Numerical Modeling and Analysis of Unreinforced Masonry Walls · Numerical Modeling and Analysis of...
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Journal of Civil Engineering and Architecture 11 (2017) 870-878 doi: 10.17265/1934-7359/2017.09.006
Numerical Modeling and Analysis of Unreinforced
Masonry Walls
Isak Idrizi1 and Zekirija Idrizi2
1. Faculty of Civil Engineering and Architecture, Mother Teresa University, Shkup 1000, Macedonia;
2. Faculty of Civil Engineering and Architecture, Hasan Prishtina University, Prishinë 10000, Kosova
Abstract: Estimation of shear strength and other mechanical characteristics of masonry wall panels through experimental research is the most reliable analysis approach. However, considering all the difficulties in performing experimental research, material costs, laboratory preparations and time expenses, it is not difficult to conclude that this approach is also not the most rational. Aside from experimental investigations, advanced analytical methods are considered cheaper and practical, which can approximately describe the mechanical behavior of masonry walls. The aim of this chapter is to demonstrate how advanced analytical methods, based on discrete and applied element methods, are capable of estimating, in close approximation, the realistic behavior of masonry walls. The use of advanced analysis methods for determination of the behavior of full-scaled masonry walls (with and without openings), avails the inclusion of infill masonry walls on the processes of modeling, analysis and design of building structures, without the need of extensive experimental investigations. This would result in achieving more approximate analytical building models in respect to their realistic behavior and ultimately achieve better optimization of structural design. Key words: URM (unreinforced masonry wall) wall, discrete methods, advanced analysis, numerical modeling.
1. Introduction
Estimation of shear strength and other mechanical
characteristics of masonry wall panels through
experimental research is the most accurate approach.
However, considering all the difficulties in performing
experimental research, material costs, laboratory
preparations and time expenses, it is not difficult to
conclude that this approach is also not the most viable.
Besides experimental investigations, as a more
practical approach, that can provide reliable estimate
on the mechanical behavior of masonry walls, is
considered the advanced analytical methods.
2. General Review on Masonry Wall Modelling Strategies
Due to the enormous progress made on reinforced
concrete structures and development of advanced
Corresponding author: Isak Idrizi, doctor of science, assistant professor; research fields: earthquake engineering and structural engineering. E-mail: [email protected], [email protected].
structural analysis techniques, knowledge on masonry
behavior improved considerably. Nevertheless, the
modeling and analysis methodologies used for RC
(reinforced concrete) elements are still impossible to
be applied directly to URM walls. Due to the highly
heterogeneous nature and orthotropic mechanical
characteristics of URM walls, a direct application of
RC modeling approach for the URM wall panels would
be wrong [1].
Hence, there was a need to develop different
constitutive models which would appropriately
consider the heterogenic nature of URM walls in the
modeling and analysis process. In the current existing
literature, there are proposed several modeling
strategies and methods of analysis.
The numerical modeling of masonry walls may be
approached either by a detailed description of
mechanical properties for each individual component
of masonry walls (micro-modeling) or by treating the
masonry wall as a composite continuous material
(macro-modeling). Ultimately, depending on the
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proximation
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aracteristics o
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lls remain i
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FEM based
on the linea
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these micro-
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red crack app
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of masonry w
ments up to to
impossible t
ntinuum meth
ls
applications
ar response
o deep nonlin
scontinuities t
state to an ent
mechanical c
use of continu
sonry walls o
ealistic nonlin
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alls, it was in
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ch considers
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tinuity at plan
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elements, is
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walls. The si
otal collapse
o be solved
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give good
of masonry
near response
thus changing
tirely discrete
characteristics
uum methods
offers a crude
near response
o-mechanical
ntroduced the
he concept of
the softening
the interface
nes of failure.
with smeared
only capable
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Numerical Modeling and Analysis of Unreinforced Masonry Walls
874
3.2 Discrete Methods
The ingenuity of discrete element method lies in the
fact that it is capable to consider an entire physical
system and separate it into its constituent discrete
components which interact with each-other through
“surface interaction laws”. The discrete elements can
be considered either as rigid bodies or as elements with
elasto-plastic mechanical characteristics described
through continuum equations. Based on this approach,
discrete methods are capable of performing refined
nonlinear analysis under large displacements between
discrete elements. Although discrete element method is
a quite recent development, it has gained enormous
interest in engineering research and, so far, there were
established several distinct numerical methods based
on the discrete element computational formwork, such
as:
RBSM (rigid bodies spring method);
DDA (discontinuous deformation analysis);
CDFE (combined discrete-finite elements);
NSCD (non-smooth contact dynamics);
MDEM (modified distinct element method); and
AEM (applied element method).
The AEM is the most recent development in discrete
analysis methods which are the only method to
accurately track and visualize the complex response of
engineering structures starting from initial stress
conditions and gradually progressing through states of
nonlinear deformations, material degradations, element
separations and collisions and up to total structural
collapse [4, 5].
As part of this paper, AEM method was extensively
used to model, analyze and simulate the nonlinear
response of a masonry wall panel being subject of
experimental research.
4. Micro-modeling and Analysis of a Classical Wall Panel
This section treats the micro-modeling, analysis and
simulation of a classical wall analytical model, and
ultimately compares its response with experimentally
obtained results from its representative physical model.
In order to generate a numerical micro-model of wall
panels, it was applied a scientifically oriented computer
program based on one of the most recent developments
in discrete analysis methods, namely AEM method.
This method of analysis is, by far, the only method to
manage to approximately track and visualize the deep
nonlinear response of structures up to their complete
failure.
Under AEM method, the wall panels are assumed to
be divided into small prismatic elements, which are
inter-connected with each other at their contact faces
through pairs of normal and shear springs. This
modeling approach is especially suitable for the
two-phase composite material structure of the masonry
walls with distinct anisotropic features.
The masonry wall structure is discretized into small
prismatic elements in a way that each brick unit, with
dimensions 250 mm × 120 mm × 60 mm, is divided
into four equal parts, in the longitudinal direction, thus
forming four equal micro-elements with dimensions
60 mm × 120 mm × 60 mm. The mortar joints are
automatically considered by the software with
thickness of 15 mm. The generated micro-model of the
wall panel is presented in Fig. 5a.
The generation of this mathematical model was done
to replicate the initially prepared physical wall model.
To this respect, all physical and mechanical
characteristics of the physical wall panel and its
components were measured and used as input
parameters on the analysis of the mathematical model,
like the mechanical features of constitutive units of the
wall panel, respectively brick units, mortar and
brick/mortar interface joints. In addition, contact
springs, between the faces of prismatic elements, are
internally calculated by the software, based on the
mechanical properties of wall panel constituents.
The sequence of external actions acting on the wall
panel models is set-up in such a way that it simulates
Fig. 5 Micro
the loading
investigation
The only
analytical lo
horizontal d
horizontal c
applied. Fo
increasing a
used.
Neverthel
studies show
terms of t
developmen
complete fa
clearly demo
Fig. 6 dem
developmen
FP_CL” sub
deformation
of 0.35 MP
Actually, th
experimenta
“Wall FP_C
If the la
N
(
o-modeling of:
g scenario c
ns.
difference b
oading condit
deformations.
yclic “deform
or numerical
and “deforma
less, both e
w very simila
their mechan
nt of cracks a
ailure of wa
onstrated by o
monstrates six
nt over a nu
bjected to a m
n, preceded by
Pa (equivalen
his analysis r
al Test 1 of t
CL”.
ast deformati
Numerical Mo
(a)
: (a) “Wall FP_
carried out b
between the e
tions is the lo
For experim
mation contro
l analysis, a
ation control
experimental
ar behavior o
nical strengt
and their prop
all panels. T
observing Fig
x characterist
umerical mic
monotonically
y a vertical co
nt to 6 t of
represents a
the so called
ion stage o
odeling and A
_CL” wall; and
by experime
experimental
oading patter
mental analys
olled” action
a monotonic
lled” action
and analy
of wall panel
th, deformat
pagation up u
This similarit
gs. 6 and 7.
ic stages of c
cro-model “W
y increasing s
onfinement st
f vertical for
“replica” of
d physical m
f the numer
Analysis of U
d (b) its shear-
ental
and
rn of
is, a
was
cally
was
ytical
ls in
tion,
until
y is
rack
Wall
hear
tress
rce).
f the
model
rical
mic
com
phy
failu
sim
she
in F
A
the
slig
thro
100
A
ana
obta
mod
T
mec
resp
wal
una
of
assu
the
nreinforced M
-displacement
cro-model “W
mpared with
ysical model
ure pattern ar
milarity is
ar-displacem
Fig. 7 (bottom
According to
numerical m
ghtly lower
ough experim
0 kN (≈ 10 t).
Additionally,
alytical mode
ained under
del “Wall FP
There are ma
chanical beh
pectively, the
ll constituent
avoidable error
wall constitu
umptions dur
level of discr
Masonry Wall
(b)
response.
Wall FP_CL
the failure
“Wall FP_
re very obviou
also valid
ment response
m).
Fig. 7 (botto
model is close
than the s
mental invest
the ultimate
l (20 mm) is
experimenta
_CL” with a
any factors th
havior betw
e variation in
ts from one
rs in estimatio
uents; appro
ring the mic
retization of w
ls
L”, Fig. 6,
pattern of
_CL”, the si
us (Fig. 7). M
d in term
e curves, as d
om), the shear
to 90 kN (≈
shear streng
tigations with
shear deform
s slightly low
al “Test 1”
value of 22 m
hat impose d
ween the tw
mechanical
location to
on of mechani
oximations a
cro-modeling
wall constitue
875
, is closely
“Test 1” of
imilarities in
Moreover, this
ms of the
demonstrated
r strength for
9 t) which is
gth obtained
h a value of
mation of the
wer than that
of physical
mm.
differences in
wo models,
properties of
another, the
ical properties
and idealized
process and
ents; etc.
5
y
f
n
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e
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r
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t
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,
f
e
s
d
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Fig. 6 Progr
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ressive collapse
Numerical Mo
e analysis over
odeling and A
r micro-model
Analysis of U
“Wall FP_CL
nreinforced M
”.
Masonry Wallls
Fig. 7 Shear
However,
between the
do exist, the
as demonstr
5. Conclus
Based on
objectives
conclusions
Along wi
technology,
computer pr
analyzing a
N
r behavior of m
, despite the
analytical an
eir close simil
ated by Fig. 7
sions
n the obtain
treated in t
are outlined.
ith the recen
there have
rograms whi
and simulatin
Numerical Mo
model “Wall FP
e fact that m
nd experimen
larity in mech
7, is remarkab
ned results f
this chapter
nt advanceme
e been deve
ich are capab
ng the behav
odeling and A
P_CL”: experi
minor differen
ntal investigat
hanical behav
ble.
from both st
, the follow
ents in comp
eloped high
ble of model
vior of maso
Analysis of U
imental vs. ana
nces
tions
vior,
tudy
wing
puter
-end
ling,
onry
wal
beh
T
real
thro
avo
phy
S
be
cha
unit
use
pro
nreinforced M
alytical studies
lls in very c
havior.
This techno
listically pre
ough use of
oids expensiv
ysical models
Specifically, e
required fo
aracteristics o
ts, mortar an
d as input
cess of analy
Masonry Wall
s.
lose approxi
ological ad
dict the beh
f advanced
ve experime
of masonry w
experimental
or determina
f wall constit
nd masonry
parameters
ytical wall pan
ls
mations to t
dvancement
havior of ma
analytical ap
ental investig
wall panels.
investigation
ation of the
tuents, i.e., tes
prisms, whic
in the mic
nels.
877
their realistic
avails to
asonry walls
pproach and
gations over
ns would only
mechanical
sting of brick
ch would be
ro-modelling
7
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o
s
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r
y
l
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e
g
Numerical Modeling and Analysis of Unreinforced Masonry Walls
878
The use of advance analysis approach for realistic
determination of the shear behavior of full-scaled
masonry walls (with and without openings), serves as a
basis for inclusion of infill masonry walls on the
processes of modeling, analysis and design of building
structures. This would result in achieving more
approximate analytical building models in respect to
their realistic behavior and ultimately achieve better
optimization of structural design.
References
[1] Bakeer, T. 2009. Collapse Analysis of Masonry Structures under Earthquake Actions: From Research to Practice. Vol. 8. Publication Series of the Chair of Structural Design,
Dresden: Dresden Technical University. [2] Lourenço, P. B. 1996. A User/Programmer Guide for the
Micro-modeling of Masonry Structures. Delft University of Technology, Faculty of Civil Engineering, TNO Building and Construction Research.
[3] Lourenço, P. B. 1994. Analysis of Masonry Structures with Interface Elements—Theory and Application. Technical report, Delft University of Technology, Faculty of Civil Engineering.
[4] Tagel-Din, H., and Meguro, K. 1999. Applied Element Simulation for Collapse Analysis of Structures. Bulletin of Earthquake Resistant Structure Research Center, Institute of Industrial Science, The University of Tokyo, No. 32, March, 1999.
[5] Tagel-Din, H., and Meguro, K. 2002. “Applied Element Method Used for Large Displacement Structural Analysis.” Journal of Natural Disaster Science 24 (1): 25-34.