Authors: F. Di Trapani, M. Malavisi, G. Bertagnoli, V.I. Carbone

1. Fabio Di Trapani Ph.D
Politecnico di Torino
Department of Structural, Building and Geotechnical Enginering (DISEG)
Evaluation of seismic fragility of infilled reinforced concrete frames subject to
aftershocks
F. Di Trapani, M. Malavisi, G. Bertagnoli, V.I. Carbone
Evaluation of seismic fragility of infilled reinforced concrete frames subject to
aftershocks
F. Di Trapani, M. Malavisi, G. Bertagnoli, V.I. Carbone

2. GLOBAL INTERACTION EFFECTS
• Modification of overall capacity
• Modification of collapse mechanisms
• Modification of dynamic properties
LOCAL INTERACTION EFFECTS
• Local modification of internal forces in RC
members
• Local shear failure of column ends end joints
• Activation of short column mechanisms
• Out of plane failure
Outline
FRAME – INFILL INTERACTION

3. Increase of stiffness and
bearing capacity
Planar regular
distribution
Regular
Distribution
over the height
Outline
GLOBAL FRAME – INFILL INTERACTION EFFECTS
(POSITIVE CONTRIBUTION OF INFILLS)

4. Outline
GLOBAL FRAME – INFILL INTERACTION EFFECTS
(Global collapse)

5. NEED FOR SEISMIC FRAGILITY ASSESSMENT OF INFILLED FRAMES
FRAMES
Case of intact structures
To assess seismic performance of new and existing buildings
To design and compare eventual retrofitting interventions
Case of structures damaged from earthquakes
To assess if infill walls contribute to a residual capacity against a sequence of
earthquakes
Bare
Infilled
Bare
Infilled
Fragility to mainshocks
Fragility to
Mainshock+Aftershock

6. FRAGILITY ASSESSMENT FRAMEWORK
FOR INTACT AND DAMAGED INFILLED FRAME STRUCTURES

7. FRAGILITY ASSESSMENT FRAMEWORK
Ground motion selection
(30 at least records)
Evaluation of LS on IDA curves
Perform IDAs
LS distribution
IM
0
1
SL1
IM
DM





 −
Φ=≥
X
X
SL
X
DMDMP
ln
lnln
)(
σ
µ
Evaluation of Fragility curves of LS
Actual CD

8. DEFINITION OF INPUTS
-3
-2
-1
0
1
2
0 10 20 30 40 50 60
acceleration[g]
Time (sec)
MAINSHOCK AFTERSHOCK
Scaling in
Amplitude
Scaling in
Amplitude
Fixed
IDA OF INTACT STRUCTURES
IDA OF PRE-DAMAGED STRUCTURES
IDA OF INTACT STRUCTURES
IDA OF PRE-DAMAGED STRUCTURES

9. AfterShock
IDA
FIXED
Mainshock
IDAs OF MAINSHOCK / AFTERSHOCK SIGNALS

10. MODELLING OF INFILLED FRAMES
(Concrete 02 Models)
FB Nonlinear
beam/column
Truss
Stress
fmd0
fmdu
εεεεmdu εεεεmd0
Width (w)
d
c
l
h
kw β
γ
λ*






=
w
t (actual thickness)








+= '
'
2'
2''
*
4
1
h
l
A
A
l
h
A
th
E
E
b
c
cc
md
λ
Asteris et al. (2015)
Papia et al. (2003)
Fiber section
Stress-strain
parameters
fmd0
εεεεmd0
fmdu
εεεεmdu Di Trapani et al. (2017)

11. DEFINITION OF COLLAPSE LIMIT STATES
Shear distribution coefficients
(Cavaleri & D Trapani 2015)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
αCNO
0 2 4 6 81 3 5 7
ψ
CNO Section
0 2 4 6 81 3 5 7
ψ
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
αCSE
l/h=2
1.08ψ-0.30
l/h=1
1.03ψ-0.35
0.96ψ-0.37
1.05ψ-0.36
CSE Section
dr=0.6% dr=0.6%
l/h=2
l/h=1
VCNO
VCSE
VCSE=ααααCSEN VCNO=ααααCNON
m0vfξλψ *
=
SHEAR FAILURE OF COLUMNS
ULTIMATE CHORD ROTATION OF COLUMS
N(ΘΘΘΘ)/Nmax
Θ/ΘΘ/ΘΘ/ΘΘ/Θflex
0
1
1
Axial force- ultimate chord
rotation domains

12. DEFINITION OF IM and DM
Selection of IM
PGA Se(T1)
PGA or Se(T1) ?????
ΘΘΘΘ
Selection of DM
Maximum drift at
the first interstorey
Se(T1) cannot be used to compare bare and infilled
frames and intact and damaged structures
PGA is preferable to compare fragility curves of structures
having substantially different proper frequencies

13. CASE STUDY

14. CASE STUDYCASE STUDY
Pinto et al. (2005)
ICONS Project

15. REFERENCE MODELS

16. Equivalent strut model
(Di Trapani et al. 2017)
Frame elements
Modelling in OpenSees

17. 30 Spectrum-compatible artificial accelerograms
Site: L’Aquila (Italy)
Return Period: 1950 years
Scaling factors to 15 PGA levels
Ground Motion Selection and Scaling factors

18. BARE AND INFILLED FRAME
(RESULTS IN CASE OF INTACT STRUCTURE)

19. Results at different scaling factors
PGA = 0.06g PGA = 0.1g
PGA = 0.24gPGA = 0.18g
Base shear (kN) Base shear (kN)
Base shear (kN) Base shear (kN)
drift (mm) drift (mm)
drift (mm)drift (mm)
INFILLED
FRAME
BARE
FRAME
INFILLED
FRAME
BARE
FRAME

20. IDA CURVES AND FRAGILITY CURVES
BARE FRAME
INFILLED
FRAME
Lognormal distribution
(µ, σ)
Cumulative distribution
from IDA results
FRAGILITY CURVES
Bare Frame Infilled Frame

21. 30 Spectrum-compatible artificial accelerograms
Site: L’Aquila (Italy)
2 MAINSHOCK LEVELS (0.1g and 0.16 g)
AFTERSHOCK Scaling factors to 15 PGA levels
BARE AND INFILLED FRAME
(CASE OF PRE-DAMAGED STRUCTURES)

22. Infilled Frame
(mainshock)
Bare Frame
(mainshock)
Infilled Frame
(aftershock)
Bare Frame
(aftershock)
0.1 g M.S.: Results at different scaling factors of A.S
Infilled Frame
(mainshock)
Infilled Frame
(aftershock)
Bare Frame
(mainshock)
Bare Frame
(aftershock)
The presence of infills reduces inelastic excursion due to the aftershocks

23. 0.1 g M.S.: IDA and FRAGILITY CURVES
BARE FRAME
INFILLED
FRAME
FRAGILITY CURVES
Bare Frame Infilled Frame
Inelastic Residual
displacement

24. Infilled Frame
(mainshock)
Bare Frame
(mainshock)
Infilled Frame
(aftershock)
Bare Frame
(aftershock)
0.16 g M.S.: Results at different scaling factors of A.S
Infilled Frame
(mainshock)
Infilled Frame
(aftershock)
Bare Frame
(mainshock)
Bare Frame
(aftershock)

25. 0.1 g M.S.: IDA and FRAGILITY CURVES
BARE FRAME
INFILLED
FRAME
FRAGILITY CURVES
Bare Frame Infilled Frame
Inelastic Residual
displacement

26. COMPARISON OF IDA CURVES
0.1g
MAINSHOCK INTENSITY
0.1g
0.16g
0.16g
Intact
Intact

27. BARE FRAME
INFILLED
FRAME
NO PRE-DAMAGE
0.1g
Mainshock
0.16g
Mainshock
NO PRE-DAMAGE
COMPARISON OF FRAGILITY CURVES
0.16g
Mainshock 0.10g
Mainshock

28. • Aftershock earthquakes of different intensities often occur after a major seismic
event.
• Fragility assessment by means of IDA has shown that masonry infills may reduce
seismic vulnerability of reinforced concrete structures against mainshock and
aftershock events.
• Residual capacity against aftershocks depends of on the extent of the damage
produced by the mainshock:
• If mainshock has induced small damage to the infills, these contribute
positively to the resistance against further shakings.
• If significant pre-damage of infills has been achieved during the mainshock,
only a limited improvement is observed.
• Obviously local collapse due to brittle failure of columns and joints plays an
opposite role and the considerations made above are true in the case of weak
infills of shear overstrength.
CONCLUSIONS

29. THANK YOU
fabio.ditrapani@polito.it