自然災害科学 J. JSNDS 38 特別号 25 -41（2019 ）Failure process and load-displacement relationship of rectangular
block and interlocking block walls
during in-plane lateral loading
Aiko FURUKAWA1, Johanes Jefry PRASETYO1 and Junji KIYONO1

Failure process and load-displacement relationship ofrectangular block and interlocking block walls during in-plane
lateral loading
Aiko FURUKAWA1, Johanes Jefry PRASETYO1 and Junji KIYONO

1

Abstract
We investigated the effectiveness of using interlocking blocks to reinforce masonry
structures. In-plane lateral loading tests were conducted on block walls constructed with three
types of block shapes: rectangular blocks, I-shaped blocks, and wave-shaped blocks. The
failure process and load-displacement relationships of these three masonry wall types werecompared under three vertical stress levels: 0.2 N/mm2, 0.4 N/mm2, and 0.6 N/mm2. It was
found that the interlocking mechanism had a strengthening effect under a small vertical stress,
and that the effectiveness of the interlocking blocks decreased as the vertical stress increased.
Key words： in-plane lateral loading test, masonry wall, rectangular block, interlocking block, failure process,force-displacement relationship

1. Introduction

collapse of buildings is the primary cause of death
and accounts for 75% of earthquake fatalities over

The collapse of masonry buildings has caused

the last century (OCHA, 2015).

a large number of fatalities during ear thquake
events (Coburn and Spence, 2002). It has been

Masonr y is the most commonly used build-reported that catastrophic earthquakes account foring type in developing countries, owing to its low

60% of worldwide casualties associated with natural

cost and availability as a construction material.

disasters (Giardini et al., 2003). Additionally, theMasonry buildings are intrinsically strong against

1

Department of Urban Management, Graduate School ofEngineering, Kyoto University, Kyoto City, Japan

25

26

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading

vertical loads, but weak against lateral loads such

Sanada et al. (2006) conducted experiments

as earthquakes. To reduce casualties related to

on a masonry wall consisting of conventional rect-

the collapse of masonr y buildings during earth-angular blocks and a wall consisting of I-shaped

quakes, the reinforcement of masonry buildings isinterlocking blocks to compare their performance.

necessary. Considering that unreinforced masonry

The walls were subjected to cyclic lateral loadingbuildings are still used as dwellings, owing to theunder a constant axial loading of 20 kN. It was ob-

low cost of the building materials and labor, it isserved that the strength of the interlocking blocknecessary to develop a new reinforcement method

walls was higher than the strength of conventionalthat is cost-efﬁcient and easy to implement.

block walls. It has also been reported that, in terms

Many studies have investigated a method ofof resisting forces, the performance of interlocking

reinforcing masonry structures. A reinforcement

blocks depends on the ductility of the block mate-method using vertical steel ties (Darbhanzi et al.,rial. Based on experimental results, Sanada et al.

2014), a method using fiber-reinforced plastics(2006) reported that ductile interlocking blocks(Marcari et al., 2007), a method using scrapped

may be effective in improving a vulnerable unrein-tires as tension materials (Turer and Golalm,

forced masonry structure.

2011), and a retrofitting method using PP bands

Our research group has investigated a rein-(polypropylene bands), which are commonly used

forcing method using interlocking blocks. First,

for packing (Sathiparan et al., 2009), have been

Furukawa et al. (2018a) conducted diagonal com-

proposed. The abovementioned reinforcement

pression tests (Fig. 1(b)) on normal masonry walls

methods require reinforcing materials, but are

made of rectangular blocks and on irregular ma-

readily available and easy to implement.

sonry walls made of interlocking blocks, as shown

In this paper, we introduce a reinforcing meth-in Fig. 1(c). Two types of rectangular blocks withod for masonr y structures that does not requiredifferent heights, and two types of interlocking

the use of reinforcement materials. The proposed

blocks with dif ferent shapes were used. Thus,

method utilizes interlocking blocks instead of con-

it was obser ved that the maximum strength ofventional rectangular blocks. The target structures

masonr y walls with interlocking blocks is lower

are newly constructed masonry structures. Special

than the maximum strength of masonry walls withmolds are necessary to make interlocking blocks,

rectangular blocks. However, the effectiveness ofbut once the molds are prepared, interlocking

using interlocking blocks is not evident. Finite-el-blocks can be made using the same materials asement analysis has been conducted to clarify thisthose used for conventional blocks. A masonr ymechanism. Thus, it has been observed that stresswall consisting of rectangular blocks resists lateralconcentration occurs at the interlocking part andloads such as earthquakes by friction force after

causes the failure of the blocks at that part.

mortar failure occurs, as shown on the left-hand

Next, Furukawa et al. (2018b) conducted diag-side of Fig. 1(a). On the other hand, a masonr yonal compression tests on masonry walls made ofwall consisting of interlocking blocks resists lateralinterlocking blocks with various shapes. I-shaped

loads through the resistance exerted by interlock-

blocks with a right angle, I-shaped blocks withing, in addition to friction force, as shown on the

an obtuse angle, hourglass-shaped blocks with aright-hand side of Fig. 1(a). In this manner, we

straight line, and hourglass-shaped blocks with a

expect interlocking blocks to reinforce the wall bywavy shape were compared as shown in Fig. 1(d).

interlocking with the adjacent blocks.

Thus, it was found that masonry walls made with27

自然災害科学 J. JSNDS 38 特別号（2019 ）

(a)

(b)

(c)

(d)
Fig. 1

Diagonal compression tests on interlocking masonry walls carried out in previous
studies: (a) difference in the resistance mechanism against lateral load between
a masonr y wall made with rectangular blocks and a masonr y wall made withinterlocking blocks; (b) diagonal compression test; (c) rectangular block wall andinterlocking block wall test specimens (Furukawa et al., 2018a); (d) test specimens ofinterlocking brick walls with various block shapes (Furukawa et al., 2018b).

hourglass-shaped blocks have higher strength

analysis has been conducted to clarify the underly-

than walls made with I-shaped blocks. Moreover, a

ing mechanism. The analysis results revealed thatmasonry wall made with hourglass-shaped blocks

walls with I-shaped blocks have lower strength,that have a wavy edge has the highest strength

owing to the stress concentration at the interlock-amongst all wall types. Furthermore, ﬁnite-elementing part. Conversely, walls with hourglass-shaped

28

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading

blocks have higher strength, owing to lower stressing test. Fig. 2(a) presents the design document

concentration.

for the masonry walls and the block size. The di-

The results obtained by the abovementioned

mensions of the masonry walls were 24 cm (width)

experiments have revealed that the performance×30 cm (height) ×10 cm (depth). Fig. 2(b) showsof an I-shaped interlocking block wall is inferior

the manufactured blocks. Each wall consisted of 12

to the performance of a rectangular block wall.

blocks. There are various possible ways to arrange

However, the strength of the interlocking blockinterlocking blocks, but we considered the simple

wall increases by using a block shape with lower

arrangement shown in Fig. 2(a)(b).

stress concentration, such as wave-shaped blocks.

The blocks at the top and bottom had two

The experiments conducted previously by ourholes with a diameter of 1 cm, where a steel bar

group (Furukawa et al. 2018a; Furukawa et al.

was inserted and connected with the steel frame.

2018b) employed diagonal compression tests (Fig.

In Fig. 2(a), an area with a height of 3 cm at the1(b)), which apply different conditions to the actu-

top and bottom was inside the steel frame. No steel

al seismic loading condition. However, we did not

frames were attached to either side of the wall incompare the performance between a rectangularorder to understand the resistance due to pure in-block wall and an interlocking block wall with aterlocking between blocks.

lower stress concentration. With this background,

In a previous study (Furukawa et al. 2018a),the objective of this study was to investigate themasonry walls were made from burned bricks, andeffectiveness of using interlocking blocks, instead

plaster was placed between the adjacent bricks.

of rectangular blocks, as a reinforcement measure

However, we observed that the variations in blockfor masonry structures under in-plane lateral load-

strength and the variations in mortar joint strength

ing tests that simulate earthquake loading. Threealso affected the experimental results. Therefore,

block shapes, namely, rectangular blocks, I-shaped

we thought it necessary to avoid the effect of block

blocks, and wave-shaped blocks, were compared.

strength variations and mortar joint strength varia-

To understand the pure effect of the interlocking

tions so as to clarify the pure block shape effect.

mechanism, plaster was not used between the

To avoid block strength variations, we usedblocks. The failure process and load-displacement

mortar blocks. All of the blocks were fabricatedrelationships of the three masonry wall types were

simultaneously and under the same conditions.

compared using the three initial vertical stress

The blocks were made using high-early-strength

levels of 0.2 N/mm2, 0.4 N/mm2, and 0.6 N/mm2,

Portland cement, sand, and water. Speciﬁcally, 25%

which correspond to the stress affecting the wall ofof the material was high-early-strength Portland

the ﬁrst ﬂoor of two-story, four-story, and six-story

cement, 60% was sand, and 15% was water. To avoid

masonry buildings, respectively. In this paper, we

joint strength variations, plaster was not used.

discuss the effect of the block shape on the performance of a masonry wall under lateral loading.

2. 2

Experimental setup

Fig. 2(c) shows the experimental setup. The

2. Lateral loading test
2. 1

Test specimen

wall was installed onto a bottom steel frame, which
was fixed under a loading machine. The wall s

In this study, a rectangular block, I-shaped

bottom part with a height of 3 cm was covered

interlocking block, and wave-shaped interlocking

by the ﬁxed bottom steel frame, and the wall was

block were chosen as the subjects of a lateral load-

fixed to the bottom steel frame using four steel

29

自然災害科学 J. JSNDS 38 特別号（2019 ）

(a)

(b)

(c)
Fig. 2

Test specimen and experimental setup: (a) design document of the test specimen for eachblock shape (unit: cm); (b) pictures of each test specimen; (c) experimental setup.

30

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loadingbars and bolts. The wall s top part with a height

ually until the desired initial vertical stress wasof 3 cm was also covered by a top steel frame, andachieved. Subsequently, the vertical displacement

the wall was ﬁxed to the top steel frame using four

was fixed and maintained constantly throughout

steel bars and bolts. A vertical load was applied to

the lateral loading test.

the top steel frame by a vertical loading machine.

Under a constant vertical displacement condi-

The vertical displacement and vertical load weretion, a gradually increasing lateral load was man-measured by the loading machine. A lateral loadually applied to the specimen using the hydraulic

was applied to the top steel frame using a hydraulicjack. In total, nine tests were conducted for the

jack. A load cell was installed between the hydrau-

three block shape types, with three levels of initial

lic jack and the top steel frame to measure the ap-

vertical stresses.

plied lateral load. Displacement transducers were
2. 4

installed at the opposite side of the hydraulic jackMaterial properties

The material properties are listed in Table 2.

to measure the specimenʼs lateral displacement.
To better understand the specimenʼs defor-

The density was obtained by averaging the density

mation through the entire loading process, theof all test specimens. Apart from density, the otherdigital correlation system VIC-3DTM (Correlatedmaterial properties were determined by averaging

Solutions) was used. VIC-3D is a powerful system

the results obtained by the three element tests us-

for measuring and visualizing both the strain anding cylinder-type test pieces with a diameter of 10

movement of the specimen. The VIC-3D system

cm and a height of 20 cm. The tensile strength wasconsists of two high-speed cameras, and a software

obtained by conducting a splitting test.

program that analyzes the image data. We captured
a picture of the specimen every 0.2 s using the two

3. Experimental results
3. 1

high-speed cameras. Then, we used the software to

Rectangular block wall

（1）Results

compute the strain distribution in the block.

First, we present the load-displacement rela2. 3

Loading conditions

tionship in Fig. 3(a). The straight line represents

Each wall type was tested under three different vertical loading conditions. This vertical

Table 1load represents the structural load exerted by theweight above the wall (such as the roof, for example) on the wall itself. The initial vertical stressvalues and their equivalent conditions are listed inTable 1. These values were determined based on
the literature (Yamaguchi et al., 2014).
First, we applied a vertical load to the wall
specimen by using a displacement-controlled load-

Initial Vertical Stress Equivalent Condition
0.2 N/mm2

The vertical stress to which the firstfloor roof of a two-stor y building issubjected

0.4 N/mm2

The vertical stress to which the firstfloor roof of a four-stor y building issubjected

0.6 N/mm2

The vertical stress to which the firstfloor roof of a six-stor y building issubjected

ing machine. We increased the vertical load gradTable 2

Initial ver tical stresses and theirequivalent conditions.

Material properties.

Density (kg/m3)

Compressive Strength (N/m2)

Young Modulus (N/m2)

Poissonʼs Ratio

Tensile Strength (N/m2)

2.1×103

3.5×107

3.0×109

0.22

3.3×106

31

自然災害科学 J. JSNDS 38 特別号（2019 ）the relationship between the lateral load and thelateral load exceeded the friction limit, the averagelateral displacement, while the dotted line rep-

friction coefﬁcient was determined as 0.438.

resents the relationship between the vertical load

The failure process was approximately theand the lateral displacement. In the cases where

same, regardless of the initial vertical stress. An

the initial vertical stresses were 0.2 N/mm2 andexample is presented in Fig. 4, which shows the

0.6 N/mm2, the lateral and vertical loads gradually

failure process when the initial vertical stress wasdecreased, and then maintained a constant value.

0.6 N/mm2. The top two blocks show the sliding

In the case where the initial vertical stress was 0.4

movement above the second-highest blocks. From

N/mm , both the lateral and ver tical loads de-the lateral-to-vertical load ratio shown in Fig. 3(b)creased suddenly after moving by 6 mm, and thenand the failure process shown in Fig. 4, it can bebecame approximately constant. Even though theseen that the sliding movement caused by friction

lateral and vertical loads were not purely constant

was dominant in the rectangular brick walls.

2and decreased gradually or suddenly, in all cases, theFig. 4 also shows the strain contour in thewall exhibited sliding movement without cracks form-

lateral direction. The strain was obtained using

ing, regardless of the initial vertical stress. Therefore,

the digital correlation system VIC-3DTM (Cor-the lateral strength was considered to be the force

related Solutions). The strain was set to zero whenexerted by friction, and the lateral and vertical loads

the lateral loading started. Therefore, the ﬁguresincreased as the initial vertical stress increased.

show the strain increasing or decreasing relative

The relationship between the lateral-to-verticalto the initial state. The red color indicates the areaload ratio and the lateral displacement is presented

where tensile strain was generated. The purple

in Fig. 3(b). The lateral-to-vertical load ratio wascolor indicates the area where compressive strain

approximately the same in all cases, and approx-

was generated. The green color indicates that theimately constant throughout the lateral loading.

strain was zero or negligible. The top-left block

The average lateral-to-vertical load ratio amongst

was subjected to compressive strain, owing to thethe three cases was calculated as 0.438. Consid-

lateral loading (Fig. 4(a, b, c)). The top-right block

ering that the sliding movement started when thewas subjected to tensile strain (Fig. 4(c)) because(a)Fig. 3(b)

Test results for the rectangular block wall: (a) load-displacement relationship; (b) relationshipbetween the lateral-to-vertical load ratio and lateral displacement.

32

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading(a)Fig. 4(b)(c)

Failure process and strain contour in the lateral direction of the rectangular block wall with an initial
vertical stress of 0.6 N/mm2: (a) lateral displacement of 2 mm; (b) lateral displacement of 6 mm; (c)lateral displacement of 12 mm.

the bottom-right part was separated from the blockcrack formed in the specimen, as shown in Fig. 6.

below.

This caused the sudden decrease in lateral force.
After the maximum strength was reached, the（2）Discussion

block entered a state of total failure. As shown in

The failure process of the rectangular block

Figs. 5(b) and 6, owing to the existence of the in-wall without plaster was the sliding movement

terlocking system, the lateral-to-vertical load ratio

caused by the friction failure. The lateral strengthof the I-shaped brick wall at 0.2 N/mm2 was higher

was inﬂuenced by the friction force. Therefore, thethan that of the rectangular block wall, which waswall with the larger initial vertical stress had theequal to a friction coefﬁcient of 0.438. The higher

highest lateral strength.

lateral-to-vertical load ratio represents the strengthening effect of the I-shaped block, in comparison

3. 2

I-shaped block wallwith the rectangular block wall. During the early（1）Results

stages of lateral loading, the interlocking system of

The load-displacement relationships of thethe I-shaped block provided the wall with substan-

I-shaped block walls are presented in Fig. 5(a).

tial strengthening because the lateral-to-verticalFig. 5(b) presents the relationship between theload ratio was much higher than 0.438. However,lateral-to-ver tical load ratio and the lateral dis-

as cracks began to develop, the strengthening ef-

placement. The failure process and strain contour

fect exerted by the interlocking system decreased

for the three cases are shown in Figs. 6, 7, and 8.

because the lateral-to-vertical ratio gradually de-Note that the gray area is the area where the strain

creased and approached a value of 0.438. The slid-

shown in Figs. 6, 7, and 8 could not be computed.

ing movement seen in Fig. 6 is absent in Fig. 6(a,First, the results for the initial vertical stressb), owing to interlocking amongst the elements. A

of 0.2 N/mm2 were investigated. As shown in Fig.

large strain was observed at the interlocking parts,

5(a), at an initial vertical stress of 0.2 N/mm , thewhich means that strain concentration occurred at

maximum lateral strength of 15.3 kN occurred at

the interlocking parts. Therefore, it is considereda lateral displacement of 21 mm. Before the max-that the I-shaped block breaks more easily, owing

imum lateral strength was observed, many otherto the strain concentration at the interlocking

peak loads were obser ved. At each peak load, aparts. The interlocking mechanism increased the2

33

自然災害科学 J. JSNDS 38 特別号（2019 ）

(b)

(a)
Fig. 5

Test results for the I-shaped block wall: (a) load-displacement relationship; (b) relationship between
the lateral-to-vertical load ratio and lateral displacement.

(a)Fig. 6(c)

Failure process and strain contour in the lateral direction of the I-shaped block wall with an initial
vertical stress of 0.2 N/mm2: (a) lateral displacement of 10 mm; (b) lateral displacement of 21 mm; (c)lateral displacement of 34 mm.

(a)Fig. 7

(b)

(b)

(c)

Failure process and strain contour in the lateral direction of the I-shaped block wall with an initial
vertical stress of 0.4 N/mm2: (a) lateral displacement of 8 mm; (b) lateral displacement of 12 mm; (c)lateral displacement of 30 mm.

34

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading(a)Fig. 8(b)(c)

Failure process and strain contour in the lateral direction of the I-shaped block wall with an initial
vertical stress of 0.6 N/mm2: (a) lateral displacement of 8 mm; (b) lateral displacement of 12 mm; (c)lateral displacement of 36 mm.

lateral-to-vertical load ratio when the strain inside

ing mechanism stopped, owing to the failure of thethe brick was smaller than the yield strain. How-

interlocking blocks. Additionally, the sliding move-

ever, cracks appeared at the interlocking par ts

ment of the wall began as shown in Fig. 7(c). As

when the strain exceeded the yield strain as thecan be seen in Fig. 5(b), the lateral-to-vertical loadlateral displacement increased. Finally, after theratio was larger than the friction coefﬁcient of 0.438

maximum strength was reached, the interlocking

before 12 mm. However, it was approximately themechanism stopped and sliding behavior was ob-

same as the friction coefﬁcient after 12 mm. Basedserved as shown in Fig. 6(c). We thought that theon these observations, we determined that the in-lateral-to-vertical load ratio reached 0.438 because

terlocking block walls underwent a strengthening

only the friction force resisted the lateral load after

effect before the maximum lateral load. However,the peak load. Moreover, we obser ved that thethe interlocking mechanism stopped when theI-shaped interlocking blocks had the advantage ofblockʼs interlocking part broke, and the value ofhigher lateral strength at the initial vertical stressthe lateral-to-vertical load ratio approached the val-of 0.2 N/mm . However, this was accompanied byue of the friction coefﬁcient.

2

brick failure and brittle behavior was observed.

Finally, the results for the initial vertical stress

Next, the results for the initial vertical stressof 0.6 N/mm2 were investigated. As shown in Fig.

of 0.4 N/mm were investigated. As shown in Fig.

5(a, b), a maximum lateral strength of 18.7 kN

5(a, b), a maximum lateral strength of 18.3 kN was

was obtained at a lateral displacement of 8 mm. As

obtained at a lateral displacement of 8 mm. At theshown in Fig. 7(a, b), the interlocking mechanism

2

initial vertical stress of 0.4 N/mm , the maximum

worked and increased the lateral resistance before

lateral strength was observed at a smaller lateral

12 mm. However, after 12 mm, the interlocking

displacement, in comparison with the case whereinmechanism stopped, owing to brick failure. Sub-the initial vertical stress was 0.2 N/mm2. At a dis-sequently, collapsing behavior, rather than sliding

placement of approximately 12 mm, the lateral load

behavior, was observed as shown in Fig. 7(c). In

suddenly decreased. Before 12 mm, the interlock-Fig. 5(c), the lateral-to-vertical load ratio for 0.6

ing mechanism worked as shown in Fig. 7(a, b),

N/mm2 was lower than the friction coefficient of

wherein strain concentration can be obser ved at

0.438 after 12 mm.

2the interlocking parts. After 12 mm, the interlock-35

自然災害科学 J. JSNDS 38 特別号（2019 ）

(b)

(a)
Fig. 9Test results for the wave-shaped block wall: (a) load-displacement relationship; (b) relationshipbetween the lateral-to-vertical load ratio and lateral displacement.

（2）Discussion

cal stress.

The failure process of the I-shaped block wallwithout plaster can be divided into two stages.

3. 3

Wave-shaped block wall

Before the maximum lateral load, the interlocking（1）Results

mechanism was in effect and the blocks resisted

First, we present the load-displacement rela-

the lateral load by interlocking with each other.

tionship in Fig. 9(a). Before the maximum lateral

Additionally, the lateral strength increased inload was reached, several smaller peak loads werecomparison with the rectangular block wall. The

obser ved. At each peak load, cracks formed andinterlocking block suffered strain concentration atcaused the sudden decrease in the lateral load. Af-

the interlocking parts, and block failure occurred

ter the maximum lateral strength was reached, theat the interlocking parts when the strain exceeded

wall lost the interlocking mechanism, total failure

the yield strain. After the maximum lateral load

occurred, and the lateral load suddenly decreased.

was reached, the interlocking part broke, the inter-

The lateral-to-vertical load ratio is presented

locking mechanism stopped working, and sliding

in Fig. 9(b). When the initial vertical stress was

movement or collapsing behavior was obser ved,

0.2 N/mm 2, the lateral-to-ver tical load ratio for

depending on the vertical stress. The wall withthe wave-shaped block wall was higher than thata larger initial vertical stress had higher lateralof the friction coef ficient with a value of 0.438.

strength, but exhibited more brittle behavior.

This suggests that the interlocking mechanism in-

By comparing the lateral-to-vertical load ra-

creased the lateral strength. However, as the initial

tios of the rectangular block wall with those of thevertical stress increased, the effect of increasing

I-shaped block wall, it was found that the I-shaped

the lateral-to-vertical load ratio decreased. The lat-

block wall had a higher lateral-to-vertical load ra-eral-to-vertical load ratio was approximately 0.438

tio for a smaller initial vertical stress, and a lower

when the initial vertical stress was 0.6 N/mm2.

lateral-to-vertical load ratio for a larger initial ver-Finally, the failure process and strain contour

tical stress. The effectiveness of using an I-shapedin the horizontal direction for the three cases areblock wall was found to be dependent on the verti-

shown in Figs. 10, 11, and 12. Even though the36

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading

(a)

(b)

(c)

Fig. 10 Failure process and strain contour in the lateral direction of the wave-shaped block wall with an initial
vertical stress of 0.2 N/mm2: (a) lateral displacement of 30 mm; (b) lateral displacement of 35 mm; (c)lateral displacement of 40 mm.

(a)

(b)

(c)

Fig. 11 Failure process and strain contour in the lateral direction of the wave-shaped block wall with an initial
vertical stress of 0.4 N/mm2: (a) lateral displacement of 18 mm; (b) lateral displacement of 33 mm; (c)lateral displacement of 36 mm.

(a)

(b)

(c)

Fig. 12 Failure process and strain contour in the lateral direction of the wave-shaped block wall with an initial
vertical stress of 0.6 N/mm2: (a) lateral displacement of 27 mm; (b) lateral displacement of 30 mm; (c)lateral displacement of 40 mm.

37

自然災害科学 J. JSNDS 38 特別号（2019 ）cracked area and crack order are different for thethe vertical stress.

three cases with different initial vertical stress, theconstricted portions of the blocks were cracked.

3. 4

Comparison of block shape effectFigs. 10(a), 11(a), and 12(a) depict the failure situ-

Fig. 13 shows the effect of the block shapeation at the peak load before the maximum lateralon the load-displacement relationship and thestrength, where a large strain at the constricted

lateral-to-vertical load ratio. Table 3 presents a

portion of the blocks can be obser ved. Because

comparison of the maximum lateral strength withof the interlocking between the elements, strain

lateral displacement, where the maximum lateralconcentration occurred at the constricted por-strength was observed. The lateral displacement istions. When a crack occurred at these constricted

not shown for the rectangular block wall.

portions, the lateral load exhibited sudden drops.

Moreover, it was found that the rectangular

Then, the lateral load increased again, while theblock wall exhibited sliding movement under theinterlocking mechanism remained active. Figs.

resistance of friction force. Additionally, the later-

10(b), 11(b), and 12(b) depict the failure situation

al load and the lateral-to-vertical load ratio wereat the maximum lateral strength, when the lastapproximately constant throughout the lateral

constricted portion cracked and the interlocking

loading. However, the I-shaped block wall andmechanism was lost. After the wall lost the inter-

the wave-shaped block wall had several peaks inlocking mechanism, the lateral load decreased

their load-displacement relationships. These peaks

drastically and the movement of the wall proceed-corresponded to the failure of the block at the in-ed as shown in Figs. 10(c), 11(c), and 12(c).

terlocking parts. In comparison with the I-shaped
block wall, the wave-shaped block wall had a slight-（2）Discussion

ly smaller maximum load; however, that maximum

The failure process of the wave-shaped blockload was observed at a larger displacement. The

wall without plaster can be divided into two stages,

wave-shaped block wall had a larger lateral load atin the same manner as the I-shaped block wall.

a larger lateral displacement, in comparison with

Before the maximum lateral load, the interlocking

the I-shaped block wall.

mechanism was in effect and the blocks resisted

When we compared the lateral-to-ver ticalthe lateral load by interlocking with each other.

load ratios, we found that the rectangular block

Additionally, the lateral strength increased in com-wall had the lowest such ratio at the initial verticalparison with the rectangular block wall. The inter-strength of 0.2 N/mm2. However, the same value

locking block suffered strain concentration at thewas generally the lowest for the I-shaped block

constricted parts, and block failure occurred at thewall at the initial vertical strength of 0.6 N/mm2.

constricted parts. The lateral load decreased when

The lateral-to-vertical load ratio of the rectangular

block failure occurred; however, the lateral load in-block wall was approximately constant, regardlesscreased and the interlocking mechanism remainedof the initial vertical stress, because the resisting

active. After the interlocking mechanism was lost,force was the friction force. Conversely, the later-

the increase in lateral displacement became easier.

al-to-vertical load ratio of the I-shaped block wall

The wall with a larger initial vertical stress had adecreased as the initial vertical stress increased,

higher lateral strength, but lower lateral-to-verti-

because the strain concentration at the interlock-cal load ratios. The effectiveness of using a wave-

ing parts was increased by the vertical stress. An

shaped block wall was found to be dependent on

I-shaped block wall can easily suffer from strain

38

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 13 Test results for different block shapes with the same initial vertical stress: (a) load-displacement
relationship (0.2 N/mm2); (b) relationship between the lateral-to-vertical load ratio and lateraldisplacement (0.2 N/mm2); (c) load-displacement relationship (0.4 N/mm2); (d) relationshipbetween the lateral-to-ver tical load ratio and lateral displacement (0.4 N/mm 2); (e) loaddisplacement relationship (0.6 N/mm2); (f) relationship between the lateral-to-vertical load ratio
and lateral displacement (0.6 N/mm2).

39

自然災害科学 J. JSNDS 38 特別号（2019 ）Table 3 Maximum lateral strength (lateral displacement where maximum lateralstrength occurred for the I-shaped and wave-shaped block walls).
Initial vertical stress

Rectangular block wall

I-shaped block wall

Wave-shaped block wall

0.2 N/mm2

2 kN

15.3 kN (21 mm)

12.4 kN (29 mm)

0.4 N/mm2

4 kN

18.3 kN (8 mm)

17.3 kN (32 mm)

0.6 N/mm2

7 kN

18.7 kN (8 mm)

18.4 kN (28 mm)

concentration, and cracks may occur under larger

lateral displacement, owing to its smooth shape.

vertical stress. The wave-shaped block wall had theThis study could reveal the effectiveness of using

highest lateral-to-vertical load ratio amongst theinterlocking blocks under different vertical stressthree block shapes, regardless of the initial verti-

conditions owing to the in-plane loading tests,

cal stress. Similar to the I-shaped block wall, thewhich was impossible in previous studies using

wave-shaped block wall also suffered from strain

diagonal compression tests.

concentration at the constricted portions. However,the strain concentration was smaller, owing to this

4. Conclusions
In this study, a lateral loading test was con-wallʼs smooth shape at the interface.
Let us compare the strain contour in the lat-

ducted for mortarless masonr y walls, namely aeral direction at the maximum lateral load for therectangular block wall, I-shaped block wall, andI-shaped block wall (Figs. 8(b), 9(b), and 10(b))

wave-shaped block wall, under three levels of initial

and the wave-shaped block wall (Figs. 12(b),vertical stress.

13(b), and 14(b)), when the initial vertical stresses

The rectangular block wall exhibited sliding

were 0.2 N/mm , 0.4 N/mm , and 0.6 N/mm , re-movement at the location where the friction force

spectively. Although it is difﬁcult to read the values

resisted the lateral loading. Therefore, the lateralfrom the figures, the maximum values (tensile

load and lateral-to-vertical load ratio were approx-

strain) for the I-shaped block wall were 3.94×10−2,

imately constant throughout the loading without

2.54×10 , and 2.24×10 , while those for thecracks appearing, regardless of the initial verticalwave-shaped block wall were 9.45×10−3, 1.13×

stress. The rectangular wall with a larger initial

10 , and 1.33×10 . Based on this tensile strain

vertical stress had a higher lateral strength. Con-

comparison, the wave-shaped block was effective

versely, the load-displacement relationships forin reducing the strain concentration, owing to its

the I-shaped block wall and the wave-shaped block

smooth shape at the interface.

wall had several peaks. Because of the interlocking

2

2

−2

−2

2

−2

−2

From the comparison, it was determined thatmechanism, strain concentration occurred at thethe interlocking block walls were effective relativeinterlocking part, where cracking occurs more eas-

to the rectangular block walls for a small initial ver-ily in comparison with other parts. Moreover, whentical stress, because the friction force was small.

a block cracks, the lateral load decreases.

However, as the initial vertical stress increased, theThe lateral load increased again while theeffectiveness of the interlocking blocks decreased,interlocking mechanism was in effect. Total fail-particularly for the I-shaped block wall. The wave-

ure occurred after the interlocking mechanism

shaped block wall had an advantage in comparison

was lost. Under a small initial vertical load, whichwith the I-shaped block wall, because the wave-

implies a small friction force, the I-shaped block

shaped block wall had larger lateral resistance andand wave-shaped block walls exhibited a higher

a higher lateral-to-vertical load ratio at a larger

lateral-to-ver tical load ratio in comparison with

40

Failure process and load-displacement relationship of rectangular block and interlocking block walls during in-plane lateral loading

the rectangular block wall. However, as the initial

References

vertical stress increased, the increasing effect of

Coburn, A., Spence, R. Earthquake protection, 2ndedition. Chichester: John Wiley and Sons, 2002.
Corelated Solutions. The VIC3D System. http://
correlatedsolutions.com/vic-3d/. [Accessed June20, 2018]
Darbhanzi, A., Marefat, M. S., Khanmohammadi, M.
Investigation of in-plane seismic retroﬁt of unreinforced masonry walls by means of vertical steel
ties. Construction and Building Materials, Vol. 52,
pp. 122-129, 2014.
Furukawa, A., Kimura, S., Kiyono, J. Study on failure
mechanism and strength increment ef fect ofmasonry walls made of interlocking bricks. Journal of Japan Society of Civil Engineers, Ser. A1(Structural Engineering & Earthquake Engineering (SE/EE)), Vol. 74, Issue 4, pp. I_699-I_711,
2018a. https://doi.org/10.2208/jscejseee.74.
I_699.
Furukawa, A., Masuda, K., Daru, G.T.S., Kiyono, J.
Shape effect of interlocking blocks on force-displacement relationship and failure behavior ofmasonry wall. Journal of Structural Engineering,Vol. 64A, pp. 241-249, 2018b.
Giardini, D., Gruenthai, G., Shedlock, K., Zhang, P.
The GSHAP global seismic hazard map, in: W.
HK. Lee, H. Kanamori, P.C. Jennings, C. Kisslinger (Eds.). International Handbook of Earthquake
and Engineering Seismology, Vol. 81B, London,
U.K.: Academic Press, pp. 1233-1239, 2003.
Marcari, G., Manfredi, G., Prota, A., Pecce, M. Inplane shear per formance of masonr y panels
strengthened with FRP. Composites: Part B, Vol.
38, pp. 887-901, 2007.
Navaratnarajah S., Kotaro S., Kimiro M. Experimental
study of PP-band retrofitted masonr y structure
made of shapeless stone. SEISAN-KENKYU, Vol.
61, Issue 6, pp. 1051-1054, 2009.
OCHA (Ofﬁce for the Coordination of Humanitarian
Af fairs). http://www.unocha.org/, 2015. [Accessed June 20, 2018]
Sanada, Y., Nakamura, Y., Yamauchi, N., Akano, Y.
Seismic per formance of masonr y walls using
interlocking units. Proceedings of the First European Conference on Earthquake Engineering andSeismology, Paper No. 508, 2006.
Turer, A., Golalm, M. Scrap tire as low-cost post

the lateral-to-vertical load ratio decreased, particularly for the I-shaped block wall. The wave-shaped
block wall had the maximum lateral strength at thelonger lateral displacement, in comparison with
the I-shaped block wall, because the strain concentration was smaller as a result of the smooth shapeat the interface. The comparison results revealed
that the wave-shaped block wall had better performance in terms of higher strength and larger
displacement. Additionally, the interlocking block
walls were not effective under a larger initial vertical stress.
In future work, we will consider the effect ofplaster between the blocks, and investigate theeffective shape of interlocking blocks with higher
strength and better ductility. It is possible thatthe advantage of the wave-shaped block wall withlower stress concentration is reduced if there isplaster between blocks. Therefore, we would liketo investigate the most advantageous block shapewith the existence of plaster.
Moreover, this study only focused on the inplane collapse behavior of the masonr y walls.
We would like to investigate the effectiveness ofinterlocking block walls regarding the out-of-plane
collapse behavior and three-dimensional collapse
behavior in our future study.

Acknowledgements
We would like to thank Professor Shiotani,
Professor Nishida, Professor Asaue, and Professor
Hashimoto from Kyoto University for letting us use
the digital correlation systems and for providing
valuable assistance during the experiment. This
study was supported in part by the Japan Society
for the Promotion of Science (JSPS) grant-in-aid(15K06178,18K04323), whose support is greatly
appreciated.

41

自然災害科学 J. JSNDS 38 特別号（2019 ）tensioning material for masonry strengthening.
Materials and Structures, Vol. 41, pp. 1345-1361,
2011.
Yamaguchi, K., Amiraslanzadeh, R., Ikemoto, T., Fukada, S., Miyajima, M., Murata, A. The static loading test on earthquake effect of reinforcing the要

block wall model. Journal of Disaster Mitigationfor Historical Cities, Vol. 8, pp. 243-248, 2014.
（投 稿 受 理：2019年 3 月 1 日
訂正稿受理：2019年 7 月 3 日）

旨

組積造壁の面内水平載荷試験により，インターロッキングブロックを用いた組積造の補強効
果について検証を行った。一般的な直方体のブロックと，I 型の形状をしたインターロッキン
グブロック，波型の形状をしたインターロッキングブロックの 3 種類のブロックから構成される 3 種類の組積造壁を試験対象とした。 2 階建， 4 階建， 6 階建の組積造建物の 1 階の壁が支える上載荷重を想定し， 3 通りの鉛直応力に対して試験を行った。試験の結果，上載荷重が小さい場合にインターロッキング組積造壁は直方ブロック組積造壁よりも強度が高いことが明らかとなった。上載荷重が増えるにつれて，摩擦力が増加し，直方ブロック組積造壁の強度が相対的に上昇するため，インターロッキング組積造壁の効果が減少することがわかった。