A Novel FRP Retrofit Solution for Improved Local and Global Seismic Performance of RC Buildings: Development of Fragility Curves and Comparative Cost-Benefit Analyses

Figures & data

Figure 1. Reference mid-rise building designed to the Portuguese REBA (1967) guidelines (in m).

Table 1. Eurocode 8 target displacements in m (and roof drifts in %) for the three buildings for a reference pga of 0.25 g.

Building	Damage limitation (DL)	Significant damage (SD)	Near collapse (NC)
Control	0.091 (0.76%)	0.117 (0.97%)	0.203 (1.69%)
Local retrofit	0.114 (0.95%)	0.147 (1.22%)	0.254 (2.12%)
Global retrofit	0.111 (0.93%)	0.143 (1.19%)	0.248 (2.10%)

Table 2. Compliance criteria for the assessment of RC structures and retrofitted members in Eurocode 8.

Mechanism	Damage limitation (DL)	Significant damage (SD)	Near collapse (NC)
Flexure	${\theta }_E\le {\theta }_y$	${\theta }_E\le 0.75\cdot {\theta }_{\mathit{um}}$	${\theta }_E\le {\theta }_{\mathit{um}}$
Shear	$V_E\le V_{\mathit{Rd}}$

Figure 2. (a) Retrofit of column and joint in both retrofit schemes; (b) additional retrofitting applied in the global retrofit scheme.

Figure 3. Detailing of the vertical FRP strands for flexural strengthening of the columns.

Figure 4. Details of beam FRP strengthening and selective weakening cuts.

Figure 5. (a) Model of the retrofitted joint; (b) section detail for FRP retrofitted RC columns.

Figure 6. Hysteresis curves of the experimental and modelled beam-column joints for the control (C1) and global FRP retrofit (C1-RT-B-sw) specimens.

Figure 7. Target and mean spectra for the 20 selected ground motion records, normalised by pga.

Table 3. List of selected 20 earthquake records for the incremental dynamic analysis.

Event ID	Event name	Country	Date	Station name
IT-1976–0002	Friuli 1st shock	Italy	06/05/1976	Codroipo
ME-1979–0012	Northwestern Balkan	Montenegro	24/05/1979	Kotor-Naselje Rakite
IT-1979–0009	Norcia	Italy	19/09/1979	Bevagna
IT-1980–0012	Irpinia	Italy	23/11/1980	Rionero In Vulture
IT-1984–0004	Lazio Abruzzo	Italy	07/05/1984	Cassino – Sant’elia
AM-1988–0001	Spitak	Armenia	07/01/1988	Gukasian
GR-1993–0007	Kallithea	Greece	18/03/1993	Patra 2
GR-1995–0047	Greece	Greece	15/06/1995	Patra A
TK-1995–0041	Turkey	Turkey	01/10/1995	Ai_133_Brd1
IT-1997–0137	Umbria Marche 3rd	Italy	14/10/1997	Cascia
TK-1998–0063	Turkey	Turkey	27/06/1998	Ai_022_Cyh_Tim
TK-1999–0415	Duzce	Turkey	12/11/1999	Ai_010_Bol
EMSC-20071129–0000090	Martinique region	France	29/11/2007	Zone Aero-Militaire (Martinique)
IT-2012–0008	Emilia 1st shock	Italy	20/05/2012	Sorbolo (Pezzani)
IT-2012–0011	Emilia 2nd shock	Italy	29/05/2012	Quarantoli 1
EMSC-20160824_0000006	Central Italy	Italy	24/08/2016	Monte Fema
EMSC-20160824_0000013	Central Italy	Italy	24/08/2016	Bevagna
EMSC-20161026_0000095	Central Italy	Italy	26/10/2016	Norcia La Castellina
EMSC-20170118_0000034	Central Italy	Italy	18/01/2017	Fiamignano
EMSC-20191126_0000013	Albania	Albania	26/11/2019	Tirana

Table 4. Inter-storey drift values for the four damage states.

Damage state		Description	Control^1	Local retrofit^1	Global retrofit^1
Light	DS1	onset of cracking	0.40%	0.50%	0.50%
Moderate	DS2	first reinforcing bar yield	0.65%	0.96%	0.95%
Extensive	DS3	peak lateral load	1.50%	2.00%	3.50%
Near collapse	DS4	20% drop in peak capacity	2.50%	3.54%	6.50%

¹Results for specimens C1, C0-RP-A-gs, C1-RT-B-sw (Pohoryles 2017) are considered, respectively.

Table 5. Damage-to-loss function for Portuguese RC buildings according to Silva et al. (2015).

Damage state		Damage ratio (%)	Coefficient of variation
Light	DS1	10	30
Moderate	DS2	30	20
Extensive	DS3	60	10
Near collapse	DS4	100	0

Table 6. Costs and areas assumed in the cost-benefit analysis.

Item	Unit price (€/m^2)	Area local retrofit (m^2)	Cost local retrofit (€)	Area global retrofit (m^2)	Cost global retrofit (€)
CFRP materials	8.0	480.9	38,476.8	1,026.7	82,137.6
CFRP labour application	24.0	480.9	11,543.0	1,026.7	24,641.3
Scaffolding	17.0	768.0	13,056.0	768.0	13,056.0
Demolition	19.0	576.0	10,944.0	576.0	10,944.0
Reconstruction	69.0	576.0	39,744.0	576.0	39,744.0
		Total	113,763.8	Total	170,522.9

Figure 8. Summary of the procedure for EAL_s calculation: (a) fragility curve; (b) damage to loss function; (c) vulnerability curve; (d) hazard curve; (e) expected annual loss.

Figure 9. Push-over curves up to ultimate roof drift for the as-built and retrofitted RC buildings.

Figure 10. Deformed shapes of the (a) control, (b) local retrofit and (c) global retrofit at the NC target displacement.

Figure 11. Fragility curves of the as-built, locally retrofitted and globally retrofitted building in terms of pga (a-c) and S_a(T₁) (d–f).

Table 7. Mean pga and standard deviation for the fragility curves of the as-built and retrofitted building.

Damage state		Existing building	Local retrofit	Global retrofit
Light	DS1	0.073(0.316)	0.088(0.294)	0.092(0.341)
Moderate	DS2	0.117(0.291)	0.156(0.287)	0.177(0.242)
Extensive	DS3	0.230(0.260)	0.304(0.329)	0.597(0.395)
Near collapse	DS4	0.388(0.376)	0.499(0.438)	N/A

Table 8. Mean S_a(T₁) and standard deviation for the fragility curves of the as-built and retrofitted building.

Damage state		Existing building Sa (0.58s)	Local retrofit Sa (0.57s)	Global retrofit Sa (0.55s)
Light	DS1	0.144(0.355)	0.177(0.332)	0.195(0.338)
Moderate	DS2	0.229(0.298)	0.313(0.271)	0.373(0.265)
Extensive	DS3	0.450(0.303)	0.610(0.382)	1.258(0.451)
Near collapse	DS4	0.759(0.450)	1.000(0.482)	N/A

Figure 12. Vulnerability curves of the as built control building, the local retrofit and the global retrofit.

Figure 13. (a) Expected annual losses and (b) payback times for the three buildings for different levels of seismic hazard.

Figure 14. Normalised losses over 30 years for an extended range of seismic hazard for the as-built and retrofitted buildings.

REBA. 1967. Governo D. Regulamento de Estruturas de Betão Armado - Decreto n^.o 47723. Vol. 119. serie I. Lisbon, Portugal.

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Pohoryles, D. A. 2017. Realistic FRP seismic strengthening schemes for interior reinforced concrete beam-column joints. PhD., University College London.

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Silva, V., H. Crowley, H. Varum, R. Pinho, and L. Sousa. 2015. Investigation of the characteristics of Portuguese regular moment-frame RC buildings and development of a vulnerability model. Bulletin of Earthquake Engineering 13 (5):1455–90. doi:10.1007/s10518-014-9669-y.

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Data Availability Statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.