluated by the non-linear static pushover analysis is depicted in Figure
3. From the push-over analysis, the first shear failure occurred at first floor in x-direction resulted ininter-story drift ratio of 0.011 (≈ 1/90). So, the limit state of the target structure assumed 1/90. The firstRC member undergoes in shear failure occurred at column no. 17 of the first floor in step no. 495 of
STERA 3D which can be seen clearly in Figure 4.

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Figure 3. Drift-shear relation in x-direction. Eachcolored line indicates the drift-shear relation of
the floors. The dashed red line indicates the driftshear relation in each floor at the first shear
failure.

Figure 4. Failure mode in the analytical model ofthe target building. The figure shows the firstmember undergoes in shear failure is Column no.
17 at the first floor in step number 495 out of1000.

Figure 5. Statistics of seismic responses of IDA.
The orange, blue and green lines indicate the 16th,50th and 84th percentile curves of each level of
PGA respectively. The different colored circles
indicate the maximum IDR responses of eachscaled intensity of the ground motions.

Figure 6. Fragility curve of the target building.
Each solid circle point in the curve represents theprobability of collapse (exceedance of the damage
parameter, which is related with maximum interstory drift ratio over the limit state value at a given
ground motion intensity parameter.

The maximum IDR (inter-story drift ratio) for scaled input of 40 ground motions appliedin the IDA (incremental dynamic analysis) was sorted in ascending order. Then, 6th, 20th and 34th lowest
data were picked for the 16th, 50th and 84th percentile data to a continuous estimation of seismicresponse. The result of the incremental dynamic analysis (IDA) depicted in Figure 5. From the result ofIDA, finally, we derived the probability of collapse of the structure by using Eq. (1), and consequently
plotted the fragility curve, as shown in Figure 6. The conditional probabilities become high as PGA
becomes large.
The design aims to achieve acceptable probabilities that the structure will not become unfit
for the use, which is ensured by bending or flexural failure mode. However, shear failure appears in themodel of the target structure. To overcome the shear failure, the target structure is re-modelling byadopting the following techniques, and all the research procedure apply in the revised model.
• Reducing the yield strength of reinforcement from 500 to 415 N/mm2.
• Increasing the size of shear reinforcement (12 mm and 10 mm for column and beam respectively).
• Providing additional shear reinforcement in the column in terms of legs, wherever is necessary.

44.2. Results of revised target building model structure
From the non-linear static pushover analysis, no shear failure was observed in the revised model. Second
floor and x-direction were found the weakest floor, and weaker direction and the failure mode wasflexural type. The result of the push-over analysis is depicted in Figure 7. For flexural failure, the limit
state is assumed to be the ultimate limit, that is 0.03 though the target drift was 1/50. The flexural failure
behavior in the analytical model can be seen clearly in Figure 8.

Figure 7. Drift-shear relation in the x-direction of therevised model of the target building. Each coloredcurvature indicates the drift-shear relation of thefloors. The dashed red line indicates the drift-shear
relation in each floor at 1/50 target drift.

Figure 8. Failure mode in the revised analyticalmodel of the target building. Yellow mark at thejoints indicates the flexural failure after yielding.
1<U<5 and 5<U indicate the ductility index formoderate damage and severe damage.

The maximum IDR (inter-story drift ratio) for scaled input of 40 ground motions appliedin the IDA was sorted in ascending order. With the help of 6th, 20th and 34th lowest data, 16th, 50thand 84th percentile data were estimated continuously. The result of the incremental dynamic analysis(IDA) for the revised model depicted in Figure 9. The probability of a collapse was computed by using
Eq. (1) moreover, consequently plotted the fragility curve for the revised model, as shown in Figure 10.

Figure 10. Fragility curve of the revised model ofthe target structure.

Figure 9. Statistics of seismic responses of IDA of
the revised model of the target structure.

4.3. Comparison of fragility evaluation between target and revised target model structure
The comparison of the fragility evaluation between target structure and revised target model structure
are depicted through conditional probabilities of collapse in Table 1 and fragility curves in Figure 11.

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Table 1. Comparison of the probabilityof collapses.

Figure 11. Comparison of the fragility curves. Orange, redand green cross and solid circles in the figure show theprobability of collapse of the fragility curves for IDR 1/90,2/100, and 3/100 respectively.
From Figure 11, the 33% of probability of collapse is found in the target structure (shearfailure type) while it is 5% probability of collapse in the revised model (flexural failure type) for 400
gals. The significant difference of probability of collapse can see from the comparison of fragility curves
accounting shear and flexural failure.

5. CONCLUSIONSThe Fragility curves of the target building and revised model building were derived with the aid of IDAand statistics analysis. The probabilities of maximum inter-story drift ratio of RC frames of both models
against earthquakes were examined using the developed fragility curves. From the fragility evaluation,
it is concluded that the seismic performance of the target structure can be increased by ensuring flexural
type failure with respect to shear failure. The results indicate that RC frame structures designed by theNBC can be achieved satisfactorily with some modification in limit state of shear design.

ACKNOWLEDGEMENTS
This research was conducted during the individual study period of the training course “Seismology,Earthquake Engineering and Tsunami Disaster Mitigation” by the Building Research Institute, JICA,and GRIPS.I would like to express my sincere gratitude to Dr. Tatsuya AZUHATA for their continuoussupport, valuable suggestion and instruction during my study.
REFERENCES
Jiang H., Lu X., and Chen L., 2012, Journal of Asian Architecture and Building Engineering/May 2012/160.
Nagae, T., Suita K., and Nakashima M., 2006, Annuals of Disas. Prev. Res. Inst., Kyoto University, No. 49 C.
NBC 105:1994, and 110:1994, Government of Nepal, Ministry of Urban Development, DUDBC.
Saito T., 2019, STERA 3D (Structural Earthquake Response Analysis 3D) Technical Manual, v 6.1, website: http://www.rc.ace.tut.ac.jp/saito/software-e.html.
Vamvatsikos, D., and Cornell, C.A., 2002, 12th European Conference on Earthquake Engineering, Paper
Reference 479.
Web site: PEER Ground Motion Database, https://ngawest2.berkeley.edu/.
Web site: Center for Engineering Strong Motion Data, CESMD, https://strongmotioncenter.org/.

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