Modelling the out-of-plane behaviour of URM infills and the in-plane/out-of-plane interaction effects

Modelling the out-of-plane behaviour of URM infills
and the in-plane/out-of-plane interaction effects
Paolo Ricci, Mariano Di Domenico, Gerardo M. Verderame
University of Naples Federico II
Department of Structures for Engineering and Architecture
Via Claudio 21 – 80125 – Naples – Italy
e-mail: paolo.ricci@unina.it
OPENSEES DAYS EUROPE 2017
1st European Conference on OpenSees
Porto, Portugal, 19-20 June 2017

Purposes of the present study
4. Out-of-plane seismic safety check of the infill walls of case-study RC frames
1. Definition of an empirical-based Out-Of-Plane (OOP) infill model
2. Definition of an empirical-based In-Plane (IP) - OOP interaction model
- by applying an Eurocode-based approach
5. Safety check results’ comparison
- by applying the proposed model in a non-linear dynamic framework
MODELLINGTHEOOPBEHAVIOUROFURMINFILLSANDTHEIP/OOPINTERACTIONEFFECTS
3. Implement the proposed model in OpenSees

Empirical-based OOP infill model
OOPforce
OOP displacement
Based on pure OOP and combined IP+OOP tests carried out by:
- Dawe and Seah (1989)
- Angel et al. (1994)
- Flanagan and Bennett (1999)
- Calvi and Bolognini (2001)
- Hak et al. (2014)
- Furtado et al. (2015)
A trilinear backbone has been assumed for the OOP behaviour of IP-undamaged and
IP-damaged URM infills

OOPforce
OOP displacement
- Hak et al. (2014)
Fcrack
Kcrack
Fcrack = 0.31 fm
′ 0.05
t
w
h1.66
Kcrack =
1
α
Et3
12 (1 − ν2)
w
h
empirical formulation
μobs/pred = 1.02
Timoshenko, 1959
μobs/pred = 0.99

OOPforce
OOP displacement
- Hak et al. (2014)
Fmax = 1.95 fm
′ 0.35
t1.59
w
h1.96
Kmax = 6.56
Ew
(h/t)3
μobs/pred = 1.01
Kadysiewski and Mosalam, 2008
μobs/pred = 0.82
Fmax
Kmax

OOPforce
OOP displacement
- Hak et al. (2014)
dmax du
du = 3.7dmax
μobs/pred = 1.00

Empirical-based IP-OOP interaction model
An empirical approach is used to model IP-OOP interaction effects.
To model IP action effects on infills OOP behaviour, experimental data are related to the maximum IDR
ratio attained during tests normalized with respect to the IDR corresponding to the complete IP resistance
loss, IDRu

To model IP action effects on infills OOP behaviour, experimental data are related to the maximum IDR
ratio attained during tests normalized with respect to the IDR corresponding to the complete IP resistance
loss, IDRu
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
IDR/IDRu
F
crack,dam
/F
crack,undam
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
IDR/IDRu
K
crack,dam
/K
crack,undam
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
IDR/IDRu
K
max,dam
/K
max,undam
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
IDR/IDRu
F
max,dam
/F
max,undam
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
IDR/IDRu
d
u,dam
/d
u,undam
Fcrack,dam
Fcrack,undam
= 0.11
IDR
IDRu
−0.89
Kmax,dam
Kmax,undam
= 0.12
IDR
IDRu
−0.69
Kcrack,dam
Kcrack,undam
= 0.07
IDR
IDRu
−0.76
Fmax,dam
Fmax,undam
= 0.27
IDR
IDRu
−0.37
Effects of IP damage on OOP response parameters:

To model OOP action effects on infills IP behaviour, experimental data by Flanagan and Bennett are
related to the maximum OOP displacement attained during tests, dOOP, normalized with respect to the
OOP collapse displacement of the reference undamaged specimen, dOOP,u
Effects of OOP damage on IP response parameters:
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
dOOP
/dOOP,u
F
IP,dam
/FIP,undam

Based on the proposed degradation relationships, the OOP and IP backbones for the undamaged infill
are modified as shown in the following figures.
OOPforce
OOP displacement
IPforce
IP displacement
IDR
IDRu
= 0
dOOP
dOOP,u
= 0

OOPforce
OOP displacement
IPforce
IP displacement
IDR
IDRu
= 0.2
dOOP
dOOP,u
= 0.2

OOPforce
OOP displacement
IPforce
IP displacement
IDR
IDRu
= 0.4
dOOP
dOOP,u
= 0.4
How can we model the evolution of the OOP response backbone due to the
increasing IP damage (and vice-versa) during the NLTH analysis?

Model implementation in OpenSees
OOPforce
OOP displacement
IDR
IDRu
= 0
Consider the OOP backbone for the IP-undamaged infill (backbone 1)

OOPforce
OOP displacement
IDR
IDRu
= 0
IDR
IDRu
= 0.2
Consider an OOP backbone for the IP-damaged infill (backbone 2)

OOPforce
OOP displacement
IDR
IDRu
= 0
𝑎𝑎𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
IDR
IDRu
= 0.2
Consider backbone 2 mirrored with respect to displacement axis (auxiliary backbone 2)
uniaxialMaterial Parallel tagAuxBb#2 tagBb#2 -factors -1

OOPforce
OOP displacement
IDR
IDRu
= 0
IDR
IDRu
= 0.2
Backbone 2 and Auxiliary backbone 2 are mutually-neutralizing

OOPforce
OOP displacement
IDR
IDRu
= 0
𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
IDR
IDRu
= 0.2
Backbone 2 and Auxiliary backbone 2 are mutually-neutralizing
Backbone 1 is the one defining the OOP behaviour of the infill

OOPforce
OOP displacement
IDR
IDRu
= 0.2
If IDR/IDRu>0.2 backbone 1 is removed

OOPforce
OOP displacement
IDR
IDRu
= 0.2
If IDR/IDRu>0.2 backbone 1 is removed…
… as well as auxiliary backbone 2

OOPforce
OOP displacement
IDR
IDRu
= 0.2 𝑎𝑎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
If IDR/IDRu>0.2 backbone 1 is removed…
… as well as auxiliary backbone 2
So, if IDR/IDRu>0.2, backbone 2 starts defining the OOP behaviour of the infill

The proposed model has been conceived to:
1. Reproduce the OOP behaviour of URM infills;
2. Take into account the OOP strength
degradation due to IP damage and vice-versa;
3. Take into account the OOP stiffness
degradation due to IP damage and vice-versa;
4. Allow modelling the IP and OOP behaviour
of infills – and the corresponding degrading
rules – adopting any trilinear material model as
well as any hysteretic rule.

OOP behaviour
IP behaviour
Node
OOP mass
‘Real’ ZeroLength Element
‘Auxiliary’ ZeroLength Element
Beam/Column Element
Hinge
Mid-span Node

Application example: Case-study RC buildings
Two case eight-storey RC buildings designed addressing EC2 and EC8 provisions are considered.
Each building has been designed on A type soil. The two buildings differs for the design PGA at Life
Safety Limit State, which is equal to 0.15 g (8P15 case-study building) and 0.35 g (8P35 case-study
building) and at Damage Limitation Limit State, which is equal to 0.06 g and 0.14 g (i.e., 0.4 times the
PGA at LS), respectively. The inter-storey height, h, is 3 m for all storeys. All bays width, w, is 4.5 m.
Eurocode 8 Type I spectrum was adopted. A behaviour factor equal to 4.68 was applied.
RC elements non-linearity was modelled by applying a code-based approach, with an elastic-perfectly
plastic backbone provided of the cracking point and with chord rotation at yielding determined
accordingly to the formulation proposed in EC8, part 3.
22.5 m
13.5m
X
Z
The case-study buildings are infilled by one-leaf 300 mm thick URM walls.
Masonry mechanical properties are the ones calculated for masonry wallets tested by Guidi et al. for
mechanical characterization of “strong” URM infills.

Application example: Case-study RC buildings
The OOP behaviour of the case-study infill panels was modelled by applying the herein proposed semi-
empirical approach. The IP behaviour was modelled by applying Panagiotakos and Fardis model, with
softening stiffness equal to -3.6% of the predicted elastic stiffness of the infill, based on Guidi et al. IP
tests’ results on strong masonry infills.
The infill wall behaviour degradation was modelled through the herein proposed empirical approach.
The IP degradation was modelled with backbones defined at steps of 0.05 times the dOOP,u (16.3 mm)
displacement while the OOP degradation was modelled with backbones defined at steps of 0.05 times
the IDRu (1.80%).
0 5 10 15 20
0
100
200
300
OOP Displacement [mm]
OOPForce[kN]
0 10 20 30 40 50
0
200
400
600
IP Displacement [mm]
IPForce[kN]

Application example: NLTH Analysis procedure
Seven bidirectional ground motions recorded on type A soil were selected
The two components of each ground motions were contemporarily matched to the design 5%-damped
response spectrum at Damage Limitation Limit State (DL) and at Life Safety Limit State (LS) through
the RspMatchBi (Grant, 2010) software.
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
EC8 target
Spectral matching period
range: 0.035 s -1.100 s
All components matched to the
0.35 g design spectrum at LS
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
T [s]
S
a
(T)[g]
mean
NS component EW component

Incremental Dynamic Analyses were carried out to obtain for each horizontal direction an incremental
PGA vs maximum IDR curve.
For records scale factor determination, a bisection procedure was implemented in order to define the
PGA associated to the first OOP infill collapse and removal from the structural model with a precision
equal to +/- 0.01 g.

Mass and tangent-stiffness proportional Rayleigh damping rules for two control vibration mode were
applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
Modes frequencies [rad/s]
OOP infill natural frequency [rad/s]
Control modes (1 and 131)
Rayleigh damping ratios (scaled for 104
)
Three groups of modes were recognizable from modal analysis.
- A first group of global “lower” modes corresponding to lower frequencies/modes involving the whole
structure;

applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
)
structure;
- A second group of local modes involving infills excited in the OOP direction corresponding to
intermediate frequencies very close the infill natural frequency in the OOP direction;

applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
)
structure;
- A third group of global “higher” modes corresponding to higher frequencies/modes involving the
whole structure.

applied.
20 40 60 80 100 120 140
0
50
100
150
200
250
300
350
400
Mode
)
structure;
- A third group of global “higher” modes corresponding to higher frequencies/modes involving the
whole structure.
In this study, the first control mode corresponds the first
natural frequency of the infilled structure, while the
second control mode corresponds to the second group
mode associated to the frequency closer to the infill
natural frequency in the OOP direction.
A damping ratio equal to 2% was assigned to each
control mode.

Incremental Dynamic Analyses were carried out on two models for each case-study building.
- W/ model accounting for:
1. backbone removal during analysis for IP and OOP stiffness, strength and displacement
capacity reduction;
2. infill removal at IP collapse displacement attainment;
3. infill removal at OOP collapse displacement attainment (OOP collapse).
- W/O model accounting for:
1. backbone removal during analysis for IP and OOP stiffness, strength and displacement
capacity reduction;
2. infill removal at IP collapse displacement attainment;
3. infill removal at OOP collapse displacement attainment (OOP collapse).

Application example: NLTH Analysis results
Median IDA curves in each direction for W/ and W/O models of all case-study buildings are shown in
the following figures
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P15-X
maximum IDRX
[%]
PGA
X
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P15-Z
maximum IDRZ
[%]
PGA
Z
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P35-X
maximum IDRX
[%]
PGA
X
[g]
W/O Model
W/ Model
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
8P35-Z
maximum IDRZ
[%]
PGA
Z
[g]
W/O Model
W/ Model
Mean OOP collapse PGAs are shown in the following table. They are, as expected, lower than the ones
predicted by applying a code-based approach (0.41 g for 8P15 case-study building and 0.38 g for the
8P35 case-study building), especially if IP-OOP interaction is accounted for (W/ model). Moreover, the
first OOP infill collapse does not occur necessary at last storeys but at intermediate storeys due to
IP-OOP interaction effects.
Clearly, if IP-OOP interaction is considered, at equal PGA a greater probability of OOP infill collapse is
expected.

Conclusions
1. An empirical based OOP infill wall model has been defined.
2. An empirical based IP-OOP interaction model has been defined.
3. The proposed model has been implemented in OpenSees.
4. IDA on 8-storey case-study buildings designed addressing EC2 and EC8 provisions were
performed
5. The PGA associated to the first OOP collapse is underestimated of about 44% if IP-OOP
interaction is neglected.
6. The PGA associated to the first OOP collapse is underestimated of up to 132% if an Eurocode-
based approach, which neglects IP-OOP interaction, the primary structure non-linearity and the
contribution to the OOP acceleration acting on infills of the primary structure’s higher modes, is
applied.
Ongoing research is focused on the application of the proposed approach for modelling the infills
of a wide range of case-study RC buildings different for number of storeys (2, 4, 6 and 8), designed
for different PGA at LS (0.05, 0.15, 0.25 and 0.35 g) and provided of different infills’ layout (‘weak’
thin infills and ‘strong’ thick infills). Numerical analyses are being performed to assess infills
acceleration and displacement demand, effective stiffness and behaviour factor accounting for IP-
OOP interaction in a non-linear dynamic framework.

Paolo Ricci, Mariano Di Domenico, Gerardo M. Verderame
University of Naples Federico II
Department of Structures for Engineering and Architecture
Via Claudio 21 – 80125 – Naples – Italy
e-mail: paolo.ricci@unina.it
Modelling the out-of-plane behaviour of URM infills
and the in-plane/out-of-plane interaction effects
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for your attention

Modelling the out-of-plane behaviour of URM infills and the in-plane/out-of-plane interaction effects

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