Journal of Applied Mechanics Vol.11, pp.615-623
Effectiveness
of wooden
(August 2008)
bond
H. PARAJULI*,
beams
JSCE
in dry stone
J. KIYONO**,
masonry
houses
Y. ONO***
* Ph. D. student,Dept of Urban Management,Kyoto University,Japan (Nishikyouku, Katsura,Kyoto,615-8540)
** AssociateProfessor, Dept.of Urban Management,Kyoto University,Japan (Nishikyouku, Katsura,Kyoto,615-8540)
*** AssistantProfessor
, Dept.of Urban Management,Kyoto University,Japan (Nishikyouku, Katsura,Kyoto,615-8540)
Stone masonry houses are the most common type of constructionin the Alpine Himalayan Belt across Pakistan, India and
Nepal.However,the seismicresistanceof these houses is highlyquestionableif constructedwithout any form of lateralsupport
In this paper,the effectivenessof wooden bond beams as a retrofitsolutionhas been examined.Dry stone masonryhouses have
been modeledby finiteelement methodconsideringstonesas linearsolid and interfacesasjoint elements.Thejoints are allowed
to open and slide satisfyingthe Mohr-Coulombcriteria.To calibratethe values used in the numericalmodelingan experiment
using a small scale wall made of wooden blocks was shaken in small custommade table.The correspondingparameterswhich
showed good agreement with experimentalresultswere taken as inputs for the non linear dynamicanalyses of various model
houses.The results showedthat wooden bond beams can be an effectivetechniquefor upgradinglow strengthmasonryhomes
in low seismicityregions
Key Words:Masonry,bond beam,joint element,dynamicanalysis
1.Introduction
If built correctly,they perform well under vertical loads. However,
due to distinctdirectionalpropertiesof stonewith its irregularshapes,
Stone has long been used as a building material for the
it is difficultto make stone walls strong against lateral loads. Lateral
construction of houses due to its availabilityand durability in the
Alpine Himalalyan Belt (Pakistan, India, Nepal etc.)
Large
strength depends upon friction between the stones and a very low
cohesive strength of mortar if it is med. Thus, these homes have
settlementsof stone masonrybuildingsconstructedwith limeor earth
sustainedheavy damages in historicearthquakesand have been the
mortar and even without mortar can be found in the area. Stone
walls are built by stackingstonesover stonesnormally in two leaves.
primarycause of fatalities.Usually,dry walls consistof two leavesof
stoneswith totalwidth of approximately45 cm. The leaves havevery
Verticaljoints are avoided as far as possible by placing various sized
weak bonding and interconnectivityand can become unstableeven in
minor earthquakes. One possible methods of upgrading the wall
could be to cncouragcthe use of wooden elementsas used Hatil1)in
stones alternately.Corner stones are chisel dressed and mid span
stones are hammer dressed. In cases where long stones are not
availableto breakthe verticaljoints,wooden pieces are used.Roofing
material may vary depending on location and can be corrugated
galvanizediron sheet,slate or thick rammed earth laid over wooden
Turkey and Bhatar2)in Pakistan.Spenceand Coburn') foundwooden
elements to be effective in mitigating against failure in their
experimental investigations.Cao and Watanabe') analyzed brick
joists and battons. One type of the dry stone masonryconstructions
using wood as bond beam called Hatill)in Turkey and Bhatar2)in
Pakistan (Fig.1) consists of single storey random rubble masonry
masonry buildings by finite element methods consideringbricks as
with horizontalwood beams at specific intervals.Similar city stone
masonry houses fairly chisel dressed but without bond beams, are
before and after retrofittingby timber frame and they were found to
solid elements and mortars as viscoelasticjoint elements providing
opening and sliding phenomenon. The buildings were analyzed
be an effectiveway of preventingfailure.
found in westernNepal also.Houses are generallyone to two storeys
and may have multiple rooms added at different stages of their
history. Storey height is typically2m and houses have small doors
Wood bond beams have been found to be effective in resisting
earthquake induced forces,hence these are known as seismic bands.
and windows and can therefore be dark inside even in day time.
People me firewood to cook their meals, and stone built homes are
have yet to be investigated.There have only been a few studies
highly fire resistantand durable against environmentaldegradation.
Locally trained masons can build these houses easily and materials
are locallyavailable makingthese types of constructioneconomical.
―615―
However,the extents to whichthey contributeto preventingfailures
testing with small dry walls examining these constructions4,5).
Here,
an attempt has been made to evaluate the performances of these
homes in earthquakes.Two typical types of homes (one and two
rooms) with and without applied wooden bond beams are modeled
the laminar nature of a materialwhich is confinedby a narrow zone
consideringstones as elasticelementsand interfacesbetween stones
such as an old fault surfaceor joint in rocks. An isoparametricjoint
as inelasticjoint elements. Subsequently,three dimensionaldynamic
analyses were carded out by applying various seismic accelerations
elementin two and threedimensionwas introduced9)to representthe
interfacebetweenshell and solidelements.The stiffnessmatrix of the
obtained from past earthquakesand the results are discussed in the
joint element was formulated considering interface as separate
isoparametricelementwith zero thickness.The non linearbehaviours
concludingpart of this paper.
of joints were characterizedby slip and separationtaking place at the
joint plane. Separation of joints was considered when it became
tensile.Recently,this concept has also been used in modeling bric
masonryt10)-12)
simulatetime dependentslidingand separationalong
mortar joints. Three dimensional finite element models were
formulatedby consideringthe relativedisplacementsbetweenthe top
and the bottom of base elements and the constitutiverelationship,
based on material properties containingshear and normal stiffness
which can be found from stressdisplacementcurves of the mortar. A
Fig.1 Contemporary
Bhatar construction,
brick masonrywall was analyzedin staticand dynamicloadings and
Tarand-NWFP-Pakistan2)
was foundto be capableof predictingappropriateresponses12).
2. Numerical
Modeling
There have also been experimental investigationsdone in dry
Even small masonryhouses are made of thousands of pieces of
stones and have joints at least three times that number. Thesejoints
are weak and are foundto deformfirst under any kind of loadingand
govern the overall behaviour and failure mechanism of these
structures. A large numbers of factors such as interior voids,
irregularshapedunits,varying propertiesof stoneto stone, qualityof
workmanshipcontributeto making the behaviourof these walls very
complex. Computational approaches to investigatethe strength of
joint cut sawn stone masonry walls subjected to in plane and
combined loadings) and similarsmall walls have been investigated
analyticallyin monotonic and reversed cyclic loadings5)considering
multi-surfaceinterfacemodel13).
From the literaturereview,we found
that most researchershave followedthe idea of modelingthe units as
solid elementsand interfacesas zero thicknessjoint elements.Thus,
the same approach consideringstones as solid elements and their
interfacesas joint elementshas been employedhere.
masonry have been conductedby various methods, ranging from
simplified methods to highly sophisticated method which uses
interfaceor joint elementto define the possible failure3,6-13).
Analyses
using distinctelement method (DEM) which is also consideredas a
simplified micro method, model the wall as an assembly of small
blocks and interfaces.The contact forces and displacementsat the
interfaces of stressed assembly of blocks are found through
evaluation of equations obtained from Newton's law of motion
which defines the movement of the blocks. There have been two
recent pieces of work using DEM in examining the behavior of
buildings: Papantonopoulos et al.6)investigated the efficiency of
DEM to predict earthquake response .of classical monuments by
comparing the numericalresults with experimentaldata. Alexandris
et al.7)investigated collapse mechanisms of non-engineeredstone
masonry houses subjected to severe earthquake excitations using
distinctelement method. Two and three dimensionalanalysesof two
types of buildings were studied. They concluded that two
dimensionalanalyseswere unableto simulaterealisticresponses.The
Fig.2 Formulationof solid andjoint elements
out of plane failure of the long wall was found to be the dominant
mode of the failuremechanismin stonemasonry.
Generally,stone walls consistof a large numbersof irregularsize
stones, and modeling each individualstone and their interfacesin
On the other hand, various investigators have utilized finite
element method (FEM) which uses elastic and inelasticinterfaces
their as-built condition would be impossible. Thus a simplified
numericalmodel has been developedmaking an equivalentgroupof
between units called discontinuitiesas having propertiesof sliding
eight node elastic solid elements for stones and eight node joint
and separations8-13).
Zienkiewiczet al.8)proposeda joint element for
elementsfor their interfacesas shown in Fig. 2. In the Fig., x, y and z
•\ 616•\
are global
of this
axes
and Ā, ā and Ā are local
dynamic
analysis
is to solve
axes.
the
The ultimate
widely
known
modulusof elasticityof stoneand has been used in this study.
objective
equation
of
In order to get the damping matrix (equation6), the mass and
motion:
stiffnessproportionalto Rayleighdamping hasbeen used.
(1)
(6)
where, [M], [C], [K], are mass, damping and stiffness matrices,{u}
where, a and 33are coefficientsselectedto control the damping ratios
,{u} and {u},are acceleration, velocity and displacement
responsesrespectivelyand {ug} is input ground acceleration.
of the lowest and highestmodes expectedto contributesignificantly
to the response.
The stiffness matrix for the system is obtained by assembling
Unfortunately,there is a sever lack of data availableon damping
individualsolid and joint element matrices.The formulationof the
stiffnessmatrix for solid elements is referencedin Chandrapatlaand
parameters in linear solid mechanics problems, and even less
informationis availableon damping in non linear dynamic analysis.
Belgundu14).The displacement of joint elements depends on the
Tzamtzis and Asteris12)did dynamic analysisof brick masonry wall
relativemovementsof the top and bottomsolid elements(Fig.2), and
the correspondingstiffnessmatrix for zero thicknessjoint elements
by using quite high damping coefficients and found that the
numerical simulation was matching with experimentalresults. At
can be formulated8)-10)
as shown in equation2.
multiple modes of vibrations, damping ratios change with natural
frequencies because
(2)
of different mass participation factors at
different modes11).For the problem under consideration the
coefficients a and 13 have been taken as 0.0555 and 0.0105
respectivelyso as to maintaininitialvalue of damping 11)16) 6%
and
maximum value 10% consideringdry masonry constructionsare
(3)
highly deformable.
3. Constitutive Relationship
where,
ksx
direction,
material
and
ksy
ksn
shear
stiffness
property
matrix
Jacobian
Normal
and
and
series
of two
other
representing
matrices,
shear
vertical
are
components
along
[k]
and Ā
stiffness
springs,
the joint
y
direction
of joint,
and ā
are
(shear
[N]
are
one
which
and
and
local
calculated
normal
[J]
are
along
x
stiffness)
shape
of
by
to the
regarding
the
stone
following
The joint is characterizedas fully elastic, perfectly plastic and
incapable of taking any tensile forces. The idealized constitutive
function,
relationshipshown in Fig. 3 has been used to denotethe sliding and
coordinates.
representing
leads
stiffness
the
wall
unit
as a
and
the
formule.
openingof joint. Separationoccurswhen the normal strain is greater
than zero and since the joint cannot take any tensile stress and both
act in the normal direction,the shearstiffnesshas also been set to zero.
Contact occurs when normal strain is less than zero, and normal
forces are assumed to be restored corresponding to the normal
(4)
stiffnessof thejoint. Slidingoccurs when the shear at joints exceeds
the value givenby the Mohr-Coulombyieldcriterion(equation7).
(5)
where Is, is normal stiffnessof joint, ksis shear stiffnessof joint, h is
height of unit (averageheight of stoneunit),Ewall
is Young's modulus
of elasticityof wall, Eunft
is Young's modulus of elasticityof unit and
is taken equal to 15,500N/mm2,and u is Poisson's ratio (assumed
equal to 0.2).
The modulus of elasticityis dependenton many factors such as
type of stone,workmanship,void insidethe wall etc. A wide range of
values have been proposed in literature15)
varying from 200-1000
N/mm2.In situ tests were carriedout in Faial Island, Azores166,
and
the modulus of elasticityof random rubble stone masonrywall was
found to be 200N/mm2. This value corresponds to 13% of the
―617―
elementswas made.
Using the above mentionedparameters and an accelerationtime
history (Fig. 5) obtained from a previous shaking test, a dynamic
analysis was carried out. The displacements obtained from the
experiment (Fig.6) and numericalsimulations(Fig. 7) were plotted.
A comparisonof displacementsmeasured alongheight of the model
wall has been plotted as shown in Fig. 8. Due to the inconsistent
friction between elements and possibly human error, this is
consideredinevitable.However, the average displacementsobtained
in the experimentof the two edges are in good agreementwith the
numerical result. The numerical simulation gives 3.4 cm
displacementat the top and the average (left edge and right edge)
displacementof the experimentalwall was also 3.5 cm.
Fig. 3 Constitutiverelationshipsforjoints in normal (top) and shear
(bottom)
(7)
where,
Ty is yield
mortar
less
shear
joint),
an
stress,
is
c is cohesion
normal
stress
(equal
and
tan
to zero
being
is coefficient
of
fiction.
4. Calibration
Stiffness
of brick
Fig. 4 Wood block wall (0.40mx0.08mx0.26m)
of parameters
parameters
masonry,
thicknesses,
represent
the strength
it is calculated
mortar
thickness
from
and the modulus
In the case of dry stone
masonry
there
stones,
stiffness
of
therefore
depending
small
the
upon
the way
experiment
Wooden
were
(0.40mx0.08mx0.26m)
was
shook
final
and
KN/m3)
assuming
the
structure
as
0.3.
were
modulus
masonry
highly
(a=0.0555, ƒÀ=0.0105)
fiction
was
simply
raising
the base
was
noted
ultimate
been
and
goal
taken
Purpose
measured
gradually.
average
focusing
of
parameters
itself.
considering
the
Finally,
was
4.47
KN/m2
5
unit
The
system
and
Rayleigh
and
is similar
The
coefficient
flat base
of
analysis
a
blocks
is
finite
as
values
house,
for
stone
to
see
element
solid
to move
was
thus
found
the
model
and
0.3.
of
the
In discontinuous
affects
the
overall
systems, behaviour
response.
of individual
However,
measured
element
residual
Our
deformation at the end of the test is consistent with numerical
have
result though positions of individual elements are not consistent.
That is because of different frictional values among the elements.
houses.
suitability
interfaces
of
and
angle
parameters
masonry
Fig. 6 deformed wood wall after experiment
damping
over
started
6
chy wall
a block
LSM
at the base of wall
KN/m3,
equations
same
the block
acceleration
and the
assumed.
appropriateness
wooden
sensor
of wood
of the
the
Fig. 5 Measured
wall
were
the
a
The acceleration
(kn=2883430
deformable
of tangent
calibration
dry
by putting
When
is to analyze
this,
as 8100000
using
13%
therefore
coefficients
taken
stiffness
was
infinity
in Fig. 4. The wall
a handle.
18) was
calculated
houses,
a
of an acceleration
The
of wall
is a discontinuous,
stone
and
The unit weight
of elasticity
ratio
ks=1201430
pieces
using
by means
the two
to
to investigate
as shown
table
zero
blocks.
into
was measured.
the modulus
Poisson's
to dry
on a small
was measured
displacement
KN/m3,
cut
wall
of bricks10).
between
be
In order
was constructed
manually
at the base
can
with wooden
In the case
between
of elasticity
is no material
joint
of thinking.
was done
blocks
of the joint.
the relationship
of
wall
as joint
•\ 618•\
But
in numerical
employed
analysis,
same
for all elements. Though
friction
coefficient
movement
was
of individual
elements and energy dissipation at each time step have effects in
overall response, it is not practical for big models which may
Table 1, Peak accelerations
have thousands of elements like stone masonry house which are
dealing here. So, the deformations of individual elements have
not been measured at each time step.
Table 2, Various models
Fig. 7 Simulated displacement
of wooden wall
Fig. 8 Comparisonof displacements
5. Analysis of masonry houses
Two typicaltypes of single storeyhouses,one with a single room
with an internalsize 4.05mx3.15mand the other with two moms of
Fig. 9 Single room house with wood bond beam
equal internal sizes of 3.15mx3.60mand both with wall thickness
0.45mwere modeled.The roof load dependson what type of roofing
is used. Approximate calculations suggest a roof load equal to
1.5KN/m2which represents a thin slate roof, would be a good
average considering roofs could also be made of thicker slate,
conugated galvanized iron (C.G.I) sheets or thick rammed earth.
Both houses were analyzedtwice with and without applying wood
bond beamsand subjectedto differentground motions.At first,static
analyses were run considering self weight and roof loads. The
stressesand strainsobtainedfrom staticanalyses were used as initial
values for dynamic analyses. In dynamic analyses,roof loads were
converted into masses by dividing accelerationdue to gravity and
allocated as lumped masses at the top nodes of walls. Material
properties for wooden bond beams and coefficientof friction were
taken same as used in calibrationanalysis.Peak accelerationsof the
Fig. 10 Two room house with wood bond beam
Four different models with varying sizes of elements,
numbers of
rooms and material used were prepared:
1.
Model
1 is single storey,
one room house
with a lintel
three components of the time histories for the Kobe earthquake of
beam over the opening.
1995and the 1940El Centro earthquakeare given in Table 1.
have the same properties
The aim of thisanalysisis to see whetherthese houses can sustain
large deformations.Therefore, solid elements have been assumed
linear and the focus is in the non linear deformationat joints. The
propertiesof the solid andjoint elementsare shown in Table 2.
•\ 619•\
2.
Model
The
lintel beam is assumed
to
of as the stone.
2 is similar to model
1 but has horizontal
wood
bond beams at 0.52m interval.
3.
Model 3 is single storey, two room house with lintel beam
above opening.
4.
Model 4 is the same as model 3 but has wood bond beams
added at 0.52m intervals.
The details of the numbers of elements, sizes etc. are shown in
Table 2. The model houses are shown in Fig. 9 and 10 in which the
pink colored continuous elements representthe wood bond beams
and the blue elementsare stone elementsand verticaland horizontal
linesarejoints.
6. Discussion
Fig. 14 Stresses in model 1 El Centro earthquake
The four models for the two houses describedabove were analyzed
using various ground motionsand their deformationsand stressesare
plottedin Figs. 11-22.Initially,model 2 was analyzedusing the Kobe
earthquake time history. The acceleration was too high for the
masonry building and the house produced large deformations(Figs.
11 and 12)within 8 secs. The reason why displacementswere much
largeralongthe x directionas comparedto the y directionwas due to
the largeaccelerationsinthat direction(Table 1).
Fig. 15 Deformations
Fig. 11 Deformations
in model 2 in El Centro earthquake
of model 2 house in Kobe earthquake
Fig. 16 Stresses in model 2 in El Centro earthquake
In all of the analyses,
program
Fig. 12, Stresses in model 2 house in Kobe earthquake
automatically
when deformation
stopped
exceeded
30 cm, the
due to the large deformations.
The
limit 30cm is arbitrarily assumed
value. It can be less or more. Even
if it is not assigned
runs to final step. It can simulate
beyond
the program
this limit also, however,
nonlinear
computation
iterations
also
as the displacement
increase
and
time. The stone masonry
cracks are formed and become
residual deformations.
Average
it directly
houses
unserviceable
increase
the
elongates
the
are very weak
and
even in few centimeters
length of random rubble
stone used
in masonry house is less than 20cm. If residual deformation
exceeds
30cm, most of the stones are dislocated from its original position and
the house is no more usable.
Our aim is not to look whole collapse
process. If we are looking for effectiveness
deformation
of such houses under seismic
than the few centimeters.
Fig. 13, Deformations
in model 1 in El Centro earthquake
•\ 620•\
of wood bond beam, the
loadings
should
be less
The stresses in all Figs. are in ton/m2and displacementsare in
meters.Model 1 does not have any seismicband and is weaker than
model 2, thus it will be meaningless to analyze using the input
motionsof the Kobe earthquake.Therefore,model 1 was analyzedin
El Centro earthquake. The deformationsand stressesare shown in
Figs. 13-14.It sustained large deformationsquickly.In Fig. 13, we
can see deformationswere higher in the back wall than in the front.
This is because rigid lintel beams were placed over the openings,
which did not deform and strengthenedthe walls and eventually,the
house failed due to the separationof the weaker wall. In model 2,
which was analyzedwith the El Centro ground motion,the structure
was found to performwell as shown in Figs. 15-16.In order to test
Fig. 20 Stresses in model 3 in El Centro earthquake
the performance limit, model 2 was analyzed again with an
amplificationof 2 of the El Centro ground motion; this deformed
with largedisplacements(Figs. 17-18).Subsequently,the responseof
the two room house as represented by model 3 was analyzed
subjectedto the El Centro earthquakeground motion.
Fig. 21, Deformations
Fig. 17, Deformations
in model 4 in El Centro earthquake
in model 2 in 200% El Centro earthquake
Fig. 22, Stressesin model 4 in El Centroearthquake
To examine the response of a two-room house, model 3 was
analyzed using the El Centro earthquakemotion. Like in model 1,
model 3 also sustained large deformations and failed due to
separation of the back wall (Figs. 19-20). Model 4 building was
Fig. 18 Stresses in model 2 in 200% El Centro earthquake
analyzedusing the same input motion and was foundto performwell
(Figs. 21-22) like model 2. In conclusion,both model 2 and model
4 houses which had been strengthened by wood bond beam
deformed less than 6mm and showed good performance under
earthquakeloading.
Stone blocks considered in the numerical analysis consist of
equivalent block of many different sized stones. If the stone sizes
vary each other, moduli of elasticityof walls also vary. It directly
affects the value of stiffness constants. As irregular sized stones
Fig. 19 Deformations
increase,wall becomes weaker and springconstantsare less than that
in model 3 in El Centro earthquake
•\ 621•\
of regular sized stonewall.However,blocks shouldbe as small as the
wood bond beams modeled here assume rigid connectionsat their
averagesize of stone in the wall. In these simulations,the wall was
edges, where elements are linear and have negligible deformation
divided making the length and breadth of the element equal to the
which in tum confinesthe wall and the stone elements.Forcesat the
width of the wall and the height equal to nearly half of the length.
Width of wall has been taken as the referencefor size of elements.In
joints develop where there are relativedisplacements.Wood beams
break verticaljoints, hold the comers effectivelyand join the two
wythes which are responsiblefor diagonalcracks, separationof wall
order to see size effect, the elementswere further subdividedand
analyzed. The differences of deformations are negligible but
computationtime increasedby far. However, even a small house
consists of thousand of units; and each unit will possess different
and formingverticalcracks at comers and splittingof wall into two
folds respectively. A single wood beam connects many stone
elementsand is thereforeresponsiblefor controllingthe deformation
propertiesand shapesand therefore show differentbehaviour.In this
regardthis model may be still too generic.If the elementsare again
further dividedinto small elements, computationtime would be too
of manyjoints.
long and is therefore governed by the level of accuracy required.
are 3 possibleexplanationsfor this:
Thus, size of elements considering the width of wall can give
reasonableresponse.
Displacementsgeneratedby models 2 and 4 were low. There
1.
Firstly,there are no precise and predeterminedvalues of
permissible displacements or drift for these types of
houses to define a credible failure mechanism. Very
small tensile forces could lead to collapse of these
We analyzedfour models from two typicaltypes of houses under
various ground motions. If a stronger earthquakesuch as the Kobe
earthquakeis expected,wooden bond beam alone would not be able
structuresbecause of bulging, which is the prominent
failure mode of double-leaved stone masonry walls.
There is no bonding between the elementsand although
to resist the collapse of these houses. Under slightly lower
acceleration levels, such as when the houses experienced an
accelerationlevel twice that of the El Centro event,the houses still
the presence of a wood beam could reduce the
sustained very large deformations and failed. In the El Centro
to the wood beam could still fail due to tensile forces at
thejoints.
deformationsubstantially,the rest of the wall not attached
earthquake,the peak accelerationwas about 0.31g and testing under
this input ground motion,the houses without wooden bond beams
still failed,but houses constructedwith the additionalwooden beam
2.
Secondly,this may be due to the methodof modeling.In
a real wall,there are many stoneblocks between the two
did not.
beams but in this model there are only two blocks along
vertical direction. Therefore, each block would be in
The main possible failure mechanismfor stone masonry houses
contact with the wooden beam, either at the top or the
are skin splitting,vertical cracking at comers, separation of wall,
underside. The faces of the joint in contact with wood
would deform less.Thus, the model may underestimate
wedge shape failure and diagonal cracking. If we looked at the
figureswe can find most of them in this study also. In Figs. 11-12,
houses failedin shearand swept to collapse.Kobe 1995 earthquake's
deformation as only one joint is free to move in the
numericalanalysiswhich is not true in the case of a real
acceleration is so high that LSM house can not resist. In usual
wall. If the houses are modeled with thousands of
practice,lintelbeams (Figs.13-14, 19-20)are often providedover the
openings even in unreinforced LSM houses. Lintel beam is not
elementsandjoints the computationtime is very long.
provided at back side wall and it is the weakest one. Thus comer
cracking starts at the junction of two walls leading to large
deformation.This may be reasonable as more than forty percent
houses had damaged in El Centro earthquake. In Figs. 17-18, two
3.
Lastly,in this analysissolid elementshave been assumed
linear and only largedeformationsat interfaceshave been
examined.Non linear deformationin solid elementscan
be significant in small deformations when the wall is
confinedby the wood bond beam.
times amplified El Centro 1940 was given, comer and diagonal
crackshave formed near openings leadingto collapse,which is quite
naturalsince area around openings are the weakest zones. Both one
analyzing this type of dry stone masonry house in detail. Using
and two roomed wooden beam reinforced houses (Figs. 15-16,
21-22) performed well under El Centro 1940 earthquake.The key
similar method, few studies3),10)
have been done in brick masonry.
They are bonded by cement sand mortar and dry stone masonry
point here is that the coefficientof frictionwas taken as 0.3 and the
houses are quitedifferentfrom brick masonry.This method has been
peak accelerationwas 0.31g. Theoretically,slidingshouldnot occur
until 0.3gthereforethe question arisesas to why model 1 failed since
it had equal friction.One possible explanationis that the house in
implementedin Pakistan2)as disastermitigationmeasure,but nobody
has investigated dry stone houses analytically,numerically and
model 1 experiencedtension first,which the caused separationand
there was nothing between the stones to control the tensionleading
ultimatelyto failure,eventhough it still had spare shearcapacity.The
―622―
To the authors' best knowledge; this was the first attempt at
experimentally.Does it resist any earthquakes? How much peak
accelerationcan be resistedwhen wood bond beams are used? These
questions have been addressed here, following the numerical
methods that can be found in open literatures.However,the problem
which we dealt is totally
new and investigation
presented
here is
novel.
7. Conclusion
The behaviors
of two types of dry stone masonry houses
various ground motions
analyses.
were investigated
From these analyses,
houses strengthened
be an effective technique
motions
similar
deformation
wood
bond beams
would
not be
such as Kobe 1995. However,
it can
in confining the walls under smaller ground
to the El Centro
earthquake
of 1940. The
small
obtained from the analyses shows that sufficient cracks
could develop
however,
detailed dynamic
it was clear that dry stone masonry
by applying
able to resist strong earthquakes
through
under
and make the houses inhabitable
after earthquakes;
the wood bond beams would prevent complete collapses
of
the dry stone masonry houses which would ensure life safety in low
intensity earthquakes
technique
Thus, this could be an appropriate
in low seismicity
zones along the Alpine Himalayan
where these houses are common
earthquakes
are expected.
the only most
vernacular
economical
upgrading
Belt
and frequent but low acceleration
Since wood can be locally available, it is
solution
for upgrading
these
kinds of
houses.
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