Sugano, S. et al.

Paper:

Strength and Deformation of Confined Brick Masonry Walls
Subjected to Lateral Forces– Review of Existing Test Data in Japan and Peru –Shunsuke Sugano∗ , Taiki Saito∗∗ , Carlos Zavala∗∗∗ , and Lourdes Cardenas∗∗∗∗ Building Research Institute1 Tachihara, Tsukuba, Ibaraki 305-0802, Japan
E-mail: sugano@hiroshima-u.ac.jp∗∗ Toyohashi Institute of Technology, Toyohashi, Japan∗∗∗ Centro Peruano Japonés de Investigaciones Sı́smicas y Mitigación de Desastres (CISMID), Lima, Peru
[Received August 11, 2014; accepted November 5, 2014]

The Japanese and Peruvian experimental databases
on confined brick masonry walls are put together as
one database, and the strength and deformation of thewalls are reviewed. First, the applicability of existing
equations for the ultimate strength of reinforced concrete or reinforced masonry walls to the estimationof the maximum strength of confined brick masonrywalls which failed in shear, flexural-shear, or flexurewhen subjected to lateral forces, is discussed. Then,empirical equations for the maximum strength, displacement at maximum strength, and ultimate stateof the walls are proposed based on multiple regression analysis, and the accuracy of the proposed equations is discussed. It is concluded that the maximum
strength can be estimated using the existing equationsor the proposed empirical equations with good accuracy. The deformations at maximum strength and theultimate state can be estimated using the proposed empirical equations, although there is a large amount of
scatter.
Keywords: confined masonry, test data, strength, deformation, lateral force, backbone model

1. Introduction
The Building Research Institute (BRI) of Japan has
been collecting research papers and test data on reinforced
masonry (RM) and confined masonry (CM) walls from allover the world to propose a backbone model for the design and analysis of masonry buildings subjected to lateralforces. The Centro Peruano-Japonés de Investigaciones
Sı́smicas y Mitigación de Desastres (CISMID) of Peru has
also been collecting papers and test data on confined brickmasonry walls in Latin American countries for the same
purpose.
In this paper, the Japanese [1–3] and Peruvian
databases [4–6] on confined brick masonry walls (Figs. 1
and 2) are put together and reviewed with respect to thefailure mode, the maximum strength, the deformations at

984

maximum strength, and the ultimate state of walls subjected to lateral forces.
This paper describes (1) the applicability of existing
equations for the design and analysis of reinforced concrete walls or reinforced masonry walls to the experimental maximum strengths of confined brick masonry walls,(2) the factors that affect the strength and deformabilityof confined brick masonry walls, (3) multiple regression
analyses of the maximum strength, the deformations at
maximum strength, and the ultimate states of walls.

2. Outline of Experimental Database
2.1. Japanese Database
Since 1992, the Chiba Institute of Technology, Building
Research Institute, Oita University, Akita University, theUniversity of Tokyo, Hokkaido University, and Mie University have conducted tests on confined masonry walls
under static cyclic loading. Among them, the test data of
Building Research Institute [1] and Oita University [2, 3]
were selected as the database for the review in this study
because (1) a large number of test specimens were included in a series of tests and (2) the effects of many
structural factors on the behavior of confined brick masonry walls were studied.
There are 55 walls in total in the Japanese database,and the ranges of structural factors are as follows:
prism compressive strength of brick masonry, Fm : 18.5–
60.6 N/mm2 ; wall length l: 1,070–1,750 mm; wall thickness t: 100–183 mm; wall height h: 665–1,663 mm;shear span ratio, h/l: 0.52–0.95; column reinforcement
ratio, Pte : 0.05–0.67%; wall lateral reinforcement ratio,
Pwe :0.00–0.64%; and axial stress, σ0 : 0.39–1.37 N/mm2 .

2.2. Peruvian Database
The Peruvian database consists of the experimental
data on the 34 confined brick masonry walls tested in
the CISMID since 1993 [4–6]. The ranges of structural
factors are as follows: prism compressive strength of
Journal of Disaster Research Vol.9 No.6, 2014V
         䣅䣱䣮䣷䣯䣰䢼䢢
䢴䢲䢲䣺䢳䢲䢲
䣙䣣䣮䣮䢢䣶䣪䣫䣥䣭䣰䣧䣵䣵凬䢳䢲䢲䣅䣱䣮䣷䣯䣰䢼䢢
䢳䢲䢲䣺䢳䢲䢲
䣙䣣䣮䣮䢢䣶䣪䣫䣥䣭䣰䣧䣵䣵凬䢳䢲䢲

Fig. 1. Confined brick masonry walls in the test of Building
Research Institute in 1994 [1].

V

Column size:
125 x 250 mm
Wall length:
1,800 – 3,600 mm
Wall thickness
115 – 250 mm
Wall height
2,300 – 4,600 mm
Shear span ratio:
0.92 – 1.44
Axial stress:
0.18 – 0.61 N/mm2

Fig. 2. Confined brick masonry walls in the test of CISMID
in peru [4–6].

masonry, Fm : 2.2–29.8 N/mm2 ; wall length, l: 1,800–
3,600 mm; wall thickness, t: 120–250 mm; wall height, h:
2,300–3,450 mm; wall shear span ratio, h/l: 0.64–1.44;
column reinforcement ratio, Pte : 0.05–0.20%; wall lateralreinforcement ratio, Pwe : 0.23–0.28%; and axial stress,
σ0 : 0.18–0.61 N/mm2 .

3. Load – Deformation RelationshipIn the review of the database, the envelope of hysteresis curves of each wall tested was idealized into thefour-line backbone curve shown in Fig. 3. The curve has
three breaking points where stiffness changes: the cracking point (C), yielding point (Y), and maximum strength
point (Max), and ultimate point (Ult). The ultimate point
is defined as the point where the strength decreases to 80%of the maximum strength. The yielding point is definedas the point where the observed strain at the flexural reinforcement exceeds the yield strain or as the point where
significant change in stiffness is observed in the hysteresis
curves.
The failure mode of a wall which has failed in shear
without yielding is defined as “shear failure” and is abbreviated as “S” in this paper. The failure mode of awall which has failed in shear after yielding is definedas “flexural-shear failure” and is abbreviated as “FS.” The
failure mode of a wall which has failed in flexure is defined as “flexural failure” and is abbreviated as “F.”

4. Application of Existing Equations
The applicability of existing equations for the design
and analysis of reinforced concrete walls or reinforced
Journal of Disaster Research Vol.9 No.6, 2014

Strength and Deformation of Confined Brick Masonry Walls
Subjected to Lateral Forces
Shear
force
ј

Maximum
Yielding Strength
Max
Y

Vmax
Vy
Vc

C

20% Vmax
Ult

Cracking

Ultimate

Failure ModeC їY їMax їUlt Flexural Failure (F)C їMax їUlt
Shear Failure (S)C їY їMax їUlt Flexural Shear Failure (FS)
ɷc
Rc

ɷy
Ry

ɷmax
Rmax

ɷu 䲑Displacement
Ru ĺDrift angle

Fig. 3. Backbone model of restoring force characteristics ofconfined brick masonry walls.

masonry walls to confined brick masonry walls is determined by comparing the observed maximum strength tothe strength calculated using the equations.

4.1. Existing Equation for Ultimate Shear Strengthof Reinforced Concrete Shear Walls
V
For design and analysis of reinforced concrete shear
walls, the following equation is used to calculate the㸧lowerboundaryoftheobserved
shear
strengthintests.
V
0.23 (F + 18)
0.053 · pte√mQsu1 =+ 0.85 pwe · σwy
M/(Q · l) + 0.12
+0.1σ0e } · te · j . . . . . . . . . . (1)where te : wall thickness and te = Aw /l, Aw : section areaof wall, l: wall length, Pte : tensile reinforcement ratio(= 100at /(te lw ), unit %), at : section area of tensile reinforcement (mm2 ), Fm : compressive strength of masonry
prism (N/mm2 ), lw : wall effective length = 0.9l, Pwe : lateral reinforcement ratio (= aw /te s) (must be 0.012 when
it exceeds 0.012), aw : section area of a pair of lateral reinforcements and s: its space, σwy : yield strength of lateralreinforcement (N/mm2 ), j: distance between centers oftensile and compressive stresses (= (7/8)l w ), σ0e : average axial stress of wall (N/mm2 ) (= Nw /Aw ), Nw : axial
force acting on the wall (N), M/(Ql): shear span ratio= h/l, h: height of inflection (loading) point, which mustbe 1.0 when it is less than or equal to 1.0 and 3.0 when it
exceeds 3.0.
Figure 4 shows the relationship between observed
strength and the strength calculated by Eq. (1), both interms of the average shear stress in N/mm2 . Eq. (1) overestimates the maximum strength for most shear failure
walls and overestimates more for all the flexural-shear
failure or flexural failure walls.

4.2. Equation for Shear Strength of Masonry Walls
The following equation has been proposed by the Architectural Institute of Japan as the equation to use toevaluate the ultimate shear strength of reinforced masonrywalls subjected to lateral forces [8]. The equation is985

Sugano, S. et al.

2.5

2.5

­ 0.053  pte 0.23 Fm  18½
 0.85 pwe  V wy  0.1V 0 e ¾  te  j®
¯ M / Q.l  0.12¿

2

Experimental Value (N/mm2)

Experimental Value (N/mm2)

Qsu1

Peru_FS
CM1_S
1.5

࣭

CM1_FS
CM1_F

1

J

J

0.5

2

V
1.5

V

Peru_FS
CM1_S
1

CM1_F
0.5

CM1: Confined Brick Wall
0.5

1

1.5

2

Number of specimen 91
Mean Value
1.01
Standard deviation
0.57
Coefficient of variation 0.57

000CM1_FS

0

2.5

0.5

1

1.5

2

2.5

Calculated Value (N/mm2)

Calculated Value (N/mm2)

Fig. 4. Evaluation of the maximum strength using existingVequation for shear strength of RC walls.

Fig. 5. Evaluation of the maximum strength using AIJ equation for shear strength of hollow concrete block walls.

based on tests conducted by Matsumura on hollow concrete block walls [9].



√
0.76
+ 0.012 Fm
Qsu3 = ku · k p
h/d + 0.7

+0.18γ · δ ph ·h σy · Fm + 0.2σ0 · t · j (2)where ku : reduction factor depending on masonry material (ku = 0.64 [8]), k p : 1.16pt0.3 (pt = 100at /(t · d), unit%), h: height of inflection point×2, d: effective lengthof wall (= l0 − t/2), l0 : wall length, t: wall thickness, at :section area of tensile reinforcements (mm2 ), Fm : compressive strength of masonry prism (N/mm2 ), γ : reduction
factor depending on reinforcement (γ = 0.6 [8]), δ : reduction factor depending on loading condition (δ = 1.0 [8]),ph : lateral reinforcement ratio (= aw /ts), aw : section areaof a pair of lateral reinforcements and s: space of thepair of lateral reinforcements, h σy : yield strength of lateral reinforcement (N/mm2 ), σ0 : average axial stress ofwall (N/mm2 ), Nw : axial force acting on the wall (N), andj: distance between centers of tensile and compressive
stresses (= (7/8)d).
Figure 5 shows the relationship between observed
maximum strength in test and the calculated shear
strength using Eq. (2), where the strengths are expressedin terms of the average shear stress in N/mm2 . It has been
observed that Eq. (2) provides the average of the observed
maximum strength, though there is a significant amount of
scatter. It is interesting that Eq. (2) provides the averageof the test results of confined brick masonry walls despite
the fact that it is based on the test results from hollow concrete block walls, another type of wall altogether.

4.3. Approximate Equation for Flexural Strength
The following equation is used to approximate the ultimate flexural strength of reinforced concrete walls. It
is known that this equation predicts the ultimate flexural
986

4

Experimental Value (N/mm2)

V

Qmu1

M u1 / h 'M u1

at  V y  0.5aw  V wy  0.5 N  lw

3
Peru_FS
CM1_S
CM1_FS

2

CM1_F

1

CM1: Confined Brick Wall
0
0

1

2

3

4

Calculated Value (N/mm2)

Fig. 6. Evaluation of the maximum strength using the approximate equation for ultimate flexural strength.

strength of walls well even though it is an approximate
equation based on simple assumptions.
Qmu1 = Mu1 /hMu1 = (at · σy + 0.5aw · σwy + 0.5N) · lw .

(3)

Vwhere Mu1 : flexural strength of wall, h : height of theinflection (loading)Vpoint, at : section area of tensile rein-

forcement (mm2 ), σy : yield strength of tensile reinforcement (N/mm2 ), awV: section area of vertical reinforcements in the wall section (mm2 ), σwy : yield strength ofvertical reinforcements in the wall section (N/mm2 ), l:length of wall, lw : wall length ×0.9, and N: axial force(N).
Journal of Disaster W
Research Vol.9 No.6, 2014

V
V

V

Strength and Deformation of Confined Brick Masonry Walls
Subjected to Lateral Forces
0.4

0.4

0.3

0.3

V

Peru

Peru

CM1_FS

0.2

CM1_S

ʏu / Fmʏu / Fm

CM1_S

CM1_FS

0.2

CM1_F

0.1

CM1_F

0.1

0
0

0.05

0.1

0.15

0

0.2

0

0.2

ʍ0 / Fm

0.4

0.6(Pwe*ʍwy) / Fm

Fig. 7. Maximum strength vs axial stress ratio.

Fig. 9. Maximum strength vs lateral reinforcement.
2.5

0.4

Peru

2

Peru
0.3

CM1_S

CM1_S

CM1_FS

CM1_FS
1.5

CM1_F

ʏu

ʏu / Fm

CM1_F

0.2

1

0.1

0.5

0

0
0

0.1

0.2

0

0.3

0.5

1

1.5

2

Qsu1 / Qmu1

(Pte*ʍy) / Fm

2.5

3

W

3.5

W

V

Fig. 10. Maximum strength vs marginVof shear strength.

Fig. 8. Maximum strength vs flexural reinforcement.

V(Qsu1 /Qmu1 : V
shear strength calculated using Eq. (1) / flexural strength calculated using Eq. (3)). The observed
WWstrength normalized by the prism compresmaximum
V
sive strengthτu /Fm increases with an increase in the axV
ial stress ratio σ0 /Fm , the amount of flexural reinforcement Pte σy /Fm , and the amount of lateral reinforcement
Pwe σwy /Fm . It decreases with an increase in the margin ofshear strength Qsu1 /Qmu1 .

Figure 6 shows the relationship between observed
maximum strength and the flexural strength as calculated
by Eq. (3). It has been observed that Eq. (3) well estimates the maximum strengths of flexural (F) or flexuralshear failure (F-S) walls, the behavior of which have been
affected by flexure, while it overestimates the maximum
strength of shear failure (S) walls.

5.2. Regression Equation for the Maximum
StrengthW
A multiple regression analysis was doneW for the observed maximum strength of all test walls (89 walls) considering the previously explained factors that affect it.
The following empirical equations
V V were then derived.
Pwe · σwyV V
σ0
Qsu1 Wτu = 1.57 + 3.23
− 11.52 − 0.31
(4)
Fm
Fm
Qmu1
VV
Pte · σy V Pwe · σwyτu
σ0= 0.0038+0.26
+0.14
+0.89
V
VFm (5)Fm
Fm
Fm

5. Analysis of the Maximum Strength
5.1. Factors Affecting the Maximum Strength
Figures 7 to 10 indicate the relationships between
the observed maximum strength and factors affecting
it, i.e., the axial stress ratio (σ0 /Fm ), the amount of
flexural reinforcement (Pte σy ) normalized by the prism
compressive strength (Fm ), the amount of lateral reinforcement (Pwe σwy ) normalized by the prism compressive strength (Fm ) and the margin of the shear strength,

V

Journal of Disaster Research Vol.9 No.6, 2014

V

W

VV

987

V

V V

W W
V V

Sugano, S. et al.

Experimental value (N/mm2)

2.5

2

1.5
Peru_FS
CM1_S

1

CM1_FS
CM1_F
0.5

Number of specimen 91
Mean Value
1.01
Standard deviation
0.28
Coefficient of variation 0.28

0
0

0.5

1

1.5

Calculated value (N/mm2)2

2.5

Fig. 11. Evaluation of the maximum strength with the proposed regression equation.

error. The correlation coefficient R is 0.70.
In Eq. (5), maximum strength is expressed in terms of
the average shear stress τu normalized by the compressive
strength of masonry prism Fm . The variables in the linear
equation are the amount of lateral reinforcement (Pwe σwy )and the amount of flexural reinforcement (Pte σy ), respectively, normalized by the compressive strength of masonry prism Fm and the axial stress ratio (σ0 /Fm ). The
correlation coefficients to τu /Fm were 0.667, -0.589, and
0.411 for Pte σy /Fm , Pwe σwy /Fm , and σ0 /Fm , respectively.
The strength calculated using Eq. (5) and that determinedthrough tests are compared in Fig. 12. The coefficient ofvariation is 28%, and 75% of the total number of walls arewithin 30% error. The correlation coefficient R is 0.97.
As shown in the figures above, these equations can predict the maximum strength of walls well regardless of
their failure mode.

6. Analysis of Deformation at the Maximum
Strength

0.4

6.1. Distribution of Deformation at the Maximum
Strength R max
Experimental value

0.3

0.2

Peru_FS
CM1_S
CM1_FS
CM1_F

0.1

Number of specimen 91
Mean Value
1.04
Standard deviation
0.29
Coefficient of variation 0.28
0
0

0.1

0.2

Calculated value

0.3

0.4

Fig. 12. Evaluation of the maximum strength using the proposed regression equation.

These equations globally predict the maximum strengthof the walls despite the failure mode. Other empirical equations corresponding to each failure mode are derived, but they will be mentioned on another occasion.
In Eq. (4), the maximum strength is expressed in termsof the average shear stress τu . The variables in the linear equation were the amount of lateral reinforcement(Pwe σwy ) normalized by the compressive strength of masonry prism (Fm ), axial stress ratio (σ0 /Fm ), and the margin of the shear strength (Qsu1 /Qmu1 ). The correlation
coefficients of each factor to τu were 0.301, -0.509, and-0.490 for Pwe σwy /Fm , σ0 /Fm , and Qsu1 /Qmu1 , respectively. The strength calculated using Eq. (4) and that determined through tests are compared in Fig. 11. The coefficient of variation (standard deviation / mean value) is
28%, and 73% of the total number of walls are within 30%
988

Figure 13 shows the distribution of the deformation
at the maximum strength Rmax in terms of the cumulative probability Pc (Pc|R=Ri(%) : Pc = Number of data|R≤Ri/ Total Number). The deformation Rmax in the Japanesedatabase (55 walls) ranges from 0.5 to 20 × 10−3 rad.
while it ranges from 2.5 to 15 × 10−3 rad. in the Peruvian
database (34 walls). However, the distribution curves are
similar, both having an “s” shape.
Figure 14 shows the distribution of the deformation at
the maximum strength Rmax in terms of the probability
density PD (probability density PD : PD|R=Rm (% per unit
drift angle R0 ) is the differential coefficient at R = Rmon the R − Pc curve). The deformation at the maximum
probable density differs in the Japanese and Peruvian
databases. The deformation at the most probable density
is 4 × 10−3 rad. in the Japanese database while is larger,
7 × 10−3 rad., in the Peruvian database.
For reference, the distribution of the deformation at
the maximum strength of reinforced concrete shear walls
is shown in Figs. 15 and 16. These data come from a1968 review by Tomii of 200 reinforced concrete shear
walls [10]. According to Fig. 15 which shows the cumulative probability of the deformation at maximum strength
Rmax , the deformation ranges from 0.5 to 15 × 10−3 rad.
The distribution curve is s-shaped, similar to the curves ofconfined brick walls seen in Fig. 13. The probability density of Rmax is shown in Fig. 16. The deformation at the
maximum probability density, at the peak of the distribution curve, is 4 × 10−3 rad. (drift angle of 1/250). Since
this figure was published, it has become well known thatthe deformation at the maximum strength of reinforced
concrete shear wall is 4 × 10−3 rad. or 1/250. In thestandard for the seismic evaluation of reinforced concretebuildings, it is assumed that the shear failure member fails
Journal of Disaster Research Vol.9 No.6, 2014

Strength and Deformation of Confined Brick Masonry Walls
Subjected to Lateral Forces120䣏䣣䣺䣫䣯䣷䣯䢢
䢢䢢䢢䣕䣶䣴䣧䣰䣩䣶䣪䢢

100
80

PC (%)

Peru n=34

RC Shear Walls

CM1 n=55

60
40

ӌCumulative Probability
Pc|R=Ri(%)
Pc=No. of data|RӌRi / Total No.

20
0
0

5

10

Rmax (10-ϯrad)15

20

Fig. 15. Distribution of Rmax of RC walls (after Tomii [10]).

Fig. 13. Distribution of Rmax of confined brick walls.
Probability Density PD
PD|R=Rm(% per unit drift angle R0) is thedifferential coefficient |R=Rm on R-Pc curve

15

RC Shear Walls

PD (%/10оϯrad )10
Peru n=34
CM1 n=55䣏䣣䣺䣫䣯䣷䣯䢢
䣕䣶䣴䣧䣰䣩䣶䣪䢢䢢

5

Fig. 16. Distribution of Rmax of RC walls (after Tomii [10]).
0
0

5

10

15

20

Rmax (10-ϯrad)Fig. 14. Distribution of Rmax of confined brick masonry walls.

in shear at the deformation 4 × 10−3 rad. or 1/250 [7].
This assumption is based on the distribution of Rmax in
Fig. 16.

6.2. Factors Affecting Deformation at the Maximum Strength R max
The multiple regression analysis indicates that the shear
span ratio (h/l) is the key factor in the deformation at
maximum strength. It shows that deformation increases
as the shear span ratio increases (Fig. 17). The correlation coefficient of Rmax and h/l are 0.214. The effects ofother factors are minor.
6.3. Regression Equations for Deformation at the
Maximum Strength Rmax
The following regression equation for the deformation
at maximum strength Rmax is derived in terms of the shear
span ratio h/l.
Rmax = 0.41 + 5.7h/l(×10−3 rad.) . . . . (6)Journal of Disaster Research Vol.9 No.6, 2014

The comparison between the calculated deformation by
Eq. (6) and the observed deformation of Rmax is shown in
Fig. 18. The coefficient of variation to mean value is 77%,
which is very large, and only 33% of the total number ofwalls are within 30% error. The correlation coefficient R
is 0.43. The range of shear span ratios is from 0.52 to
2.09.
As indicated by these statistical values, the deformation
at maximum strength can be evaluated using the empiricalequation above, but there is a large amount of scatter.

7. Analysis of Deformation at the Ultimate
State R u
7.1. Distribution of Ultimate Deformation R u
The distribution of the ultimate deformation Ru fromboth the Japanese and Peruvian databases is shown interms of the cumulative probability Pc in Fig. 19 and interms of the probability density PD in Fig. 20. The ultimate deformation Ru ranges from 1 to 19 × 10−3 rad. in
the Japanese database and from 2 to 16 × 10−3 rad. in
the Peruvian database. As seen in Fig. 19, the distribution
forms “s” curves, as do those of Rmax in Fig. 13.
989

Sugano, S. et al.

120

20

100
Peru
15

CM1_S

80

CM1_FS

Peru n=34

Rmax

PC (%)

CM1_F
10

CM1 n=54

60
40

5

20
0

0
0

0.5

1

1.5

2

0

2.5

h/l

10

20

30

Ru (10-ϯrad)Fig. 19. Cumulative probability of Pc .

Fig. 17. Deformation at the maximum strength Rmax vsshear span ratio h/l.
1520Peru n=34

PD (%/10оϯrad )Experimental value (x10-ϯ)CM1 n=54

10

15

10

Peru_FS
CM1_S
CM1_FS
CM1_F

5

0

5

10

0

Number of specimen 89
Mean Value
1.00
Standard deviation
0.77
Coefficient of variation 0.77

rad)g. 18 Distribution ofRRu
of-ϯConfined
Brick Wau (1015Fig. 20. Probability density of PD .

0

Calculated value (x10-ϯ)

20

Fig. 18. Evaluation of the displacement at the maximum
strength Rmax using the proposed regression equation.

The deformation at the maximum probability density
is 9 × 10−3 rad., which is 2.3 times the deformation at
the maximum probability density of Ru in the Japanesedatabase and 11 × 10−3 rad., which is 1.6 times the deformation at the maximum probability density of Ru in the
Peruvian database.

7.2. Factors Affecting Ultimate Deformation R u
The relationships between observed ultimate deformation Ru and the factors affecting it are shown in Figs. 21
to 23. The observed ultimate deformation is affected by
the influencing factors as shown below.
It can be seen that the ultimate deformation Ru increases as the flexural reinforcement (Pte σy /Fm ) increases
for shear failure-type walls while it decreases for flexuralor flexural-shear failure-type walls (Fig. 21). It can also
990

5

0

10

20

30

be seen that Ru increases as the margin of shear strength
Qsu1 /Qmu1 increases (Fig. 22). The correlation coefficientof Ru and Pte σy /Fm is 0.187, and that of Ru and Qsu1 /Qmu1
is 0.138. The effect of axial stress ratio σ0 /Fm is not clear(Fig. 23).

7.3. Regression Equation for Ultimate Deformation
Ru
The following linear regression equation for ultimate
deformation Ru is derived in terms of the amount of flexural reinforcement Pte σy /Fm , axial stress ratio σ0 /Fm , andthe margin of shear strength Qsu1 /Qmu .
Ru =7.32 + 30.92

Pteσy
σ0
Qsu1
− 68.3 + 1.47
Fm
Fm
Qmu1
−3
(×10 rad.)(7)

Deformation values calculated using Eq. (6) are shownin Fig. 24. The coefficient of variation to mean value is54%, smaller than that for Rmax , and 40% of the values for
Journal of Disaster Research Vol.9 No.6, 2014

V

V

Strength and Deformation of Confined Brick Masonry Walls
Subjected to Lateral Forces
30

30

CM1_S
20

CM1_FS
CM1_F

Ru

V
V

10

V
V
0.2

0

V0
V

0.1

0.3

Experimental value (x10-ϯ)

Peru

20

Peru_FS

V

10

Fig. 21. Ultimate deformation Ru vs flexural reinforcement.

CM1_FS
CM1_F

Number of specimen 88
Mean Value
0.99
Standard deviation
0.54
Coefficient of variation 0.54
00(Pte*ʍy) / Fm

CM1_S

10

20

Calculated value (x10-ϯ)

30

Fig. 24. Evaluation of the ultimate deformation Ru using the
proposed regression equation.

30
Peru
CM1_S

the total number of walls are within 30% error. The rangeof Pte σy /Fm is from 0.0055 to 0.29, that of σ0 /Fm is from
0.0 to 0.19, and that of Qsu1 /Qmu1 is from 0.44 to 4.57.

CM1_FS
CM1_F

Ru

20

8. Concluding Remarks

10

0
0

0.5

1

1.5

2

2.5

3

3.5

Qsu1 / Qmu1
Fig. 22. Ultimate deformation Ru vs margin of shear strength.

(1) Applicability of existing equations used to estimate
the maximum strength of confined brick masonry walls
The observed maximum strength of confined brick masonry walls was much smaller than the shear strength calculated using the existing equation for the ultimate shear
strength of reinforced concrete shear walls.
The equation for the shear strength of hollow concrete
block walls proposed by the Architectural Institute ofJapan (AIJ) provided the average of the observed maximum strength of confined brick masonry walls, though
the scatter of the evaluation was large.
The approximate equation for the ultimate flexuralstrength of reinforced concrete walls estimated the observed maximum strength of flexural or flexural-shear
failure-type of confined brick masonry walls well, but it
overestimated the maximum strength of the shear failure
type of confined masonry walls.

30

Peru
CM1_S
20

The results of tests on confined brick masonry walls in
the Japanese database (55 walls) and Peruvian database(34 walls) were reviewed as one group of 89 walls interms of failure mode maximum strength, deformation at
maximum strength, and ultimate deformation. Results of
the review can be summarized as follows.

CM1_FS

Ru

CM1_F

10

0
0

0.05

0.1

0.15

0.2

ʍ0 / Fm
Fig. 23. Ultimate deformation Ru vs axial stress.

Journal of Disaster Research Vol.9 No.6, 2014

(2) Deformation of confined brick masonry walls
The deformation at the maximum strength of confinedbrick masonry walls was equal to or larger than that ofreinforced concrete shear walls (4 × 10−3 rad.). The ulti991

Sugano, S. et al.

mate deformation was 1.6 to 2.3 times the deformation at
maximum strength.

Name:
Shunsuke Sugano(3) Multiple regression analysis and empirical equations
to estimate the maximum strength
The obtained empirical equation based on the multiple
regression analysis of the maximum strength estimatedthe maximum strength of any type of failure mode of confined brick masonry walls with good accuracy and little
error.

Affiliation:
Visiting Research Fellow/Lecturer, Building Research Institute

Address:
1-Tatehara, Tsukuba, Ibaraki, Japan(4) Multiple regression analysis and empirical equations
used to estimate deformations
The empirical equations obtained, which were basedon the multiple regression analysis of the deformation at
maximum strength and ultimate deformation, did estimate
the deformations. However, as errors were large, the estimates were inaccurate.

Brief Career:
1971- Joined Takenaka Corporation, Technical Research Laboratory
2000- Professor, Hiroshima University
2009- Visiting Research Fellow/Lecturer, Building Research InstituteSelected Publications:• S. Sugano (Ed.), “Seismic Rehabilitation of Reinforced Concrete
Structures,” International Publication Series 2 (IPS-2), American Concrete
Institute, 2007.
• S. Sugano, “Lessons on Seismic Rehabilitation of Reinforced Concrete
Buildings Learned from Recent Earthquakes,” Proceedings of the
Symposium Honoring Jim Jirsa, American Concrete Institute, 2014.

Academic Societies & Scientific Organizations:Acknowledgements
This study was conducted as a part of the research project “Enhancement of Earthquake and Tsunami Disaster Mitigation Technology in Peru” supported by the Japan International Cooperation
Agency (JICA) and the Japan Science and Technology Agency(JST).

• Architectural Institute of Japan (AIJ)• Japan Concrete Institute (JCI)• American Concrete Institute (ACI)• Earthquake Engineering Research Institute (EERI)• Japan Association for Earthquake Engineering (JAEE)

References:[1] H. Kato, T. Goto, and H. Mizuno, “Cyclic loading test of confined
masonry wall elements for structural design development of apartment houses in the Third World,” Proceedings of the Tenth World
Conference on Earthquake Engineering (10WCEE), Madrid, Spain,
1992.
[2] K. Yoshimura and K. T. Kim, “Experimental Study for Higher Seismic Performance of Confined Brick Masonry Walls,” Journal of
Structural and Construction Engineering, Architectural Institute ofJapan, No.571, pp. 169-176, Sept. 2003 (in Japanese).
[3] K. Yoshimura, K. Kikuchi, M. Kuroki, H. Nonaka, K. T. Kim,
and A. Oshikata, “Experimental Study for Developing Higher Seismic Performance of Brick Masonry Walls,” Proceedings of the 13th
World Conference on Earthquake Engineering (13WCEE), Vancouver, Canada, August 2004.
[4] C. Zavala, P. Gibu, C. Homma, L. Chang, and G. Huaco, “Comportamiento Frente a Cargas Laterales de una Vivienda de Albañileriade Dos Pisos Mediante Ensayo en Linea,” Proceedings of the XIV
Congreso Nacional de Ingenieria Civil – Iquitos, Peru, 2003 (inSpanish).
[5] C. Zavala, C. Homma, P. Gibu, and G. Huaco, “Sesimic Behavior of
Two Stories Masonry Building,” Proceedings of Japan-Peru Workshop on Earthquake Disaster Mitigation, Lima, 2005.
[6] R. Salinas, F. Lázares, “La Alnañilerı́a Tubular y su Uso en Viviendas en Zona Sı́simicas,” Proc. of the Conferncia Internacianal en
Ingenieria Sı́smica, Agost, 2007 (in Spanish).
[7] Japan Building Disaster Prevention Association, “Standard for Seismic Evaluation of Existing Reinforced Concrete Buildings, 2001
and Guidelines for Seismic Retrofit of Existing Reinforced Concrete Buildings, 2001,” English Version, 1st , January, 2005.
[8] Architecrural Institute of Japan, “Ultimate Strength and Deformation Capacity of Buildings in Seismic Design (1990),” October,1990 (in Japanese).
[9] A. Matsumura, “Shear Strength of Reinforced Masonry Walls, Proceedings of the 9th World Conference on Earthquake Engineering,pp. VI-121-126, Tokyo, Kyoto, 1988.
[10] M. Tomii and M. Takeuchi, “The Relations between the Deformed
Angle and the Shearing Force Ratio (0.80 – 1.00) with Regard to
200 Shear Walls,” Transaction of Architectural Institute of Japan,
No.153, November 1968.

992

Journal of Disaster Research Vol.9 No.6, 2014