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: isak.idrizi@unt.edu.mk, isak_idrizi@hotmail.com.

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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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

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f the numer

Analysis of U

d (b) its shear-

ental

and

rn of

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was

cally

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Wall

hear

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in F

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mec

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una

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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).

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model is close

than the s

mental invest

the ultimate

l (20 mm) is

experimenta

_CL” with a

any factors th

havior betw

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ring the mic

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L”, Fig. 6,

pattern of

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us (Fig. 7). M

d in term

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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

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mechanical

location to

on of mechani

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wall constitue

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, is closely

“Test 1” of

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Moreover, this

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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

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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

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ng the behav

odeling and A

P_CL”: experi

minor differen

ntal investigat

hanical behav

ble.

from both st

, the follow

ents in comp

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ble of model

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Analysis of U

imental vs. ana

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real

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alytical studies

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Specifically, e

required fo

aracteristics o

ts, mortar an

d as input

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Masonry Wall

s.

lose approxi

ological ad

dict the beh

f advanced

ve experime

of masonry w

experimental

or determina

f wall constit

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parameters

ytical wall pan

ls

mations to t

dvancement

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analytical ap

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wall panels.

investigation

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tuents, i.e., tes

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in the mic

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877

their realistic

avails to

asonry walls

pproach and

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mechanical

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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.