Presentazione standard di PowerPoint - murature.com · between the masonry infill panel and the surrounding frame. The typical in-plain collapse mechanisms can be classified(*) :

3th International Workshop on Traditional and Innovative Approaches in Seismic Design - Guimaraes, 26 - 28 April 2018

1

A geometrically consistent discrete macro-modelling approach of Infilled Frames

Bartolomeo Pantò [email protected]

University of Catania

(Italy)

26-28 Aprile 2018 - Guimaraes


2

Confined Reinforced Concrete Masonry

Structures (CRCMS)

Infilled Frame Structures

(IFS)

Construction Stages :

1: Masonry walls

2: RC frame

Construction Stages :

1: RC frame

2: Masonry walls

“structural” masonry infill “non-structural” masonry infill


3

This construction typology represented one of the first “Earthquake resistant” construction

typologies. For example, it was introduced in the first Italian Seismic Code (1909) after the 1908

Messina Earthquake1.

They continue to represent a “low-cost” construction typology, currently employed in several

seismic prone regions 2

They guarantee high seismic performance by masonry confinement, obtained following specific

construction details, such as the confinement of the building corners and openings 3.

University residence (1930) - Messina (Italy)

(1) Regio Decreto 18 aprile 1909 n.193

(2) K. Iyer et al (2012). Build a Safe House with CONFINED MASONRY. Gujarat

State Disaster Management Authority Government of Gujarat.

(2) S. Brzev (2008). Earthquake-Resistant Confined Masonry Construction. National Information Center of EarthQuake

Engineering. Indian Institute of Technology Kanpur.


4

The key aspect is related to the failure mechanisms

characterizing the in-plane unreinforced masonry panels:

(2) Nucera, F., Tripodi, E., Santini, A., & Caliò, I. (2012). Seismic vulnerability assessment of confined masonry buildings by

macro-element modeling: a case study. In Proc. of the 15th WCEE Conference, Lisboa (Portugal).


5

A large percentage of IFS were built without a specific seismic-code, designed to resist

only to gravity loads (non-ductile frames). Infills are added for architectural needs.

Catania (Italy)

L’Aquila

(Italy)


6

The presence of infill walls can significantly :

- modify the initial lateral stiffness and change the fundamental the period of vibration of

the structure;

- increase the ultimate and residual lateral strength;

- change the ductility spatial distribution along the structure.

Furthermore, strong irregularity in the plan location of infills or opening distribution may

cause unexpected effects during the seismic motions, such as :

- torsional mechanisms

- soft-storey mechanisms.


7

-Infilled frames exhibit a highly nonlinear inelastic behaviour as a result of the interaction

between the masonry infill panel and the surrounding frame. The typical in-plain collapse

mechanisms can be classified(*) :

a) The Corner

Crushing mode

associated with

the crushing of

the infill at one

of the loaded

corners

b) The Shear

Diagonal mode

which manifests

by cracking along

the compressed

diagonal of the

infill.

c) The Sliding

Shear mode,

associated to

the sliding

shear failure

through bed

joints.

d) The Frame

Failure mode,

corresponding to

the activation of a

distribution of

plastic hinges

producing a

mechanism.

(*) Asteris PG, Antoniou ST, Sophianopoulos D, Chrysostomou CZ. (2006). Mathematical macromodeling

of infilled frames: state of the art. J Struct Eng (ASCE). 2011;137(12):1508–17.


8

- Refined finite element models can be effectively employed to predict the complex non-

linear mechanical behaviour of infill frames. E.g. smeared cracked models (1,2,3) or

discrete crack models (4,5).

- N.B.: the simulation of material degradation and the non-linear contact interaction

between the infills to the frame, require sophisticated constitutive laws and strong

computational effort, often unsuitable for large structures and professional purposes.

1. Ghosh AK, Amde AM (2002) Finite element analysis of infilled frames. J Struct Eng 128(7):881–889

2. Asteris PG. Finite element micro-modeling of infilled frames. Electron J Struct Eng 2008;8:1–11.

3. Stavridis A, Shing PB (2010) Finite-element modeling of nonlinear behavior of masonry-infilled RC

frames. J Struct Eng 136(3):285–296

4. D’Ayala D, Worthb J, Riddle O. Realistic shear capacity assessment of infill frames: comparison of

two numerical procedures. Eng Struct 2009;31:1745–61.

5. Macorini L, Izzuddin BA (2011) A non-linear interface element for 3D mesoscale analysis of brick-

masonry structures. Int J Numer Methods Eng 85:1584–1608. ISSN 0029-5981


9

Aiming to provide numerical tools suitable for engineering practice, many

authors developed simplified methodologies to predict the non-linear seismic

behaviour of IFS

They are based on a macro-modelling strategy, where the infills are modelled

according to equivalent simplified mechanical schemes capable of accounting

for their influence on the structural response.

1. Rodrigues H, Varum H, Costa A (2010) Simplified macro-model for infill masonry panels. J Earthq Eng.

14(3):390–416.

2. Ellul F, D’Ayala D (2012) Realistic FE models to enable push-over non linear analysis of masonry infilled frames. Open

Constr Build Technol J 6(1):213–235.

3. Asteris P, Cavaleri L, Di Trapani F, Sarhosis V (2015) A macro-modelling approach for the analysis of infilled frame

structures considering the effects of openings and vertical loads. Struct Infrastruct Eng 12(5):551–566.

Rodrigues et al. 2010


10

The most commonly used practical approach is the so-

called ‘diagonal strut model’: the masonry infills are

represented by a “single” or “multiple” diagonal strut.

- Polyakov SV (1960) On the interaction between masonry filler walls and enclosing frame when loading in the plane of

the wall. Translation in earthquake engineering. Earthquake Engineering, Research Institute, San Francisco, pp 36–42.

- Holmes M (1984) Steel frame with brickwork and concrete infilling. In: Proceedings of the Institution of Civil

Engineers, London, England, Part 2, vol 73, pp 473–478.

- Farid MN (ed) (1996) Experimental and numerical investigations on the seismic response of RC infilled frames and

recommendations for code provisions. ECOEST/PREC 8, report no. 6. LNEC, Lisbon.

Constitutive law proposed by Fardis

(1996) and modified by Dolsek and

Fajfar (2008) is mentioned.

max0,6yF F


11

The proposed model is based to a hybrid approach simulating :

-surrounding frame using concentrated plasticity beam–column elements

-infill by means of a plane discrete macro-element;

-masonry-frame interaction by means of non-linear discrete interfaces

Two important aspects characterize the model :

1- allows a geometrically coherent modelling of the infills, also in the presence of openings;

2- can be used in mesh (the use in mesh is not mandatory but leads to a better prediction of the

failure mechanism and the bending moment distribution of the frame).


12

- I. Caliò, M. Marletta, B. Pantò (2005). A simplified model for the evaluation of the seismic behaviour of masonry buildings.

10th International Conference on Civil, Structural and Environmental Engineering Computing, Rome.

This element is characterised by a plane mechanical scheme

constituted by an articulated quadrilateral with rigid edges

connected by four hinges and two diagonal non-linear springs.

Each panel side interacts with other elements by means of a

discrete distribution of non-linear springs, denoted as interface.

Each interface is constituted by a row of non-linear Links

perpendicular to the panel side, and an additional

longitudinal Link, parallel to the panel edge. The interfaces

rule the flexural behaviour of masonry (a) and relative

sliding motion between two contiguous panels (b)

u3

u1

2uu4

1u u3

u2 u4

1F

F4

F3

F2

(a)

(b)

The model kinematics is ruled

by 4 degrees for each

quadrilateral. No further

Lagrangian parameters are

needed in order to describe the interface kinematics


13

- I. Caliò, M. Marletta, B. Pantò (2005). A simplified model for the evaluation of the seismic behaviour of masonry buildings.

10th International Conference on Civil, Structural and Environmental Engineering Computing, Rome.

- I. Caliò, M. Marletta, B. Pantò (2012). A new discrete element model for the evaluation of the seismic behaviour of

unreinforced masonry buildings. Engineering Structures 40 327–338.


14

beam/column internal degrees of freedom

beam/column esternal degrees of freedom

u1

v1

up3

1

u2

2

v2

up2

rigid edge

um

ks

vonvo1

o1 on

k1 knkn-1

vo2

o2

k2

up4

up1

2D beam–column lumped plasticity elements are included in the model interacting macro-

elements by means of non-linear discrete links, along the entire length.

I.Caliò, B. Pantò (2014), “A macro-element modelling approach of Infilled Frame Structures”. 2014 Computers and

Structures, 143 pp. 91-107

- Each frame is subdivided in sub-elements according to the

distribution of the interface links.

- An elasto-plastic behaviour governed by three-dimensional

NMxMy yielding surface is considered for the plastic hinges.

- The plastic hinges can activate at each sub-element

following an associate plastic flow-rule.


15



u1

v1

up3

1

u2

2

v2

up2

rigid edge

um

ks

vonvo1

o1 on

k1 knkn-1

vo2

o2

k2

up4

up1

- The kinematics of the panel is still ruled by 4-degrees of freedom: Up=[up1 ,up2 ,up3 ,up4]

- The frame kinematics is governed by 6 external degrees: Uf=[u1 ,v1 ,1 , u2 ,v2 ,2] and

3n-internal degrees : Uint=[u01 ,v01 ,01 , … , u0n ,v0n ,0n]

I.Caliò, B. Pantò (2014), “A macro-element modelling approach of Infilled Frame Structures”. 2014 Computers and

Structures, 143 pp. 91-107


The number of non-linear

links considered does not

influence the number of

the degrees of freedom

The calibration of the non-linear links orthogonal to the interfaces is performed

considering the deformability of masonry and the afference volume


The sliding springs are modelled by means of a rigid-plastic constitutive behaviour which

is governed by a Mohr–Coulomb yielding surface, sliding occurs in particular when the

force in the nonlinear link reaches its limit value:

in which c is a cohesion parameter and m is the friction

coefficient; sm is the current compression action acting

on the interface and Ao is the effective contact area of

the interface.



u1

v1

up3

1

u2

2

v2

up2

rigid edge

um

ks

vonvo1

o1 on

k1 knkn-1

vo2

o2

k2

up4

up1

lim 0F cA N


The shear strength is defined according to

a Mohr Coulomb law:

N

( )( )

2cos( )

v tu

f N AF N

Continuous model Discrete model beam/column internal degrees of freedom


u1

v1

up3

1

u2

2

v2

up2

rigid edge

um

ks

vonvo1

o1 on

k1 knkn-1

vo2

o2

k2

up4

up1

0v v t cf f A N Where:

fvo : shear strength associated to

a zero compression strength;

c : friction coefficient;

N : current compression action.

N

The diagonal links are calibrated imposing a

simple equivalence between the discrete and

continuous model of the represented masonry

portion.

uF


19

The model is able to simulate the main failure mechanisms of IFS

- The crushing corner mode is simulated by the transversal Links of the interfaces;

- The diagonal failure mode is governed by the diagonal links of the macro-elements;

-The sliding failure motion is governed by the longitudinal interface links;

-The frame failure is simulated by the distribution of the plastic hinges


20

0

25

50

75

100

0 10 20 30 40

ba

se s

hea

r [K

N]

top displacement [mm]

3x3 exp 4X4

2x2 5x5

2x2

3x3

4x4

5x5


21

I.Caliò, B. Pantò, “A macro-element modelling approach of Infilled Frame Structures”. 2014 Comp. and Struct., 143 91-107

A Micro-model can be employed to

validate the macro-model. Each discrete

element corresponds to a single brick and

is assigned to represent both the brick

and the mortar joint properties according

to the corresponding influence area.

Ma

cro

- M

od

el

Mic

ro -

Mo

de

l c

om

pa

ris

on


Simulation of a recent experimental campaign carried out at the University of Minho(**)

[*] B. Pantò, I. Caliò, P.B. Lourenço, (2017). Seismic safety evaluation of reinforced concrete masonry

infilled frames using macro modelling approach. Bulletin of Earthquake Engineering, 15(9), 3871-3895.

Prototype without rendering (Wall Ref-01)

Prototype with rendering (Wall Ref-02)

(**) Pereira MFP (2013) Avaliaçaõ do desempenho das envolventes dos edifıćios face a` acçaõ dos sismos. PhD thesis,

University of Minho (tese de Doutoramento Engenharia Civil Manuel Fernando Paulo Pereira, na Universidade do Minho)


Numerical vs experimental capacity curves

- B. Pantò, I. Caliò, P.B. Lourenço, (2017). Seismic safety evaluation of reinforced concrete masonry

infilled frames using macro modelling approach. Bulletin of Earthquake Engineering, 15(9), 3871-3895.

Prototype without rendering (Wall Ref-01) Prototype with rendering (Wall Ref-02)


The Influence of the openings – comparison with FE numerical modelling (*):

(*) Akhoundi F, Lourenço PB, Vasconcelos G (2015) Numerically based

proposals for the stiffness and strength of masonry infills with openings

in reinforced concrete frames. Earthq Eng Struct Dyn.


The bare frame and full-infill

frame layouts were

experimentally tested(*).The

windowed configuration was

numerically investigated

through strut model (**)

(*) Carvalho EC, Coelho E (2001) Seismic assessment, strengthening and repair of structures. radECOEST2- ICONS

report no. 2, European Commission—Training and Mobility of Researchers Programme.

(**) Dolsek M, Fajfar P (2005) Simplified non-linear seismic analysis of infilled reinforced concrete frames. Earthq Eng

Struct Dyn 34:49–66

A case study of a four-storey 2D frame is here investigated with different geometrical layouts


The first numerical

investigation is

focused on the

linear dynamic

properties of the

system

The presence of the

non-structural

infills strongly

modifies the

modes.

A satisfactory

agreement is

observed between

the strut model and

the plane macro

model


Plain macro-model Strut model

The prototype is conceived to be representative of typical RC buildings designed without

seismic provisions and built from the 1960s - 1980s in Southern Europe and in the

Mediterranean area. Its non-linear behaviour under seismic loads is investigated by

performing non-linear static analyses with horizontal distribution loads consistent with the

first mode of vibration.


Considerable differences

can be found between the

strut model and the DMM

in terms of distribution of

the frame bending

moments due to the

difference in the modelling

of the interaction between

the infill and the

surrounding frame.

Different damage distributions at the collapse are predicted: the DMM predicts a partial

collapse mechanism with a damage distribution mainly concentrated at the first level, while

the strut model shows a collapse in which the damage is distributed at all levels.

Plane macro model Diagonal strut model Bare Frame

Diagonal strut model Plane macro model


DDL DL=DDL/Dy

SD=DSD/Dy

NC=DNC/Dy

dam

age

limit

atio

n

Sign

ific

ativ

e d

amag

e

DSD

DNC

Nea

r C

olla

pse

The capacity curve is idealized as a multi-linear force–displacement relation rather than

simply elasto-plastic, as suggested by Dolsek and Fajfar (*)

(*) M. Dolsek, P. Fajfar (2005). Simplified non-linear seismic analysis of infilled reinforced concrete frames. Earthq Eng Struct Dyn 34:49–66.


Where:

m* = effective mass of the SDOF system

T* = period of the SDOF system

= modal participation factor;

Sd, Sa = spectra displacement and acceleration

Elastic Spectra

Non-Linear Spectra

(*) M. Dolsˇek, P. Fajfar (2004). Inelastic spectra for infilled reinforced concrete frames. Earthq Eng Struct Dyn 33:1395–1416

-The reduction factor R()= SAE/SA() is computed by using the relations proposed in Dolsˇek and

Fajfar (*) for the infill model while the equal displacement rule (R = ) is used for the bare frame

for the bare frame.

-The admissible PGA for each limit state is computed by equating the acceleration associated

with the fundamental period of the system and the inelastic spectra acceleration.


Full infill frame Windowed infill frame

SD limit State


32

Infill Frame structures are particularly vulnerable to the out-of-plane actions which produce

the expulsion of the infill anticipating the in-plane collapses.

-The in-plane damage strongly

influences the out-of-plane

behaviour (and strength) of infills.

- The bond-degradation of the infill

to the frame leads to dangerous

rocking mechanisms of the infills.

Mosalam, K. M., & Günay, S. (2015). Progressive collapse analysis of reinforced concrete frames with unreinforced

masonry infill walls considering in-plane/out-of-plane interaction. Earth. Spectra, 31(2), 921-943.

Furtado, A., Rodrigues, H., Arêde, A., & Varum, H. (2016). Experimental evaluation of out-of-plane capacity of masonry

infill walls. Engineering Structures, 111, 48-63.

Tondelli, M., Beyer, K., & DeJong, M. (2016). Influence of boundary conditions on the out‐of‐plane response of brick

masonry walls in buildings with RC slabs. Earth. Eng. Struct. Dyn., 45(8), 1337-1356.

Pereira MFP (2013) Avaliaçaõ do desempenho das envolventes dos edifıćios face a` acçaõ dos sismos. PhD thesis,

University of Minho.


33

From 2D to 3D Macro-Model:

Three additional degrees-of-freedom are needed to describe the out-of-plane

kinematics of each panel;

Further nonlinear links account for the three dimensional mechanical behaviour

Besides the longitudinal spring, ruling the in-plane sliding motion, two

additional transversal sliding springs are needed to control the out-of-plane

sliding and torsion mechanisms.

Plain (2D)

Macro – Element

(4 DoF)

Spatial (3D)

Macro-Element

(7 DoF)

B Pantò, F. Cannizzaro, I. Caliò, PB Lourenço (2017). Numerical and experimental validation of a 3D macro-model for the

in-plane and out-of-lane behaviour of unreinforced masonry walls, Int. J. of Architectural Heritage, 11(7): 946,964.


Flexural calibration: The interface transversal non-

linear links are calibrated according to a fibre approach.

The ortotropic behaviour

of masonry is effectively

taken into account in

during the calibration of

the horizontal and vertical interfaces.

Elasto-plastic with linear softening

constitutive law employed for the transversal links


4

4

12 0,21 1

3

s sd s

B B

Out-of-plane sliding and torsional calibration

The elastic stiffness (ks) and the yielding strength (fy)

are calibrated according to the out-of-plane shear

behaviour:

The distance (d) between the two links is computed

imposing an equivalence between the discrete model and

the equivalent (rectangular cross-section) continuous

model (*).

H

H/2

(*)Torsion stiffness of a rectangular cross-section


With the aim to simulate the bond actions at the contact masonry-frame surface, a new 3D

interface, able to simulate the bond-failure mechanisms of the infill, has been developed.

The model aims to simulate the non-linear in-plane and out-of-plane behaviour and its

interaction.

The model is able to predict the damage propagation on the infill taking into account the

“arch effect” within the wall thanks to the fiber discretization of the interfaces.

B Pantò, I. Caliò, PB Lourenço (2018). A 3D discrete macro-element for modelling the out-of-plane behaviour of Infilled

Frame Structures, Engineering Structures (under review).


The interface is constituted by :

- m rows of orthogonal links (three in figure) corresponding to

fibre discretization of the macro-element;

- a single row of in-plane shear-sliding links;

- a single row of out-of-plane shear-sliding links;

The central links are directly connected to the internal nodes while the external rows are

linked to the beam through rigid braces, whose ends displacements are simply related to

the corresponding node-beam torsion degree.


1 2 1 2IU v v u w w

f i i j j i i j j i j i jU v v w w u u

int 1 1 1 1 1 1 ..... n n n n n nU u v w u v w

The kinematic of the interface is governed by the 6 DoFs of the rigid plane (Uf) related to

the independent seven degrees of freedom of the macro-element), 12 degrees associated

to the frame external nodes (Uf) and nx6 internal degrees of freedom related to the internal

nodes (UIf).


k1r k2r knr

13

p=1

2

3kpm

t

node i

1

node j

v2v1

1

2

Internal degrees of freedom

External degrees of freedom

p

vp

p=1 ... n

vi v1 v2 vn vj

kp1

r=1 ... m

r=1

r=m

p=np=2

wp

i 2 n j

u

uj

node j

t

2

1u1

1

u2 un

2 n

ui

w1 w2 wn

w2w1

1 2 n

node j

wi wj

t

p

wp

node i3

1

2

3kIS1

node i kIS2 kISn

kOS1 kOS2 kOSn

i j

p=1 ... n

kOSp

(a) (b)

(c)

The following mechanical

schemes explain the adopted

discretization strategy of the

interface and the interaction

between the flexural, torsional

and sliding behaviour due to the

thickness of the interface.

Flexural-torsion Interaction

Sliding - torsion Interaction

Out-of-plane sliding

In-plane sliding


H/2

t

H/2

t

t

H/2

H/2

H/2

H/2

The calibration of the links, according to the macro-modelling strategy, is performed

following a fibre discretization. The following schemes show the afference volumes

associated to the transversal, in-plane sliding and out-of-plane sliding links.

Transversal Springs

Sliding Springs


0

2

4

6

8

10

0 0,5 1 1,5 2 2,5L

ate

ral l

oa

d [k

N/m

2]

drift at the centre of infill [%]

Experiment

proposed Macro-model

Finite Element model

Servo Hydraulic actuator

F= 200kNF= 200kN

p

F= 200kN

In plane test scheme Out plane test scheme

2450300 300

300

300

165

750

150

8Ø22300

250 8Ø15

Coloumn

Beam

300

450

R Angel et al. (1994). Behavior of Reinforced Concrete Frames with Masonry Infills. Civil Engrg. Studies, Structural

Research Series No. 589, UILU-ENG-94- 2005, Dept. of Civil Engineering, University of Illinois at Urbana Champaign.

Test Layout

Plastic damage and Failure mechanism

Experimental and numerical

capacity curves

Last step Peak load

A numerical validation, in the non-

linear field, has been performed

considering a prototype subjected

to a monotonic loading action on the

out-of-plane direction (Angel 1994).


0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

La

tera

l lo

ad

[kN

]

lateral displacement [mm]

Full infill

D1

D2

D3

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

La

tera

l lo

ad

[kN

]


Full infill

W1

W2

W3

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40 45 50

La

tera

l lo

ad

[kN

]


Full infill DFWF DDWW DW

Influence of the irregular disposition of openings on

IF response considering typical geometries for south

European and Mediterranean area (*)

Influence of the opening size

(regular opening)


Infill Frame Structures (IFS) represent a high percentage of existing buildings

in numerous high seismic areas. They show a high seismic vulnerability, even

when exposed to moderate earthquakes;

The numerical modelling of the masonry infills is necessary to obtain reliable

seismic vulnerability evaluations. However, rigorous modelling in often

unsuitable with engineering purposes. For this reason simplified macro-

models have been proposed in the literature.

A new geometrically coherent macro-modelling strategy, able to simulate the

in-plane and out-of-plane behaviour of infills has been developed and

numerically validated in 2D and 3D loading conditions.

A critical apraisal between the new model and the classic “Strut model” has

been provided with reference to a simple benchmark.

Documents

Presentazione standard di PowerPoint - murature.com · between the masonry infill panel and the surrounding frame. The typical in-plain collapse mechanisms can be classified(*) :