LIFE-CYCLE AND RESILIENCE ANALYSIS OF RC BUILDINGS IN

BUCHAREST, ROMANIA

Florin PAVEL1, Dan STANESCU2, Radu VACAREANU3, Veronica COLIBA4, Ionut CRACIUN5

ABSTRACT

This paper focuses on the life-cycle and resilience analysis for three RC frame structures. The three seven-story

RC structures are designed for three levels of design peak ground acceleration corresponding to different mean

return periods. Multiple-stripe analyses are performed in order to assess the fragility parameters of the analyzed

structures. The seismic resilience and life-cycle assessment are based on the results of a seismic risk analyses

performed using both the site-specific seismic hazard curve, as well as a Monte-Carlo simulated earthquake catalog

for the Vrancea intermediate-depth seismic source. Moreover, the collapse fragility is also evaluated based on

several methodologies proposed in the literature. The results of the seismic resilience and the life-cycle analysis

show smaller losses during the life-cycle of the analysis for the structure designed for the largest considered peak

ground acceleration and a faster recovery of the functionality for the same structure.

Keywords: pushover analysis; epistemic uncertainty; aleatory variability; fragility curves; ground motion

recordings

1. INTRODUCTION

In this paper, an assessment of the life-cycle costs and of the resilience is performed for three seven

story RC frame structures situated in Bucharest (Romania). The difference between the three frame

structures is that each one was designed using a different peak ground acceleration so as to mimic the

evolution of the Romanian seismic design code. Three random variables, namely concrete and steel

strength, as well as the gravitational loading are taken into consideration. Both nonlinear static, as well

as dynamic time-history analyses are performed using the SeismoStruct code. The nonlinear time-

history analyses are performed using a dataset of ground motions recorded during the Vrancea

earthquakes of March 1977 (moment magnitude MW = 7.4 and focal depth h = 94 km), August 1986

(MW = 7.1, h = 131 km) and May 1990 (MW = 6.9, h = 91 km). Multiple-stripe analyses (Jalayer and

Cornell, 2009) are performed in order to evaluate the seismic fragility of the analyzed structures. The

fragility assessment for several damage states including collapse for the structure designed using the

current version of the Romanian seismic design code P100-1/2013 (2014) is performed using several

approaches given in the literature. The seismic resilience and life-cycle analyses are based on the results

of a seismic risk analysis performed using as input both the site-specific seismic hazard curve, as well

as the ground motion amplitudes derived from a Monte-Carlo simulated earthquake catalog coupled

with a ground motion model, approach previously used by Pavel et al. (2017).

1Lecturer, Technical University of Civil Engineering Bucharest, Bucharest, Romania, florin.pavel@utcb.ro 2Engineer, Technical University of Civil Engineering Bucharest, Bucharest, Romania,

dan.constantion.stanescu@gmail.com 3Professor, Technical University of Civil Engineering Bucharest, Bucharest, Romania, radu.vacareanu@utcb.ro 4PhD student, Technical University of Civil Engineering Bucharest, Bucharest, Romania, veronica.coliba@utcb.ro 5PhD student, Technical University of Civil Engineering Bucharest, Bucharest, Romania, ionut.craciun@utcb.ro

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2. DESCRIPTION OF STRUCTURES

The three RC frame structures have a doubly symmetrical section (18.0 x 18.0 m) consisting of columns

and beams. The thickness of the RC slab is 15 cm. A concrete class C30/37 and steel grade S500 are

used for all the structural elements. The structural design was performed according to the current version

of the Romanian seismic design code P100-/2013 (2014) which follows the EN 1998-1/2004 (2004)

format. The design peak ground acceleration was 0.24 g (value corresponding to a mean return period

of 100 years as in the 2006 version of the Romanian seismic design code), 0.30 g (value corresponding

to a mean return period of 225 years as in the 2014 version of the Romanian seismic design code) and

0.36 g (value corresponding to a mean return period of 475 years). P100-1/2013 (2014) is based on a

performance-based approach with two fundamental requirements: damage control (serviceability limit

state SLS) and life safety (ultimate limit state ULS). Contrary to EN 1998-1/2004 (2004), in the

Romanian seismic code the inter-story drifts are checked for both performance levels. The mean return

period of the seismic action associated to the two limit states is 40 years for SLS and 225 years for ULS.

The structural design was performed for ductility class high (DCH) with a behavior factor q = 6.75. The

three structures will be denoted hereafter as S1 (deign peak ground acceleration of 0.24 g), S2 (design

peak ground acceleration of 0.30 g) and S3 (design peak ground acceleration of 0.36 g).

The planar view of the analyzed structures is shown in Figure 1. The cross-section of the columns is

55x55 cm and is similar for all three structures (the reinforcement is larger for structures S2 and S3)

while the beam cross-section increases from 25x50 cm for S1 to 25x55 cm for S2 and 30x60 cm for S3.

As such, the reinforcement pattern does not change too much from structure to structure. The shear

reinforcement in both columns and beams was computed so as to avoid any brittle shear failure

(considering also the minimum requirements specified by the current seismic design code). Due to its

symmetry, it was decided to perform the pushover analyses on a simplified structure, namely a planar

frame also highlighted in Figure 1.

Due to the shape of the design response spectrum from the Romanian code P100-1/2013 (2014) which

has a long constant acceleration plateau up to the control period TC = 1.6s, the resulting design spectral

accelerations are 0.66 g for structure S1, 0.75 g for structure S2 and 0.90 g for structure S3.

Figure 1. Planar view of the analyzed structures

Three random variables, namely the concrete compressive strength fc, steel strength fy and gravitational

loading on beams Q are considered in the analyses as sources of epistemic uncertainties. The mean

values of the three considered random variables are: fc = 38 MPa, fy = 550 MPa and Q = 35 kN/m, while

their associated coefficients of variation are 0.15, 0.05 and 0.40, respectively.

The pushover analyses were performed firstly using mean values of the strengths of materials and

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gravitational loading. A comparison of the three pushover curves obtained using SeismoStruct code is

shown in Figure 2. A bilinear model was used for the reinforcement, while for concrete the Mander et

al. (1988) model was applied.

Figure 2. Comparison of pushover curves for the three analyzed structures

3. NONLINEAR TIME-HISTORY ANALYSES

The nonlinear time-history analyses are performed using a ground motion dataset consisting of 20

horizontal components recorded during the Vrancea intermediate-depth seismic events of March 1977

(moment magnitude MW = 7.4 and focal depth h = 94 km), August 1986 (MW = 7.1, h = 131 km) and

May 1990 (MW = 6.9, h = 91 km).

Figure 3. Absolute acceleration response spectra for the 20 horizontal components used for nonlinear time-

history analyses, as well as mean value and mean ± one standard deviations values (green contour)

The multiple-stripe analysis (Jalayer and Cornell, 2009) is performed for a range of SA(T1) values

between 0.1 g and 1.6 g. The same ground motion dataset is used for each individual stripe. Besides the

analysis using mean values of strengths and loading, a second approach is also applied in the multiple-

stripe analysis. The procedure proposed by Franchin et al. (2017) of associating a single random model

to a single individual ground motion recording is also used in this study, as well. The results in terms of

median curves (in format SA(T1) and top displacement), as well as 16th and 84th percentile curves are

shown in Figure 4. One can notice that the curves are characterized by a sort of weaving behavior

(Vamvatsikos and Cornell, 2002) followed by the beginning of a softening plateau (more visible on the

84th percentile curves). It is noticeable the fact that the length of the softening plateau decreases with the

design peak ground acceleration, thus showing the onset of collapse.

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Figure 4. Median, 16th and 84th percentile curves obtained from multiple-stripe analyses for the three analyzed

structures. The median curves are shown with full lines, while the 16th and 84th percentile curves are shown with

dashed lines.

4. SEISMIC FRAGILITY ANALYSIS

In order to perform the seismic risk, as well as the life-cycle and resilience analyses of the three RC

frame structures, the seismic fragility is firstly evaluated. Four damage state, namely slight damage,

moderate damage, extensive damage and complete damage are defined, similarly as in HAZUS (2012).

The roof drift ratio (RDR) is the preferred IM (intensity measure) due to its simplicity and its direct

connection with the response of single degree of freedom systems (SDOF) used subsequently in the

evaluation of seismic demand. The corresponding RDR ratios for the first three damage states were

taken identical for all three structures due to the similarity of the pushover curves. However, in the case

of the collapse damage state, the procedure proposed by Camata et al. (2017) is applied. More

specifically, the RDR for collapse is taken as the value corresponding to a 50% decrease of the base

shear force on the pushover curve. More details about this procedure can be found in the paper of Camata

et al. (2017).

Table 2. Parameters of the fragility functions (median value and logarithmic standard deviation) for the three

structures (with mean strengths and loadings)

Structure Slight damage Moderate damage Extensive damage Complete damage

Median St. dev. Median St. dev. Median St. dev. Median St. dev.

S1 0.310 0.458 0.521 0.494 1.088 0.366 1.621 0.488

S2 0.338 0.435 0.565 0.478 1.174 0.412 1.709 0.317

S3 0.376 0.409 0.629 0.435 1.284 0.372 1.841 0.367

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The fragility parameters for the three structures with mean strengths and loadings and which are to be

employed in the seismic risk analysis are given in Table 2. The annual collapse frequency of the analyzed

structure is obtained by convolving the structural fragility with the corresponding seismic hazard curves

for SA(T1). The seismic hazard curves for each SA(T1) for Bucharest are based on the results from Pavel

and Vacareanu (2017).

5. SENSITIVITY ANALYSIS

A sensitivity analysis is subsequently conducted in order to evaluate the impact of varying the values of

the random variables on the results obtained from multiple-stripe analysis. Only structure S2 is

considered in the analysis, since it is designed using the current version of the Romanian seismic deisgn

code.

Some results for structure S2 are shown in Figure 5 in which the median, 16th and 84th percentile curves

are compared for the models in which the concrete strength, steel strength and gravitational loading on

beams are taken as the mean value ± one standard deviation.

Figure 5. Median, 16th and 84th percentile curves obtained from multiple-stripe analyses for the models with

mean ± 1 standard deviation strengths and loadings. The median curves are shown with full lines, while the 16 th

and 84th percentile curves are shown with dashed lines.

For structure S2, the three random variables were varied within the range ± 1 standard deviations away

from the mean value and combined with each other. Finally, response surfaces were constructed both

for the median value of the collapse SA(T1), as well as for the SA(T1) value corresponding to a 1% inter-

story drift.

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Figure 6. Response surfaces computed for the three random variables for SA(T1) corresponding to collapse.

Figure 7. Response surfaces computed for the three random variables for SA(T1) corresponding to an inter-story

drift of 1%.

Based on the computed response surface for collapse SA(T1), 10000 Monte Carlo random samples are

generated consistent with the assumed probability distribution for each random variable. For each

sample, the median collapse capacity is determined. The resulting collapse fragility is compared with

the results for the same structure shown in Table 2 in Figure 8. It is obvious that the median collapse

SA(T1) is smaller when considering the model uncertainties while the logarithmic standard deviation is

larger, an observation similar with the one made by Liel et al. (2009). However, the differences between

the two collapse fragility curves (less than 10% for both median value and logarithmic standard

deviation) are smaller than in the case of Liel et al. (2009).

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Figure 8. Comparison of collapse fragilities obtained for the mean model and from Monte Carlo sampling based

on the response surface

Subsequently, the fragility parameters for the same structure were analyzed using three more

approaches, namely:

• Response spectrum method taking into consideration the correlation between the three selected

random variables (similarly as in the study of Liel et al. (2009));

• FOSM (First order second moment) reliability method described by Vamvatsikos and

Fragiadakis (2010) or Bradley and Lee (2010);

• ASOSM (Approximated second order second moment) described by Liel et al. (2009).

The results in terms of collapse fragility parameters are summarized in Table 3. One can notice that both

the median collapse SA(T1) and its logarithmic standard deviation are quite well constrained.

Table 3. Comparison of the collapse fragility parameters for structure S2

Method

of assessment

Collapse

Median St. dev.

Mean model 1.709 0.317

Response surface (no

correlation) 1.575 0.332

Response surface

(correlation = 0.5) 1.608 0.333

Response surface

(correlation = 1.0) 1.657 0.359

FOSM 1.709 0.373

ASOSM 1.714 0.355

6. SEISMIC RISK, LIFE-CYCLE AND RESILIENCE ANALYSES

Firstly, the annual rates of collapse are computed for all three structures using the fragility parameters

defined in Table 2 and Table 3. In addition, the collapse probability for various SA(T1) value is also

determined for each of the above-mentioned structures. The annual rate of collapse is 3.1‧10-4 for

structure S1, 2.9‧10-5 for structure S2 and 3.6‧10-5 for structure S3. The annual rates of collapse obtained

using the fragility parameters for structure S2 defined in Table 3 are shown in Table 4. One can easily

notice that the smallest annual rate of collapse is obtained for the model using mean strengths and

loadings mentioned in Section 2.

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Table 4. Comparison of the annual collapse rates for the structures defined in Table 3

Method

of assessment

Annual rate of

collapse

Mean model (S2) 2.9‧10-5

Response surface (no

correlation) 6.3‧10-5

Response surface

(correlation = 0.5) 5.6‧10-5

Response surface

(correlation = 1.0) 6.6‧10-5

FOSM 6.5‧10-5

ASOSM 4.9‧10-5

Next, the annual frequency of collapse in terms of mean value and its corresponding standard deviations

conditioned on the value of SA(T1) is assessed, using the relations given by Baker and Cornell (2008).

The results are summarized in Table 5. One can notice that the mean collapse rate corresponding to the

design spectral acceleration is of the order 10-2…10-3, while in the case of a 50% increase of SA(T1), the

collapse rate is of the order 1.6…2.0‧10-1.

Table 5. Conditional rate of collapse for structures S1 – S3

SA(T1)

Conditional rate of collapse Structure S1 Structure S2 Structure S3 Mean Std. deviation Mean Std. deviation Mean Std. deviation

0.20 g 9.0‧10-6 1.0‧10-3 6.5‧10-12 8.7‧10-7 7.3‧10-10 9.2‧10-6 0.40 g 2.1‧10-3 1.5‧10-2 2.3‧10-6 5.2‧10-4 1.6‧10-5 1.4‧10-4 0.60 g 2.1‧10-2 4.9‧10-2 4.8‧10-4 7.4‧10-3 1.1‧10-3 1.1‧10-2 0.80 g 7.4‧10-2 9.2‧10-2 8.3‧10-3 3.1‧10-2 1.2‧10-2 3.7‧10-2 1.00 g 1.6‧10-1 1.4‧10-1 4.6‧10-2 7.2‧10-2 4.8‧10-2 7.4‧10-2 1.20 g 2.7‧10-1 1.8‧10-1 1.3‧10-1 1.2‧10-1 1.2‧10-1 1.2‧10-1 1.40 g 3.8‧10-1 2.1‧10-1 2.7‧10-1 1.7‧10-1 2.3‧10-1 1.6‧10-1

Subsequently, in order to evaluate the seismic resilience and the life-cycle analysis, the annual seismic

losses are obtained for structures S1 – S3 using the fragility parameters from Table 2. Two approaches

are applied in order to derive the annual seismic losses, namely the convolution between the seismic

fragility and the site-specific seismic hazard curve and by using a Monte-Carlo simulated earthquake

catalog (with a duration of 50000 years and containing only MW ≥ 6.0 events) for the Vrancea

intermediate-depth seismic source. The latter approach has also been employed in the seismic risk study

of Pavel et al. (2017). The results in terms of mean annual losses are shown in Table 6. One can observe

that the results derived from the seismic hazard curve are slightly larger than the one based on Monte-

Carlo simulations. However, in the case of the standard deviations, the results from Monte-Carlos

simulations are more than four times larger as compared to their corresponding mean values.

Table 6. Comparison of mean annual losses obtained for structures S1 – S3

Structure

Annual loss Hazard curve Monte-Carlo simulation Mean Std. deviation Mean Std. deviation

S1 0.63% 0.14% 0.57% 2.45%

S2 0.53% 0.11% 0.46% 2.15%

S3 0.38% 0.06% 0.33% 1.66%

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The seismic loss curves for the three structures are computed using the results from the two approaches.

The two approaches show good agreement for annual rates of exceedance of up to 10-3.

Figure 9. Comparison of the loss hazard curves computed for the three structures

Subsequently, the loss conditioned on various SA(T1) levels is evaluated for the three structures using

also the relations provided by Baker and Cornell (2008). The results show, as expected, an increasing

trend for the mean relative losses with the increase of SA(T1) and a capping of the corresponding

standard deviations for SA(T1) in excess of 1.0 g.

Figure 9. Comparison of the mean loss curves (left) and their corresponding standard deviation (right)

conditioned on various SA(T1) values

Based on the results of the above-mentioned seismic risk analyses, the resilience and the life-cycle costs

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are assessed. The resilience assessment is based on the procedure proposed in the work of Burton et al.

(2015), which was also employed in the study of Pavel and Vacareanu (2016), while the life-cycle

analysis applied the methodology described in the study of Kappos and Dimitrakopoulos (2008). The

seismic resilience curves (in terms of mean curve and COV for functionality) showing the recovery of

the functionality in the aftermath of the earthquake are plotted in Figure 10. The results are obtained

based on the previously discussed Monte-Carlos simulated earthquake catalog for the Vrancea

intermediate-depth seismic source. One can notice that there is a quite rapid recovery of the functionality

in the case of structure S3. In addition, the variability in the results decreases with the increase of the

design peak ground acceleration.

Figure 10. Seismic resilience curves for the three structures – mean values (left) and coefficients of variation

(right)

Figure 11. Life-cycle costs computed for the three structures as a function of planning horizon and for a discount

rate of 4%. With green color is shown the area between the mean ± one standard deviations.

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The life-cycle analyses of the three structures is shown in Figure 11. The mean expected relative cost

with respect to the initial value of the structures, as well as the corresponding standard deviations are

obtained using the procedure of Kappos and Dimitrakopoulos (2008) and for a discount rate of 4%.

7. CONCLUSIONS

In this paper, a life-cycle and resilience analysis are performed for three RC frame structures situated in

Bucharest (Romania) and which were designed for three levels of design peak ground acceleration

corresponding to mean return periods of 100 years, 225 years and 475 years. The effects of varying three

random variables (concrete compressive strength, steel yield strength and gravitational loading on

beams) on the nonlinear seismic response are assessed using the response surface approach. Firstly, a

fragility assessment based on multiple-stripe analyses using a ground motion database of 20 horizontal

components recorded during the Vrancea intermediate-depth seismic events of March 1977, August

1986 and May 1990 is performed. The SA(T1) – top displacement curves computed using mean values

are similar with the ones obtained thorough an approach in which a distinct ground motion recording is

coupled with a distinct structural model. The collapse fragility for the structure designed for a peak

ground acceleration of 0.30 g is assessed using several approaches given in the literature and the results

show quite well-constrained median SA(T1) and corresponding logarithmic standard deviations. The

seismic losses in terms of annual exceedance rates and conditional on SA(T1) are determined using two

procedures for the evaluation of the ground motion amplitudes, namely the site-specific seismic hazard

curve and a Monte-Carlo simulated earthquake catalog coupled with a ground motion model, a

procedure previously used in the study of Pavel et al. (2017). The seismic resilience and the life-cycle

analysis show smaller losses during the life-cycle of the analysis for the S3 structure (designed for the

largest considered peak ground acceleration) and a faster recovery of the functionality for the same

structure.

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