V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10
88
Focussed on Modelling in Mechanics
Nume ical simula ions o es s mason y walls om
ce amic block using a de ailed ini e elemen model
V. Salajka
B no Uni e si y o Technologye, Czech Republic
salajka. @ ce. u b .cz, h p://www. u b .cz
J. Klouda
Technical and Tes Ins i u e o Cons uc ion P ague, Czech Republic
klo[email p o ec ed], h p://www. zus.cz
P. H adil
B no Uni e si y o Technologye, Czech Republic
[email p o ec ed], h p://www. u b .cz
ABSTRACT. This a icle deals wi h an analysis o he beha iou o b ick
ce amic walls. The beha iou o he walls was analysed expe imen ally in
o de o ob ain hei bea ing capaci y unde s a ic loading and hei seismic
esis ance. Simul aneously, nume ical simula ions o he expe imen s we e
ca ied ou in o de o ob ain addi ional in o ma ion on he beha iou o
mason y walls made o ce amic blocks. The esul s o he geome ically and
ma e ially nonlinea compu a ions we e compa ed o he esul s o he
pe o med es s.
KEYWORDS. Ce amic blocks; Ma hema ical model o a wall; Fini e Elemen
Me hod; Nonlinea compu a ions.
Ci a ion: Salajka, V., Klouda, J., H adil, P.,
Nume ical simula ions o es s mason y walls
om ce amic block using a de ailed ini e
elemen model, F a u a ed In eg i à
S u u ale, 39 (2017) 88-99.
Recei ed: 11.07.2016
Accep ed: 22.09.2016
Published: 01.01.2017
Copy igh : © 2017 This is an open access
a icle unde he e ms o he CC-BY 4.0,
which pe mi s un es ic ed use, dis ibu ion,
and ep oduc ion in any medium, p o ided
he o iginal au ho and sou ce a e c edi ed.
INTRODUCTION
e o e i s in oduc ion o he ma ke , mason y made om inno a i e clay hollow blocks illed wi h mine al wool,
had o be es ed o unc ionali y and eaching he con o mi y wi h calcula ion models acco ding o he Eu ocode
6 [1] and/o Eu ocode 8 [2], in mo e complex cases o load, be o e i was launched on he ma ke . Du ing he
yea s 2011 – 2014, an ex ensi e p ojec [3-6] de o ed o he assessmen o he p oduc s a ic cha ac e is ics as well as he
beha iou o he walls lined om hese blocks was ealized on Technical and Tes Ins i u e o Cons uc ion P ague,
Czech Republic (TZÚS P aha). The basic as well as he ex ended es s we e ealized, including he e alua ion o i s esul s,
B
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in TZÚS b unch o ice in B no. The clay block mason y walls we e es ed o a load capaci y unde he sho - e m and
long- e m s a ic load on small mason y walls [3, 4], possibly on walls and pilla s o an ac ual size [5, 6].
Seismic esis ance es ing was ca ied ou acco ding o he ins uc ions o Klouda, J. K. and wi h his a endance in a
es ing depa men o he Na ional Building and Ci il Enginee ing Ins i u e (ZAG) Ljubljana, Slo enia. Shea es s o he
cyclic loading o ou (2+2) cons an ly e ically p eloaded walls we e conduc ed. The walls we e 2750 mm high and
440 mm hick. They di e ed in he leng h. Two o he walls we e 2500 mm long and he o he wo 1500 mm, he wall
wid h and heigh a io was hen ca. 1 : 1 and 1 : 2. The e ical p eload was designed a wo le els, a a nominal amoun o
app oxima ely 1/3 o 2/3 o he alue o he wall e ical design load capaci y. A he same ime, nume ical simula ions o
he expe imen s o ob aining addi ional in o ma ion on he clay block mason y wall beha iou we e ca ied ou – he
same as by eccen ic loaded pilla s [7]. The ma hema ical analyses we e ca ied ou using he ini e elemen me hod on he
de ailed wall models. Block ma e ial p ope ies (modulus o elas ici y, ensile s eng h, comp ession s eng h, ensile
s eng h in bending, e c.) we e de e mined expe imen ally be o e pe o ming he calcula ions. The models we e
conside ed as geome ically and ma e ially nonlinea , including unila e al bonds. The calcula ion esul s a e u he
compa ed wi h he esul s o he conduc ed es s.
THE CLAY BLOCK MASONRY WALLS UNDER THE STATIC LOAD
he load-bea ing capaci y o b ick walls ab ica ed om ce amic blocks (Fig. 1) unde s a ic loading was i s es ed
on small specimens consis ing o h ee ows in he single block o ma , hen on medium-heigh pilla s consis ing
o se en ows o blocks and inally on high wall pilla s consis ing o ele en ows o blocks. The es specimens
we e loaded cen ically and eccen ically.
Figu e 1: Mason y block used in expe imen al walls and FEM model o mason y block.
De ails ega ding he execu ed es s a e shown in [5] and [6]. De ailed models we e c ea ed using he Fini e Elemen
Me hod o use in he nume ical simula ion o s a ic es s. The b ick blocks we e modelled along wi h he mo a in he
bed join s, he s eel pla es unde and abo e he pilla s, and he s eel appa a us o imposing load. Plana elemen s unde
he bo om pla e simula e he possible lexibili y o he placemen o he s eel pla e. Con ac pai s (elemen s) o he
modelling o in e ac ion be ween he blocks, mo a and s eel pla es a e inse ed be ween he blocks and he a eas adjacen
o hem. These con ac elemen s ans e only comp essi e and shea o ces. Please see Fig. 2 a) o an example
compu a ional model o a wall pilla . Fig. 1 and 2 b) illus a es he di ision o a block in o olume ic ini e elemen s. The
loading ca ied ou in acco dance wi h he es was conside ed o be o ced displacemen load. De ails abou he
calcula ions can be ound in [7]. Fig. 3 shows he dependence o ela i e ans o ma ion in he e ical di ec ion on load.
The dashed lines show he measu ed esul s and he ull (FLX – lexible suppo ) and do ed (SLD – solid suppo ) cu es
show he esul s o he calcula ions. Calcula ed alues o de o ma ion a e iden ical in a ious le els. I is appa en ha he
suppo o he wall needs o be modelled ca e ully as he seemingly s i ness o suppo he es specimen can in luence
he esul s o he measu emen s signi ican ly.
T
V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10
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a) Model o a pilla , including de o me e s b)
T
h ee neighbou ing blocks
Figu e 2: Compu a ional model o a high b ick pilla .
a)
T
op a ea
–
alues om he de o me e . b) Bo om a ea
–
alues om he de o me e .
Figu e 3: A sample o C 1-1 Specimen – load-dependen e ical s ain ε.
ANALYSIS OF BEHAVIOR OF CYCLIC LOADED CLAY BLOCK WALLS
es s o he s uc u e o he mason y walls buil om p ecise bu n mason y elemen s o he clay blocks
POROTHERM 44 T P o i loaded by a cyclically o ced loading co espond o he shea es s o walls o he ac ual
size. Fou walls o he di e en wid h we e es ed. The walls o he g ea e leng h a e ma ked “L” and he sho e
walls a e ma ked “S”, (Fig. 4).
The e ical walls we e buil on a igid ein o ced-conc e e beam ha was a ached i mly o he loo so ha he shea
displacemen along he loo and beam il ing we e elimina ed. The ansmission o he e ical o ces was ca ied ou by
s eel sec ions and ou independen hyd aulic cylinde s and one p og am-con olled hyd aulic cylinde b inging in he
la e al displacemen (along he wall) cyclically co esponding o he seismic loading. The con olled la e al displacemen
was in oduced o he beam by he p edomina ing mason y wall. The indi idual blocks we e lined on hin join mo a
o 1 mm hickness. The mo a is only in ho izon al join s, e ical inden ed join s a e d y.
Idealized and eal la e al displacemen ime his o y is shown on he Fig. 5. Du ing he expe imen , he e ical and
ho izon al o ces and he displacemen s a p ede e mined poin s we e measu ed (Fig. 6). An op ical came a measu emen
sys em was used o de e mine he mo ion o he wall su aces. The la e al o ce ( esis ance) dependencies on he la e al
displacemen we e he esul o he measu emen . The measu emen s p o ided da a ega ding dependencies o e ical
o ce ( esis ance) on ans e se displacemen . The esul s o he expe imen s a e a anged in a abula o m.
T
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Speci ica ion: L1 (L12112/4/3) Speci ica ion: S2 (L12112/4/4)
L 4
L 3
L 1
L 2
L1
Fh
90 (208)
395 (245)
110 (210)
375 (245)
250 (19)
L2
L1
770
Fh
F 4
590
590
(50)
1380
2000
2506 (2561)
2507 (2560)
E1
(baza 3125)
E2
(baza 3122)
2745 2742
L 4
L 3
L 1
L 2
L1
Fh
108 (230)
194 (245)
88 (230)
183 (250)
276 (18)
L2
L1
770
Fh
F 4
590
590
(62)
900
2000
1505 (1568)
1505 (1555)
E1
baza 2570 mm
E2
baza 2570 mm
2746 2747
Figu e 4: Diag ams o walls “L” and “S”.
Time [s] Time [s]
Figu e 5: Idealized and eal imposed la e al displacemen ime his o y.
Wall models
In acco dance wi h he da a, nume ical models o he walls we e c ea ed using he ini e elemen me hod (FEM). Only he
undamen al di e ence in he geome y, ha is he di e ence in he leng h o he walls, was aken in o conside a ion while
modelling by he FEM model. On he basis o his conside a ion, wo compu a ional models we e only c ea ed: One o
he analysis o he long “L” walls and he second one o analyze he sho “S” walls. The calcula ions also di e by e ical
p eload and exci a ion unc ions. The e ical p eload alues (including he gi de and he conc e e block) a e conside ed
o each model as ollows:
L1 - 1/3 cd - e ical p eload 807 kN,
L2 - 2/3 cd - e ical p eload 1613 kN,
S1 - 1/3 cd - e ical p eload 484 kN,
S2 - 2/3 cd - e ical p eload 968 kN.
On he basis o he da a, see he diag ams in Fig. 4, models o long “L” on he le and sho “S” walls on he igh side
including unde lay and deli e ing elemen s o e he walls we e c ea ed in he ANSYS so wa e.
Conside ing he symme y o ealized complemen a y s uc u es and walls o he e ical plane in he longi udinal
di ec ion and he manne o loading, he compu a ional models we e c ea ed using his symme y ( he x-z plane). The
g aphic ep esen a ion is including he mi o ed pa o he model.
The compu a ional models a e mainly c ea ed om he 3-D ini e elemen s o he SOLID45 ype, see ( ig. 7). They a e he
blocks, he mo a , he conc e e base beam, he conc e e beam and he main s eel gi de s and wo addi ional beams
di ec ly unde he p essu e cylinde s a he “S” ype walls (Fig. 8). The conc e e base beam o he dimensions
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3980x500x500 o he “L” model, o 2074x500x500 he “S” model, is conside ed as elas ically placed in he calcula ions,
because he loo showed o be yielding. Rela i ely igid beam placing is modelled by he COMBIN14 and SHELL181
elemen s. The clay blocks a e bound by he mo a a he ho izon al di ec ion and hey a e wi hou illing in he e ical
join s.
Figu e 6: Scheme o loca ions o indica o s – walls L and a angemen o de ice o e ical loading.
a) “L” ype model b) “S” ype model
Figu e 7: Axonome ic iew on models – ini e elemen s mesh.
The in e ac ion be ween he blocks, possibly he mo a is modelled using con ac pai s – he elemen s o CONTA173
and TARG170 ype (Fig. 8). Simila ly, hese elemen s a e pu be ween he mo a and he conc e e beams. The wall heigh
including he mo a is 2,749 mm. The uppe conc e e beam is 2,928 mm long (1,789 mm “S” ype), 150 mm high and
500 mm wide. The s eel gi de is bound wi h he conc e e beam i mly. The ex e nal con ou o he gi de ha is
3,500 mm long is 300x250 mm.
Down p essu e ( he cons an e ical load) is b ough in o he s uc u e using special PRETS179 elemen s in connec ion
wi h BEAM44 elemen s ha allow a ho izon al slip a he leaning poin on he gi de and a deli e ing a ea o SHELL63
elemen s. The se ing depends on he comp essi e o ce and igidi y in he e ical di ec ion. Thus, he down p essu e is
implemen ed a ou loca ions a he “L” ype walls (Fig. 6). This me hod o he p essu e o ces se ing did no p o e
success ul wi h he sho wall models. The uppe gi de ended o il du ing he mo emen because o he eccen ic
ac ion o he e ical o ces. The models we e supplemen ed wi h wo sliding beams on he main load dis ibu ion beam.
Thanks o his, he gi de guiding a he o ced ho izon al displacemen was ensu ed. These beams o he leng h o
1,000 mm, he heigh and he wid h o 250 mm a e modelled in a simpli ied manne . The comp essi e o ce is applied by
he special PRETS179 elemen s in he connec ion wi h he LINK8 elemen s and again a ou poin s. The modi ied

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model e lec s he eal beha iou o he comp essi e de ice in a be e way. The eal e sion o he comp essi e de ice is
in he Fig. 6.
Figu e 8: Con ac ini e elemen s (on le ) and he beams and he conc e e blocks (on igh ) o “S” ype model.
B ick body and mo a p ope ies a e de i ed om he measu emen [3]. The ma e ial model o he s eel gi de s and
conc e e beams is conside ed as iso opic and linea ly elas ic. On he con a y, he ma e ial model o he b ick body and
mo a is conside ed as nonlinea wi h di e en ensile and comp ession s eng h. A summa y o he p ope ies o he
indi idual pa s o he model ha e been used in calcula ions as i is men ioned in Tab. 1.
B ick body Mo a Conc e e S eel
Modulus o Elas ici y E [GPa] 14.0 7.9 30 210.0
La e al Con ac ion Coe icien ν [-] 0.1 0.2 0.2 0.3
Speci ic Weigh ρ [kg.m-3] 1390 1400 2300 7850
Comp ession S eng h c [MPa] 19.2 17.3 - -
Tensile S eng h [MPa] 3.7 4.6 - -
Table 1: Ma e ial p ope ies.
The o al compu a ional model o al e na i e solu ions wi h he “L” ype wall consis s o 113,337 ini e elemen s
localized by 134,550 nodes and has 399,477 deg ees o eedom.
The o al compu a ional model o al e na i e solu ions wi h he “S” ype wall consis s o 68,799 ini e elemen s localized
by 83,177 nodes and has 246,013 deg ees o eedom.
The imposed unc ions a e modi ied unc ions aken om esponse a he expe imen s. The majo adjus men consis s
o he co ec ion o he exci a ion poin loca ion. The esponse unc ions a e moni o ed a he heigh o 2,824 mm (“L”
ype) abo e he wall bed join , while he exci a ion poin by he o ced mo ion o he gi de is a he di e en place,
a highe le el om he cen e o he bo om o he wall du ing he expe imen . The displacemen co ec ion co esponds
o app oxima ely 5 o 6 pe cen . Tha means ha he imposed la e al displacemen unc ion used as he exci a ion we e
inc eased by 6 pe cen .
Calcula ion
Fou calcula ions we e ca ied ou on models L1, L2, S1 and S2. The calcula ions a e nonlinea , ime-consuming and
equi ed la ge disc space. The solu ion is conside ed as quasi-s a ic due o he slow loading p ocess. The ime s ep is
conside ed as a iable wi h he la ges s ep o 15 s. In each ime s ep an i e a i e s a e o equilib ium is sea ched. In case
ha he ime s ep canno be al eady dec eased and he calcula ion does no con e ge, he calcula ion p ocess is
e mina ed.
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The displacemen , s ain and s ess ields a he disc e e poin s o he models we e ob ained by he calcula ions on he L1,
L2, S1 and S2 models. Conside ing he scope o he da a, he esul s we e mainly p ocessed in a o m o g aphs and
igu es.
L1 Wall
The cyclic esponse solu ion on he L1 model wi h he p eload 807 kN (including he gi de and he conc e e block) was
compa ed wi h he alues ob ained om he es .
Exci a ion unc ion o ime his o y la e al displacemen is shown on he Fig. 9.
The esponses o he la e al displacemen on he su ace in he cen e o he conc e e beam ob ained om he
measu emen and by he calcula ion a e p esen ed in Fig. 9. The la e al displacemen ob ained om he measu emen is
ep esen ed by a ed dashed line and he la e al displacemen o he same a iable ob ained by he calcula ion is shown by
a blue line. In Fig. 10, he e is a ep esen a ion o he eac ion o ce dependence on he la e al displacemen o he bo h
cases o he expe imen and he calcula ion.
Figu e 9: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a
cen al poin o he beam (on igh side).
 expe imen ── calcula ion
Figu e 10: Reac ion o ce dependence on displacemen .
L2 Wall
Du ing he solu ion o he L2 wall he p eload was 1,613 kN (including he gi de and he conc e e block). The esul s o
he compa ison a e in Figs. 11 and 12.
The mode o “s ep-by-s ep” des uc ion and ele an s ages o he walls a e es ing a e shown in Fig. 13.
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Figu e 11: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a
cen al poin o he beam (on igh side)
 expe imen ── calcula ion
Figu e 12: Reac ion o ce dependence on displacemen .
Figu e 13: Typical iew on he walls a e es ing.
S1 Wall and S2 Wall
The cyclic esponse solu ion on he S1 model and S2 model wi h he p eload 484 kN, esp. 968 kN (including he gi de
and he conc e e block) was compa ed wi h he alues ob ained om he es . Exci a ion unc ion o ime his o y la e al
displacemen is shown on he Fig. 14, esp. Fig. 16. The esul s o he compa ison a e in Figs. om 14 o 17.
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Figu e 14: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a
cen al poin o he beam (on igh side).
 expe imen ── calcula ion
Figu e 15: Reac ion o ce dependence on displacemen .
Figu e 16: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a
cen al poin o he beam (on igh side).