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CHAPTER – 5

FINITE ELEMENT MODELING

5.1 INTRODUCTION

Masonry is a composite material with the building brick units and the mortar as the joining

material, which are bonded together. Guinea [2000]51

reported that the basic mechanical

properties of the masonry are strongly influenced by the mechanical properties of its constituents

namely, brick and mortar. Utilizing the material properties obtained from the experiments and

using actual geometric details of both components and joints, the behavior of the brick masonry

was numerically analyzed using ANSYS. There is a need for developing a comprehensive finite

element model, as a numerical analysis method becomes more popular in solving numerous

engineering problems. The finite element model was developed to understand the behaviour of

the brick masonry walls. A three dimensional linear finite element model was developed to

determine the strength, lateral displacement and the stress distribution throughout the masonry

wall. Masonry itself is a composite material that consists of two materials depending upon the

properties of the masonry unit (brick) and the mortar. Paulo Lorenco [2006]118

has discussed that,

there are three approaches towards its numerical representation depending upon the level of

accuracy and simplicity desired. They are (i) micro level modeling (ii) meso level modeling and

(iii) macro level modeling. The five brick stack bonded clay brick masonry prism and fly ash

brick masonry prism is considered to determine the masonry strength. The clay brick masonry

prism of size 220mm x 110mm x 400mm is considered. The size of the masonry unit is 220 x

110 x 70mm. The size of the mortar joint is 220 x 110 x 10mm as shown in Fig. 5.1. The finite

element model was used to understand the results of the shear – compression diagonal

compression / tests on masonry wall panel.

(a) (b) (c)

Fig. 5.1 (a) Micro level modeling (b) Meso level modeling (c) Macro level modeling

tba tb

tm

151

Zuchini [2009]145

used these different simulations depend upon the methods offered by different

degrees of accuracy and therefore they should be used according to the requirements of

individual situations. The first approach offers the detailed interaction between the masonry units

(brick) and the mortar as it is most suitable for the current study. The five brick stack bonded

prism provides the most detailed accuracy during simulation. The second approach offers a better

accuracy of the behaviour of a masonry structure and is suitable for simulation of five brick stack

bonded prism to study the concentration of stress. The last approach studies a general behaviour

simulation of the structure and is better suited for studying large size structures for the global in-

plane shear behaviour of the masonry wall.

5.2 FORMULATION OF THE MODEL

Masonry strength is dependent upon the characteristics of the masonry unit, the mortar and the

bond between them. Empirical formulae as well as analytical and finite element models have

been developed to predict the structural behaviour of the masonry. When the masonry is under

compression, the masonry unit and the mortar will be under multi-axial state of stress. Hence, the

present investigation is an attempt to develop a finite element model to predict the masonry

prism compressive strength subjected to concentric compressive loading while using some

failure theories developed for brittle materials under multi-axial state of stress. The finite element

model is validated by comparing the predicted values with those obtained from the controlled

experimental results. In the present study, models with two different material assumptions are

presented: in one, masonry as a composite material consisting of brick unit and mortar joint ; the

other, treats both phases of the material are replaced with an equivalent material property,

assuming it to be a homogenized material, Luisa Berto [2008]85

. Equivalent elastic modulus for

brick masonry had been studied assuming that no slippage occurs between the mortar layers and

brick unit with the head joints considered to be continuous as considered by Jahangir [2004]72

. In

this method, the behavior of the masonry is roughly approximated by linear elasticity and perfect

interface bonding hypothesis. Brick unit was modeled using solid 185, eight-node iso-parametric

brick element type with three degrees of freedom: translations in the nodal x, y, and z directions

as shown in Fig 5.2 (a). The element has plasticity, hyper-elasticity, stress stiffening, creep, large

deflection and large strain capabilities. It also has mixed formulation capability for simulating

the deformations of nearly incompressible elasto-plastic materials and fully incompressible

hyper-elastic materials. Mortar joint was modeled using SOLID45, the 3-D modeling of the

152

element with eight nodes having three degrees of freedom at each node: translations in the nodal

x, y, and z directions as shown in Fig 5.2 (b). The solid 45 element has plasticity, creep,

swelling, stress stiffening, large deflection and large strain capabilities. The unit properties of the

brick and the mortar joint required for the analysis were obtained by conducting experiments

described in chapter -3 of this thesis.

(a) (b)

Fig. 5.2 (a) Solid 185, 3D solid element type used for the brick unit

(b) Solid 45, 3D solid element type used for the mortar joint

The clay brick masonry reinforced with woven wire mesh in the alternate bed course of the brick

masonry is modeled using shell 63 element as it has both bending and membrane capabilities in

the ANSYS and the element detail is shown in Fig.5.3.

Fig 5.3 Shell 63 for the woven wire mesh

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SHELL63 element has six degrees of freedom at each node: translations in the nodal x, y, and z

directions and rotations about the nodal x, y, and z-axes. Stress stiffening and large deflection

capabilities are also included.

5.3 MICRO LEVEL MODELING OF THE BRICK MASONRY

The micro level models consider the units and the mortar joints separately, characterized by

different constitutive laws; thus, the structural analysis is performed considering each constituent

of the masonry material. The mechanical properties that characterize the models adopted for the

brick units and the mortar joints are obtained through experimental tests conducted on the single

material components.

Compressive strength of the brick masonry:

The compression testing was performed according to Indian masonry code IS: 1905[1987]65

.

Four stack bonded prisms of five bricks each, were constructed and tested under axial loading.

The main purpose was to examine the effects of brick unit and the mortar properties on the

strength and deformation characteristics of the masonry prisms as discussed by Olivera

[2000]111

. The stack bonded brick masonry prism constructed with five clay bricks having

dimensions of 220 mm x 110 mm x 70 mm in 10mm thick cement mortar having the ratio of 1:6

with partial replacement of fine aggregate with fly ash. The discretization is such that, the bricks

and the mortar joints had been represented by separate layers of elements. Each type of element

was represented with its own properties in terms of its respective uni-axial compressive strength

and initial modulus of elasticity. The applied loading was on the top surface of the model in the

negative ‗y‘ direction representing the compressive loading with the pinned boundary condition

as all the nodes at the base of the models are supported in the test platform. Brick and the mortar

joint were modeled using the micro-modeling approach representing joints as continuum

elements and assuming a perfect bond between the brick unit and the mortar joint. Each model

was assumed to be subjected to axial compressive load, as shown in Fig 5.4 (a).

154

(a) (b)

Fig 5.4 (a) Micro level modeling of brick masonry prism

(b) Stress distribution on unreinforced clay brick masonry prism (UCBP)

This approach leads to structural analyses characterized by great computational effort.

Nevertheless, this approach can be successfully adopted for reproducing experimental tests. The

simulation was carried out in sub-steps. The failure of masonry under concentric compression is

related to the interaction between the masonry unit and the mortar as a result of their differing

deformation characteristics.

Shear strength of the brick masonry:

In order to determine the shear behaviour parameter, a double shear test method using triplet

specimens has been suggested by Gabor [2005]43

. The triplet shear model is assumed to be made

from two different materials, namely brick units and mortar. The non-linearity considered in the

analysis of the model was only material non-linearity. The 3-D finite element analysis on the

unreinforced clay brick masonry with the ratio of 1:6 cement mortar, UCBP was modeled and

analyzed. The results are obtained for the maximum deflection, the shear stress and the vertical

shear strains in the triplet prism. When the maximum stress level was reached, the behavior of

the brick masonry specimens was characterized by a (quasi fragile) softening behavior and by a

sliding movement between the adjacent bricks as reported by Fazia Fouchal [2009]42

. The triplet

prism modeled indicates that the shear behaviour of masonry is weak along the mortar joint are

shown in Fig. 5.5 (a, b & c).

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(a) (b)

Fig. 5.5 (a) Deformation of the unreinforced clay brick masonry under triplet shear test

(b) Element stress distribution in the clay brick masonry under triplet shear test

(c)

Fig. 5.5 (c) Nodal stress distribution in the clay brick masonry under triplet shear test

The displacement pattern predicted by the finite element model shows vertical sliding between

the brick and the mortar of the brick masonry prism.

5.4 MESO LEVEL MODELING OF THE BRICK MASONRY

In meso-level modeling expanded units are represented by continuum elements. The behaviour

of the mortar joints and the unit/mortar interface are lumped into discontinuum elements as

shown in Fig 5.6. In this approach, the units are expanded to retain the initial geometry of the

masonry assemblage. Due to the assumption of the zero thickness of mortar joints, the elastic

properties of the expanded brick units are adjusted to yield the elastic modulus of the represented

masonry. In the stack bonded brick masonry prism, the bricks are assumed as a series of chain

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connection of the components results in the uniform stress distributions both in the brick unit and

the mortar. The adjusted average elastic stiffness of the expanded brick units are simply derived

from Krit [2007]79

by considering the elastic properties of the masonry components (brick and

mortar) and the expanded thickness as,

Adjusted Elastic modulus, Eba = bmmb

mbmb

EtEt

ttEE )(; Adjusted brick thickness, tba = tb + tm

The hexagonal woven wire mesh (reinforcement material) used in the brick masonry was

modeled as shell 63 and modeled in between the expanded bricks. The stress behaviour of the

clay brick masonry (unreinforced and reinforced) is shown in Fig 5.7 (a & b).

Fig. 5.6 Meso level modeling of the brick masonry prism

(a) (b)

Fig 5.7 (a) Stress distribution on unreinforced clay brick masonry prism (UCBP)

(b) Stress distribution on clay brick masonry prism reinforced with wire mesh (RCBP)

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From the finite element modeling of unreinforced clay brick prism, it was understood that the

stress is found to be uniform throughout the unreinforced masonry brick prism specimen.

Whereas, in clay brick masonry prism reinforced with woven wire mesh the stress is

concentrated at the reinforcement (mesh) placed in between the expanded brick units at the bed

joint of the brick masonry prism.

5.5 MACRO LEVEL MODELING OF THE BRICK MASONRY

In this analysis, the brick masonry which is made from two different materials of the clay bricks

and the mortar had been replaced by an equivalent homogenous material. The macro-models are

based on the use of constitutive laws for the masonry material; i.e. the stress-strain relationships

adopted for the structural analysis are derived by performing tests on masonry, without

distinguishing the bricks and the mortar behavior. Equivalent homogeneous material or macro-

level simulation approach of the brick masonry is shown in Fig 5.8. Homogenization involves

using the analytical micro models for small masonry assemblages to determine the combined

response. The meso level and the macro level modeling technique are unable to model the local

failure modes (unlike the micro-modeling technique).

(a) (b)

Fig. 5.8 (a) Macro level modeling of brick masonry prism

(b) Stress distribution on the unreinforced clay brick masonry prism (UCBP)

Masonry sustains damage in the form of cracks in the early stage of the loading as the mortar

break at the low level of the load compared to the brick units. The micro-modeling has been

compared with the meso-level and the macro-level modeling along with the experimental results.

Stress - strain behaviour of the unreinforced clay brick masonry prism is predicted using finite

element modeling and verified with the experimental data. The comparison of the predicted

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values of masonry compressive strength obtained by different numerical modeling techniques

such as (ANSYS) and with the experimental results are shown in Fig. 5.9

Fig 5.9 Stress – strain curve of the unreinforced clay brick masonry prism (UCBP)

The stress-strain curve obtained from the finite element analyses shows that the maximum

compressive strength of the brick masonry was slightly higher for the case of homogenized

material than that of the composite material. The actual compressive strength of the masonry

determined by experimental method was much higher than the strength obtained by numerical

method. However, in reality, the brickwork was constructed from two layered materials, namely

brick and mortar. Therefore, the idealization of composite material for the analysis should be

adopted. The comparison of experimental and numerical results indicates that the compressive

strength of masonry obtained by experimental method was 47% higher than those obtained by

the finite element method which are in accordance with the theories proposed by Hendry

[1990]56

. Therefore, for the design purposes, the strength obtained for the brick masonry from

finite element analysis should be magnified with a factor of 1.52 in order to get the actual

strength of the brick masonry.

5.6 IN-PLANE SHEAR STRENGTH OF THE BRICK MASONRY WALL

The structural shear walls of a masonry building subjected to horizontal loading commonly

present two types of failure. The first one is out-of-plane failure, where cracks appear along the

horizontal mortar joints. The second one is in-plane failure, generally characterized by a diagonal

tensile crack. Zuchini [2009]145

stated that if the out-of-plane failure is avoided, then the

structural resistance is mainly influenced by the in-plane behaviour of the shear wall. Use of

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.000 0.002 0.004 0.006 0.008

Str

ess

, N

/mm

2

Strain

Stress strain curve of unreinfoced clay brick masonry

prism, UCBP

Experimental

Micro model

Meso model

Homogenized model

159

macro level modeling requires less number of elements and hence produces quick numerical

solutions. The macro-modeling technique is suitable for modeling large sections of masonry,

where only a simplified representation of composite behaviour is required and local failure

modes are not so important. As macro modeling of masonry is advantageous for the global

behaviour of the structure, the macro modeling has been adopted in preference to the micro

modeling to study the behaviour of the masonry wall panel as reported by Gabor [2006]43

. In this

macro level modeling, the brick masonry made from two different materials of clay bricks and

mortar had been replaced by an equivalent homogenous material and analyzed. The finite

element model was used to understand the in-plane behaviour of the masonry and is verified with

the shear-compression tests and diagonal compression tests.

Shear-compression test:

Unreinforced masonry shear walls are often used as the main structural component of masonry

buildings responsible for carrying the lateral loading such as wind and earthquake loads. The

lateral and vertical loads lead to tension and shear combined with compression within the

masonry wall. Krit Chaimoon [2007]79

stated that the fracture and failure of the masonry walls

under shear-compression is intricate because of the complex interaction of the shear failure along

the mortar joints and compression failure often at the toe of the wall. The modeling of the shear-

compression test on brick masonry wall panel predicted the stress behaviour of the clay brick

masonry wall and is shown in Fig 5.10 (a & b) and in Fig 5.11(a & b).

(a) (b)

Fig 5.10 (a) Macro level modeling of brick masonry wall under shear – compression test

(b) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP)

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Homogenized model behaves as one material and the dispersion of the load in the model will be

at about 45o. However, in the case of models assumed to be made from composite materials,

similar dispersion of vertical loads cannot be expected as reported by Luisa Berto [2008]85

. The

detailed modeling of the geometrical structure of the masonry requires important computational

resources and renders the modeling quite laborious. Thus, if the goal of the modeling is to obtain

an approximation of the average behaviour of the masonry in terms of loads and deformations, it

is conceivable to build an equivalent material model without considering the internal geometry

of the masonry.

(a) (b)

Fig 5.11 (a) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP10)

(b) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP20)

From Fig. 5.11 (a & b), the stress distribution of the specimen CBP20 was widened along the

diagonal of the wall panel than the specimen CBP10. Finally, the finite element modeling results

are compared with the obtained experimental results and discussed the reliability of the finite

element models.

Diagonal compression test:

The diagonal compression test mechanism was composed of a set of metallic elements fixed at

the two corners of a diagonal end of the panel. In this test, a compressive force was applied

gradually along a diagonal end of the specimen to study the in-plane shear behaviour of the

masonry wall panel. The applied compressive force may cause a diagonal tension in the

specimen which in turn led to the failure of the specimen with splitting cracks parallel to the

direction of the load. The finite element model used to simulate the behaviour of the masonry

under diagonal compression tests is described in Fig 5.12 (a). The material properties required

161

for the masonry model were determined from the experimental characterization tests in chapter 3

of this thesis. The failure pattern and the load deformation behaviour of the specimen are studied.

(a) (b)

Fig 5.12 (a) Macro level modeling of brick masonry wall panel under diagonal compression

test

(b) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP)

As the diagonal load was applied on the wall panel specimen, the deformation occured and the

stress was formed as the diagonal band along the direction of the application of the load. The

stress propagation on the unreinforced clay brick masonry wall panel (with the ratio of 1:6

cement mortar with partial replacement of fine aggregate with fly ash as 0%, 10% and 20%) was

in the form of the diagonal band as shown in Fig. 5.12(b) and Fig 5.13 (a & b). The behaviour of

the clay brick masonry reinforced with woven wire mesh is depicted in Fig. 5.14.

(a) (b)

Fig 5.13 (a) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP10)

(b) Stress behaviour on unreinforced clay brick masonry wall specimen (CBP20)

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Fig 5.14 Stress behaviour of reinforced clay brick masonry wall specimen (CBPR)

The ANSYS modeling was compared with the test results and the behaviour had been observed.

The numerical load versus displacement curve is plotted in Fig 5.15 and Fig 5.16 and compared

with the experimental results. A reasonably good agreement has been found.

Fig 5.15 Load-deformation curve of unreinforced clay brick masonry wall panel (CBP)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 5 10 15 20

Lo

ad

(N

)

Horizontal deformation (mm)

Load -deformation curve of unreinforced clay brick

masonry wall panel (CBP)

Experiment Ansys

163

Fig 5.16 Load-deformation curve of unreinforced clay brick masonry wall panel

with 10% replacement of fine aggregate with fly ash in the mortar (CBP10)

The comparison of the shear stress obtained from the ANSYS and the experimental stress value

are reported in Table 5.1

Table 5.1 Comparison of shear stress obtained through ANSYS and experiment

Type of wall

Maximum shear stress

through the experiment

(MPa)

Maximum shear stress

through ANSYS

(MPa)

Shear stress obtained

through ANSYS /

Shear stress obtained

through Experiment

CBP 0.048 0.092 1.92

CBP10 0.056 0.123 2.21

CBP20 0.080 0.154 1.92

CBP0R 0.064 0.124 1.93

CBP10R 0.080 0.155 1.92

CBP20R 0.096 0.186 1.94

FBP 0.064 0.123 1.93

FBP10 0.145 0.278 1.93

FBP20 0.112 0.216 1.93

FBP0R 0.169 0.325 1.94

FBP10R 0.257 0.495 1.96

FBP20R 0.201 0.386 1.93

Review of the numerical data leads to recognize that, if macro-modeling strategy was applied,

the overall response of the masonry panels can be well predicted in terms of the collapse load

and the deformation values as well as sufficiently accurate failure mechanisms can be predicted.

0

2000

4000

6000

8000

10000

12000

14000

0 5 10 15 20 25

loa

d (

N)

Horizontal deformation (mm)

Load - deformation curve of brick masonry CBP10

Experiment

Ansys

164

The compressive strength of the brick masonry obtained from ANSYS analysis are magnified by

the factor 1.52 in order to obtain the experimental results which are in accordance with Jahanghir

et al [2004]72

. Similarly the maximum shear stress obtained from ANSYS is to be magnified by

the factor 1.95 to obtain the experimental shear stress.

5.7 CONCLUSIONS

(i) The finite element model traces the progressive crack growth and the stress distribution

patterns in the masonry units and the mortar.

(ii) Monitoring of crack patterns as the applied stress intensity increases shows the progress

of crack development and the crack propagation in the masonry prism. The crack pattern

predicted by the finite element model leads to vertical splitting cracks in the prism. Such

vertical splitting cracks across the prism height were seen in the masonry prisms tested

for compressive strength.

(iii) The compressive strength of the brick masonry prism (both unreinforced and reinforced

clay brick masonry and fly ash brick masonry) predicted by the finite element models is

47% higher than the experimental values which are in accordance with the theories

proposed by Hendry [1990]56

.

(iv) The comparison of experimental and numerical results indicates that the compressive

strength of the masonry derived by the finite element method has to be magnified by

1.52 times to arrive the experimental data. Also to get the actual in-plane shear stress of

brick masonry, the finite element analysis results should be enhanced by a factor 1.95.