PREDICTION OF REINFORCED MASONRY WALL
BEHAVIOR BY SIMPLE MODEL ANALYSIS AND FINITEELEMENT ANALYSIS
Rolando Jose Alvarado Funes∗
MEE09190

Supervisor: Shunsuke SUGANO∗∗

ABSTRACTReinforced masonry wall specimens were experimentally tested under the context of TAISHIN projectin El Salvador in 2005. The specimens were built using concrete block units, which is one of the mostcommon masonry types used for dwelling in the country. A total of 4 specimens will be analyzed inthis study with two main variables: ratio of horizontal reinforcement and lateral load pattern. In case of
the former case, a horizontal bar spacing of 400 mm and 600 mm is given according to the provisions
given in both codes: the actual code of 1997 and the new code draft of 2004, respectively. In case of
the latter, monotonic and cyclic load pattern is given. Failure of all specimens resulted to be due to
flexural behavior in the wall. A prediction of the observed experimental behavior of wall specimens is
intended to be simulated using two different methods: a simple model analysis proposed by MihaTomaževiþ and a discrete cracking model in finite element method. The suitability of the prediction ofboth methods is checked by the comparison of several characteristics of the behavior of masonry walls
under lateral loads observed in the experimental program. Both methods show good prediction for
flexural behavior. However, fitting of some parameters in both methods should be carried out torepresent other possible failure modes expected in masonry walls.
Keywords: Reinforced masonry, interface elements, flexural behavior.

1. INTRODUCTION
From the observation of damages and death toll caused by most recent seismic events in El Salvador,
it can easily be said that masonry structures represent the structural system with highest vulnerability
along the national territory. Also, masonry structures represent the highest percentage of use in single
and two-floor dwellings in both rural and urban areas. As a response, the national government throughthe Ministry of Public Works and some other institutions has proposed in 2004, a new design code formasonry structures but, it is not officially authorized yet and intended to substitute the actual code of
1997. Some other efforts have been done with the assist of the Japan International Cooperation
Agency (JICA) and other national institutions involved in the develop of an experimental programwith the objective of achieve a better comprehension of masonry structures commonly used in El
Salvador leading to the development of TAISHIN project in 2005 and with the main objective ofimprove the design and construction practices suggested in the codes in case of masonry. Manydifferent masonry types were tested, however only concrete block masonry is analyzed due to the highuse in the construction of dwellings in the country.
A total of four specimens are analyzed in this study. The experimental results from thespecimens are studied under the point of view of their resistant mechanism and failure mode whensubjected to the lateral loads including: initial lateral stiffness, behavior of steel reinforcing bars,
maximum strength of the wall and degradation of the stiffness and strength. Also, special attention is∗

University of El Salvador (UES).
Visiting Research Fellow, Building Research Institute, Tsukuba, Japan.

∗∗− 67 −

paid to the cracking patterns developed in each important stage of the behavior of the wall.
Displacement transducers, strain gauges and pictures record are available from the experimental
program and are used in the description of the resistant mechanism of each specimen.
As a main objective of this study is the prediction of the behavior of the specimens analyzed
in the experimental program. This is done by the use of two methods: a simple analytical model andfinite element method. The selected analytical model is the well-known proposal by Miha Tomaževiþ
in 2000. This model includes three types of failure modes: sliding, flexural and shear failure in thewall panel. Several formulations in order to evaluate each failure mode are given by the author andused for the prediction of the behavior of the wall. In case of finite element method, a discrete
cracking model is chosen for the definition of the models due to the cracking pattern observed in theexperimental program which in case of diagonal cracking, runs through the vertical and horizontal
mortar joints, and in some cases pass through the brick units. The discrete crack model is then definedby the use of plane-stress continuum elements and line interface elements in order to represent themasonry units and the potential cracking paths in the mortar joints and bricks, respectively.
Constitutive laws of materials are given to these elements in order to simulate the expected behavior
within the wall.

2. OBSERVED EXPERIMENTAL RESULTS
2.1. Description of masonry wall specimens
Geometrical characteristics were kept constantin all four specimens. Concrete block units
with nominal dimensions of 100x200x400 mm
were used in 14 layers from bottom to the topof the wall. The total length of the masonrywall panel was 3000 mm and the height was
2800 mm. The vertical reinforcement consistedof 5 deformed steel bars spaced at 600 mm
with a diameter of 9.5 mm. One extra verticalbar (Ø 9.5 mm) was included near the extreme
sides of the wall with a spacing of 200 mm assuggested in 1997 and 2004 codes making a
total of 7 vertical bars. Horizontal
reinforcement was placed within the mortar
joint and consisted of deformed steel bars
spaced at 400 mm or 600 mm (provisions of1997 code and 2004 code, respectively) of 6.35mm of diameter in both cases. Reinforced
concrete foundation beam with dimensions
300x200x3800 mm (width x height x length)
was provided, with longitudinal reinforcementof 6 bars Ø9.5 mm and stirrups space at 200
mm with bars of Ø6.35 mm of diameter. A top
beam was also included at the top end of themasonry wall panel, made of reinforced
concrete, with dimensions of 150x200x3000
mm and 4 longitudinal reinforcement bars ofØ9.5 mm of diameter and stirrups spaced at
200 mm with a diameter of Ø6.35 mm.
Monotonic and cyclic load was applied at the

Figure 1. Experimental set-up of all specimens.

top portion of the top beam. Further
description regarding the experimental
program is given in the report developed in
TAISHIN project: “Results of investigation ofreinforce concrete block construction system”(2008).
The
set-upofspecimens
experimentally tested for in-plane loading isshown in Figure 1.

− 68 −

2.2. Observed experimental behavior
120

D

100

D

C
C

80

Load (kN)

A
A

60

E

B

B
40
(A) First yielding vertical reinf.
(B) First cracking(C) First yielding horizontal reinf.
(D) Maximum Strength(E) Ultimate state

20

0
0

5

10

15

20

25

30

35

40

45

50

Displacement (mm)Experimental (Monotonic)
Experimental (Cyclic)

Figure 2. Load-displacement curves for
specimens designed under 1997 codeprovisions.

120

D
100

D
E

80

B

C
C

Load (kN)

The behavior observed during the tests of eachspecimen will be the main characteristic to becompared with the prediction of the models
mentioned above. It can be said that all
specimens showed a common behavior whensubjected to monotonic and cyclic load. The
main failure mode observed was flexural
failure. This was concluded after analysis ofdamage process, load and displacement curves
and cracking pattern in the wall along the test.
The observed resistant mechanism was asfollows: First horizontal cracks appeared in themortar joints at early stages of loading due tothe tension stresses developed due to thebending moment induced to the wall. Due tothe opening of these cracks, verticalreinforcement with the compression ofmasonry units is the mechanism holding thewall. After some load increments, yielding ofvertical reinforcement was observed. Visible
diagonal cracks were found in the wall
following the compressive strut of the panel.
Due to the increase of tension stress, the crack
opening leaded to a significant reduction oflateral stiffness of the specimen. This point istreated as the first cracking point even thoughseveral cracks have already appeared in thewall. Appropriate amount of horizontal
reinforcement withstand the tension stresses
developed in this cracks and the wall was able
to resists more load increments. Yielding ofhorizontal reinforcement was observed and all
the resistance of the wall panel is re-located in
the compression strut of the wall in the mostcompressed side. At this point, considerable
damage is already seen in the wall. The
achievement of the maximum strength
corresponded to achievement of the maximum
deformation of masonry units in thecompression zone, when crushing of units wasobserved. Finally, the wall was subjected tomore displacement until reaching the ultimate
state, when heavy damage was observed in thewall. Load and displacement curves wereobtained for all specimens and are shown on
Figure 2 and Figure 3 according to the design
provision used in the wall (1997 code or 2004code). Characteristic cracking pattern is alsostudied using the pictures record and is definedby the formation of horizontal cracks running

E

60

40

B
A

− 69 −(A) First yielding vertical reinf.
(B) First cracking(C) First yielding horizontal reinf.
(D) Maximum Strength(E) Ultimate state

A

20

0
0

5

10

15

20
25
30
Displacement (mm)Experimental (Monotonic)

35

40

45

50

Experimental (Cyclic)

Figure 3. Load-displacement curves for
specimens designed under 2004 codeprovisions.

through the mortar joints in the tension side of
the wall, diagonal cracking running throughthe mortar joints and some brick units andfinally, crushing of the masonry units in thecompression side of the wall.
Suitability of design provisions are
not discussed in this study, but as can be seen,no significant contribution is giving fordifferent horizontal reinforcement ratios. This
could not be accounted due to the induced
flexural failure in all specimens.

3. PREDICTED WALL BEHAVIOR BY SIMPLE ANALYTICAL MODEL3.1. Description of analytical model
The simple analytical model chosen for this study is proposed by Miha Tomaževiþ in 2000. Thismodel is considered due to its well-known acceptance worldwide, its experimental basis supporting
the formulations and the failure modes considered in the wall behavior. The three failure modes
considered in this model are divided in: sliding, shear and flexural failure. The calculation of thestrength for each failure mode is given by the following assumptions:• Sliding strength: In case of reinforced masonry, it is assumed that the resistance is given only by
the dowel effect of the vertical reinforcement located in the horizontal cracks along the sliding
plane (dowel action as defined by M.J.N. Priestley and D.O. Bridgeman, 1974).
• Flexural strength: It is calculated as equilibrium in the section analysis of the wall, assuming thatthe yielding of the vertical reinforcement located in the tensioned side of the wall happens
simultaneously with the crushing of the masonry units located in the compression side, as given in
EC6.
• Shear strength: It is based on the contribution of arch-beam mechanism and truss mechanism
proposed by M. Wakabayashi and T. Nakamura, 1998. The combination of arch-beam assumes
that compression is carried by an arch formed by the vertical reinforcement and masonry. Trussmechanism assumes that tension is carried out by the remaining part of vertical and horizontal
steel and masonry (Tomaževiþ, 2000).
Specific equations are given for each calculation of strength and some parameters are suggested by
the author. The suitability of these equations is checked plotting the levels of the calculated strength in
the load-displacement curve in order to define the calculated failure process of each specimen.
3.2. Results of calculation by simple analytical model
In Figure 4 and Figure 5 it is plotted each calculated strength against the load-displacement curves of
specimens designed under 1997 code and 2004 code provisions, respectively. As can be observed inboth figures, flexural strength is well predicted in all cases, more accurately in case of cyclic loadingcases. This is due to the fact that code provisions aim to induce flexural failure on the wall by the useof horizontal reinforcement, as observed in the experimental program. However, it is expected at firstthe sliding failure of the specimens but this did not happen in the experimental program. It can be said
that sliding strength is underestimated and some other mechanisms such as friction in the mortar joint,
increment of the friction coefficient due to compressive stress in the compressed side of the wall andinterlocking is not taken into account in the formulation. It is discussed in here that the contribution of
the dowel action of vertical reinforcement is given just after the formation of the cracks in the joints
and may not be taken as the only resistant mechanism accounted for sliding behavior.
280

280

240

240

200

Experimental (Monotonic)

200

Experimental (Monotonic)

Sliding Strength160

Flexural Strength

Shear Strength

Load (kN)

Load (kN)

Experimental (Cyclic)
Sliding Strength
Flexural Strength

120
80

160

Experimental (Cyclic)
Shear Strength

120

80

40

40

0
0

5

10

15

20

25

30

35

40

45

50

Displacement (mm)

0
0

5

10

15

20

25

30

35

40

Displacement (mm)Figure 4. Calculated strengths for specimens
designed under 1997 code provisions.

Figure 5. Calculated strengths for specimens
designed under 2004 code provisions.

− 70 −

Shear strength is considered as overestimated in the calculation. This is attributed at the suggested
tribute area considered in the arch-beam mechanism of 50% of the total width of the wall. This
percentage is considered as excessive and it is proved with the finite element results. However, it isnecessary to evaluate experimentally the actual value of shear strength of the specimens. Future tests
with similar specimens but with induced shear behavior are needed to accurately asses the validity of
the formulation by Tomaževiþ.
4. PREDICTED WALL BEHAVIOR USING FINITE ELEMENT METHOD
4.1. Description of the discrete model
A discrete cracking model is chosen for this study due to its advantages against smeared crack modelin terms of the cracking paths expected in the wall. From observation of the experimental results, it iseasily seen that most of the cracks occurred in the bed and head joints of the wall. Because of this, thediscrete model proposed in this study consists in the combination of 8-noded plane stress continuum
elements (QU8), 4-noded line interface elements (IL22) and truss elements (BE2). The software tool is
DIANA v. 9.3. Plane stress elements are used for the simulation of masonry units and concreteelements (top and foundation beams) and are given with the compressive behavior intended toreproduce crushing of these elements using a Von-Mises ideal plasticity model. Interface elements
represent the mortar joints (head and bed joints) which are given with frictional behavior to reproduce
sliding with the use of a Mohr-Coulomb friction model. Also, a potential vertical crack running
through the masonry units is given at every half brick and simulated with interface elements. The
behavior given to these cracks is representing tensional behavior by the use of a linear
tension-softening model. Finally, truss elements are representing the vertical and horizontal
reinforcing bars under tensional behavior and described by a Von-Mises ideal plasticity model. The
constitutive laws parameters were obtained from the available test results in the experimental program,and, some other are obtained from past researches (Cabrera, 2003 and Lourenço and Rots, 1997).
The simulation is only done in case of monotonic loading specimens. Lateral load iscontrolled by displacement increments with a step size of 0.05 mm until reaching 20 mm of total
horizontal displacement at the top of the wall (1/150). Regular Newton-Raphson method with force
tolerance of 10 kN is given for the iterative procedure. Vertical load simulating the self-weight of thepanel was distributed in 3 points along the top beam. High capacity of deformation is given to
constitutive laws in order to keep the stability of the calculation. Finally, perfect bonding is considered
for the reinforcing bars.
4.2. Results of prediction by finite element analysis
Load-displacement curves are obtained as a result of calculation and plotted against the experimental
one. Figure 6 and Figure 7 shown the results for the 1997 code and 2004 code specimens, respectively.
It can be seen in this Figures that the behavior of the wall can be well-predicted by this method.
Higher strength values were obtained and may be attributed to the use of perfect bonding in thereinforcement. Lateral stiffness, yielding of bars and crushing of the units is well predicted in theprocess of failure of the wall. Cracking pattern at each step is also calculated and a good agreement
can be observed. Particular cracking such as horizontal cracks in bed joints, diagonal cracking in bed
and head joints and crushing of units is well predicted. Maximum crack width calculated is 4 mm andis in compliance with the observed in the experiments. Behavior and yielding of vertical andhorizontal reinforcement can be also calculated and roughly well predicted. In case of verticalreinforcement, the calculation of reinforcement is accurately done. Finally, it can be checked theformation of the arch-beam mechanism of the wall. However, at maximum strength point(corresponding to the crushing of the units), a compressed total length of 20% of the length of the wall
is found to be under high compressive stresses. This can be used to calibrate the 50% suggested byTomaževiþ and that is supposed to lead to overestimation of shear strength of the wall.

− 71 −

120

140

D
100

120

D

C

D

C
100

80

A

C
B

60

Load (kN)

Load (kN)

A

B
A

80

A

B
C

60

B

40

40
(A) First yielding vertical reinf.
(B) First cracking(C) First yielding horizontal reinf.
(D) Maximum Strength(E) Ultimate state

20(A) First yielding vertical reinf.
(B) First cracking(C) First yielding horizontal reinf.
(D) Maximum Strength(E) Ultimate state

A
20

0

0
0

2

4

6

8

10

12

14

16

18

20

0

Displacement (mm)Experimental (Monotonic)

2

Calculated (FEM)

4

6

8

10
12
Displacement (mm)Experimental (Monotonic)

Figure 6. Load-displacement curve obtained forspecimen designed under 1997 code.

14

16

18

20

22

Calculated (FEM)

Figure 7. Load-displacement curve obtained forspecimen designed under 2004 code.

5. CONCLUSIONS
The applicability of two methods of analysis of reinforced masonry walls is checked. It is seen thatboth gives accurate results in case of masonry walls governed by flexural behavior. However, in caseof simple model analysis, some parameters should be fit prior to its use in practical applications. Someexperimental studies should be carried out in order to establish the actual sliding and shear strength ofthe masonry walls due to the fact that it is not well captured by the equations proposed by the author in
the cases studied in here. In the other hand, finite element method is able to capture the process offailure and strength of the specimens. It is suggested to carry out some experimental tests in order tovalidate the parameters chosen for the frictional behavior of the mortar joints, which are obtained frompast researches. Also, it has to be experimentally tested the bond-slip behavior of reinforcing bars.
AKNOWLEDGEMENT
I would like to express my gratitude to my supervisor Prof. Shunsuke Sugano for his advices andsuggestions. Also, special thanks to Dr. Tomohisa Mukai, Dr. Hiroshi Fukuyama and Dr. HaruhikoSuwada for the valuable help and good disposition to the successfully realization of this study.
REFERENCES
Cabrera, A.M. (2003). Nonlinear analysis of masonry structures using finite element method.
International Institute of Seismology and Earthquake Engineering.
DIANA, version 9.3. (2006). Department of Engineering Mechanics and Information Technology,
TNO Building and Construction Research, Delft, The Netherlands.
Eurocode 6: Design of Masonry structures (1995). Part 1-1: General rules for buildings. Rules forreinforce and unreinforced masonry. ENV 1996-1-1: 1995.
Lourenço, P.B., & Rots, J.G. (1997). Multisurface interface model for analysis of masonry structures.
Journal of Engineering Mechanics, 660-665.
Paulson, T.J., & Abrams, D.P. (1990). Correlation between static and dynamic response of model
masonry structures. Earthquake Spectra, Vol. 6, No.3, 573-591.
Priestley, M.J.N., & Bridgeman, D.O. (1974). Seismic resistance of brick masonry walls. Bulletin of
the New Zealand National Society for Earthquake Engineering, 167-187.
Tomaževiþ, M. (2000). Earthquake-resistant design of masonry buildings. Series on innovation in
structures and construction, Vol. 1. Imperial College Press.
Wakabayashi, M., & Nakamura, T. (1984). Reinforcing principle and seismic resistance of brickmasonry walls. Proc. 8th World Conference on Earthquake Enigneering, Vol. 5, 661-667.

− 72 −