Assessmen o ancien mason y slende
owe s unde seismic loading:
dynamic cha ac e iza ion o he
Cua o i as owe
P. Pineda & A. Sáez
Depa men o Con inuum Mechanics and S uc u al Analysis,
School o A chi ec u e, Uni e si y o Se ille, Spain
Abs ac
The Cua o i as owe is a XII h cen u y almohad mina e loca ed in he
p o ince o Se ille (Spain) and i is conside ed he bes p ese ed almohad
eligious building in he Ibe ian Peninsula. As i is placed in a seismic a ea, i is
c ucial o i s p ese a ion o e alua e i s dynamic esponse unde ea hquake
loading and o assess he sa e y le el in i s p esen s a e o conse a ion. In his
pape a numbe o h ee-dimensional linea and non-linea ini e elemen models
wi h di e en le els o complexi y and simpli ica ions a e de eloped, using 3-D
solid elemen s o 3-D beams elemen s. All he models assume ha he mason y
s uc u e is homogeneous and he ma e ial non-linea beha iou – including
c ushing and c acking – is simula ed by means o di e en cons i u i e models.
Subsequen non-linea s a ic and non-linea dynamic analyses a e pe o med.
P e ious s a ic and ime-his o y dynamic analyses wi h a simpli ied elas ic
ma e ial model a e e alua ed o calib a e he non-linea esponse, and o ake in o
accoun ha c ack opening may in oduce nume ical ins abili ies. Compa ison
among he di e en models is ho oughly discussed, in pa icula as p edic ed
local and global collapse mechanisms a e conce ned, in o de o e alua e he
sui abili y, accu acy and limi a ions o each analysis. To conclude, a gene al
me hodology is p oposed o assess sa e y and o imp o e seismic esis ance o
his and o he simila cul u al he i age buildings.
Keywo ds: ancien mason y owe , almohad a chi ec u e, non-linea dynamic
analysis, ea hquake loading.
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doi:10.2495/STR090 154
1 In oduc ion
His o ic mason y owe s placed in seismically ac i e egions could be se e ely
damaged by ea hquakes. Indeed, hese s uc u es a e able o esis g a i a ional
ac ions, bu as hey we e no explici ly designed o wi hs and seismic e ec s,
hey show pa icula ly weakness wi h ega d o ho izon al loadings induced by
dynamic exci a ions. The high ulne abili y o hese cons uc ions unde
ho izon al ac ions is mos ly due o he absence o adequa e s uc u al
connec ions, which leads o o e u ning collapse [1]. Rega ding Almohad
mina s, hey a e medie al owe s o a ype ha is p one o su e damages unde
ea hquakes, mainly due o hei slende ness, low shea s eng h and low
duc ili y. Mo eo e , hei possible lack o e ec i e connec ions among s uc u al
elemen s – co e, aul s and ex e nal walls – needs o be e alua ed. Due o hese
easons, i is c ucial o hei p ese a ion o assess seismic sa e y in o de o
e alua e hei dynamic esponse and, i necessa y, o imp o e hei s uc u al
s eng h. Indeed, p e en ion and ehabili a ion can be success ully achie ed only
i diagnosis o he building is ca e ully analysed [2].
I is well known ha analysis and e alua ion o seismic eliabili y o mason y
cul u al he i age buildings is a di icul ask, owing o unce ain ies ha mainly
a ec s uc u al beha iou and mechanical ma e ial p ope ies. The o me
includes lack o in o ma ion on model de ini ion – geome y, cons ain s,
ma e ials, cons uc i e de ails.– and he la e is ocused on non-linea mason y
beha iou and low ensile s eng h. Fu he mo e, i a comp ehensi e s udy o
s uc u al beha iou is going o be pe o med, accu acy and sui abili y o he
analy ical o nume ical me hod selec ed a e essen ial issues.
A con ibu ion o dynamic cha ac e iza ion, la e al capaci y and seismic
assessmen o Almohad mina e s is p o ided in a single case s udy, e ealing
ad an ages o disad an ages o di e en nume ical analyses – s a ic, modal,
linea ansien , non-linea ansien and non-linea s a ic. Simpli ied and de ailed
models based on he Fini e Elemen Me hod a e pe o med, and b i le non-linea
beha iou o mason y is conside ed a he mac o-le el.
This esea ch aims a p edic ing local and global collapse mechanisms, hus
de eloping an accu a e and p ac ical me hod o analysis o dynamic esponse in
Almohad cons uc ions.
2 His o ical su ey
The Cua o i as medie al owe is a XII h cen u y mina e loca ed in Bollullos
de la Mi ación, in he p o ince o Se ille, Spain, and nowadays i is pa o he
Nues a Seño a de Cua o i as Chu ch, ig. 1. Fu he mo e, i is conside ed he
bes p ese ed Almohad eligious cons uc ion e ec ed in he Ibe ian Peninsula,
and due o i s p opo ions, sob ie y and deco a ion i is a mas e piece o i s
a chi ec onical s yle.
Mina s we e in oduced a he end o he second cen u y o Islam in Abbasid
Mesopo amia. They we e a ached o a mosque in o de o signi y he accep a ion
deg ee o he eligious edi ice as an ins i u ion in Islamic socie y. In Almohad
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Figu e 1: (a) Gene al on al iew, and No h and wes açades; (b) Chu ch
plan sec ion; (c) owe longi udinal sec ion; (d) owe plan sec ion.
(Sou ce: Ca álogo a queológico de la p o incia de Se illa.)
imes, mosque owe s had symbolic unc ion oo, since hey we e concei ed as
a chi ec u al s a emen s o Islam du ing he Ch is ian Reconques o Spain. The
i s o he g ea mina e s o his pe iod, he Ku ubiyya owe , was e ec ed in
1158 in Ma akesh, Mo occo, a he le end o he quibla wall o he mosque.
When Se ille became he Ibe ian capi al o Almohads, he owe o i s g ea
mosque was cons uc ed by Ahmad ibn Basu in 1184 on o de s om Abu
Ya’qub Yusu . Un o una ely, he las o he mo e signi ican mina s belonging
o his epoch, he owe a he mosque o Hassan a Raba , is un inished. In his
his o ical con ex he analysed mina e was buil . Al hough no men ioned in any
sou ces, he mina has been da ed in 1175-1180 by s ylis ic s udies [3].
Compa ison wi h he a o emen ioned owe s sugges s ha he Cua o i as
Mina e has simila shape and s yle o deco a ion. Besides, all o hem a e
loca ed in ac i e seismic a eas. These monumen s a e essen ial in e olu ion o
Islamic eligious a chi ec u e as hey we e models o mina e s buil in he
me opoli an cen es o he Magh eb un il O oman imes [4].
As a e e ence o he alue o he monumen s udied in his wo k, i is
impo an o men ion ha i has been insc ibed in he Spanish He i age
Monumen Lis ing since 1931.
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3 Geome ical and s uc u al su ey
The Cua o i as mina e is a ee-s anding owe si ua ed nex o he no h açade
o he chu ch, walling in he shan- he o iginal mosque cou -. This ele an
a chi ec u al monumen is o mode a e size, 3.25*3.25 m2 in lowe plan,
3.10*3.10 m2 in uppe plan and i ises 14.8 m abo e he cu en g ound le el. I s
plan-heigh ela ion is 1/4.21, complying wi h Almohad slende ness canons. The
açade is deco a ed wi h ec angula panels and dual blind a ches – i e- oiled o
ho seshoe a ches – aming small openings along he ex e nal walls, as i is in he
na u e o he pu es Uni a ian s yle.
Mo phologically, he mina e is di isible in o h ee s uc u al pa s: ex e nal
walls, cen al co e and ba el aul s, ig. 1. The a e age hickness o walls is
0.425m, co e c oss-sec ion is 0.90*0.90 m2 and ba el aul s c oss sec ion is
0.14m. The inne chambe consis s o an an iclockwise s ai case co e ed by
ho izon al ba el aul s, which ascend a ound he squa e cen al solid co e. The
whole s uc u e is buil o clay b icks and lime mo a join s, o iginally co e ed
wi h pain ed plas e . The a o emen ioned building ma e ials a e essen ial in
Islamic Andalusian cons uc ions. B ick a e age size is 0.28*0.14*0.045 m3 and
a e age lime hickness is 0.035 m. A ca e ul isual su ey o he s uc u e
e ealed i egula mo a -b ick disposi ion in se e al zones, whe e b icks we e
subs i u ed by mo a , ig. 2. Mo eo e he owe only exhibi s supe icial c acks.
No in o ma ion on he cha ac e o he ounda ion is a ailable, bu he s uc u e
is supposed o be embedded in he soil. To conclude i is impo an o men ion
ha no se e e damage is obse ed.
Fo a comple e epo on his building e e o [3]. In addi ion, a
comp ehensi e su ey o he a chaeological ea u es can be ound in [5].
Figu e 2: Aspec s o he i egula mo a -b ick disposi ion.
4 S a ic analysis
4.1 S a ic analysis wi h linea ma e ial
The i s analysis ca ied ou ocused on s a ic assessmen o he de ailed h ee-
dimensional ini e elemen model, which allows one o conside accu a ely all
he essen ial s uc u al ea u es. The ANSYS ini e elemen so wa e was used o
cons uc he model, and h ee-dimensional eigh node solid elemen s,
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Figu e 3: Fini e Elemen model mesh.
SOLID 45, we e employed o mason y ma e ial [6]. The mesh consis s o
65,152 elemen s, 52,188 nodes and 154,956 ac i e deg ees o eedom; a e age
elemen size is 0.11m. The wall hickness was disc e ized wi h ou elemen s.
This model comp ises he mos signi ican s uc u al pa s, namely eal load-
bea ing wall hickness – eplica ing he ec angula panels aming openings,
which educe he a e age c oss sec ion – openings, aul s and cen al co e, ig. 3.
The s ai case sel -weigh was applied on he aul s, due o i s cons uc i e
ea u es. No in o ma ion ega ding physical ma e ial p ope ies is a ailable, hus
he p ope ies o con empo a y s uc u es in he egion wi h he Cua o i as
mina we e conside ed [7]. Fu he mo e, a smea ed model wi h homogenized
p ope ies was pe o med, and i s linea elas ic ma e ial p ope ies we e assumed
as Young modulus E = 1GPa, Poisson a io ν =0.2, and speci ic weigh
w=17,000 N/m3.
Wi h ega ds o bounda y condi ions, he base o he owe was conside ed as
comple ely cons ained and con ibu ion o he adjoining chu ch was assumed o
be negligible.
This p elimina y s udy p o ides aluable in o ma ion bo h on global
beha iou and on in e ac ion among he s uc u al pa s. Indeed, he analysis o
he s uc u e unde g a i y loading yields signi ican da a, such as s ess
dis ibu ion, weak elemen s o po en ial ailu e and displacemen s, able 1.
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F om he s a ic nume ical app oach i may be obse ed ha maximum
comp ession le el – 0.45 Mpa – was eached by he basemen , as expec ed,
whe eas maximum ensile s esses –0.17 MPa– appea ed in he aul s.
Fu he mo e, high s ess concen a ions we e ob ained in he connec ions among
s uc u al pa s. The comp essi e s esses a e admissible, bu as s esses highe
han ensile s eng h we e ob ained, he use o non-linea ma e ial is ad isable.
Fu he mo e, hose esul s allow one o conclude ha connec ions be ween aul s
and walls a e con i med o be a ulne able pa o he building. Wi h ega d o
displacemen s, he maximum ho izon al alues we e eached by he aul s and
he co e.
4.2 S a ic analysis wi h non-linea ma e ial
A second s a ic analysis was pe o med on he same de ailed h ee-dimensional
ini e elemen model, aking in o accoun he ma e ial non-linea beha iou . The
D ucke -P age pe ec ly plas ic c i e ion [8] and he Willam-Wa ncke ailu e
su ace [9] we e employed in he model. I is impo an o men ion ha hose
c i e ia p o ide nei he s i ness deg ada ion o b i le ma e ial caused by
successi e plas ic de o ma ion, no c acks esul ing om low cycle a igue [10,
11]. Howe e , bo h heo ies yield accu a e esul s on h ee-dimensional solid
models, in pa icula when p edic ed c acking p og ession is conce ned.
Fu he mo e, he p e ious s a ic analysis and he ollowing non-linea analysis
show ha ei he c ushing o plas ic de o ma ion due o high comp essi e le els
we e no ound in he analysed s uc u e. P io li e a u e on mason y s uc u al
analysis [10, 12–14] has used hose c i e ia in o de o de e mine he on ie
be ween linea and non-linea beha iou .
Th ee-dimensional eigh -noded solid isopa ame ic elemen , SOLID 65, was
employed o model he b i le ma e ial. The elemen is capable o c acking in
ension – in h ee o hogonal di ec ions – and c ushing in comp ession. The
mason y was assumed o be ini ially iso opic, un il ei he one o he ensile o
he comp essi e s eng h was exceeded. When c acking occu ed, i was modeled
h ough an adjus men o ma e ial p ope ies which e ec i ely ea s he c acking
as a “smea ed band” o c acks. The s ess-s ain ma ix was adjus ed by
in oducing a plane o weakness in a di ec ion no mal o he c ack ace, and wo
shea ans e coe icien s o open and closed c acks, β = 0.15 and βc= 0.75 we e
conside ed. The β ep esen s a shea s eng h educ ion ac o o hose
subsequen loads which induce sliding –shea – ac oss he c ack ace. I c ushing
occu s, he comple e de e io a ion o he s uc u al in eg i y o he ma e ial is
conside ed, and con ibu ion o he s i ness o an elemen a he in eg a ion poin
is igno ed.
The ailu e c i e ion was de ined by means o wo uniaxial s eng hs, namely
uniaxial comp essi e s eng h, c, and uniaxial ensile s eng h, . A pa ame e
a ia ion s udy o esul s conce ning he uniaxial ensile s eng h as a pe cen age
o he comp essi e s eng h was pe o med. The alue hus selec ed was
consis en wi h he p esen conse a ion s a e. Wi h ega d o he D ucke -P age
pa ame e s, he exp essions p oposed by Lou enço [15] we e conside ed, as
shown in able 2.
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Table 1: S a ic analysis esul s.
Table 2: Model calib a ing pa ame e s.
The esul s hus ob ained we e consis en wi h he linea analysis. Maximum
comp essi e s esses – 0.36 Mpa – we e eached by he basemen , as expec ed.
Maximum ensile s esses – 0.17 Mpa – appea ed in he aul s, op le el o he
co e and windows, as well as, high s ess concen a ions we e ob ained in he
connec ions among s uc u al pa s. The comp essi e s esses a e admissible, bu
s esses highe han ensile s eng h caused c acks, as ig. 4 shows. Wi h ega d
o displacemen s, he maximum ho izon al alues we e eached by he aul s and
he co e.
5 Modal analysis
A modal analysis was compu ed on he a o emen ioned e ined elas ic h ee-
dimensional ini e elemen model, in o de o ob ain he dynamic p ope ies –
na u al equencies, ωn, and modal shapes, ζn – and o se e as a s a ing poin o
he ansien dynamic analysis. Damping was no aken in o accoun . The sum o
he e ec i e modal masses o he conside ed modes is mo e han he 90% o he
o al mass-133,208.49 kg-. All hese modes ha e an e ec i e mass g ea e han
5% o he o al mass. The i s 4 modal shapes a e p o ided in ig. 5 and he
modal pa icipa ing mass a ios o each p incipal di ec ion a e epo ed in
able 3.
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Figu e 4: S a ic analysis wi h non-linea ma e ial esul s.
F om he eigen alue analysis esul s, i may be concluded ha he i s and he
second modal shapes p o ide he highes mass con ibu ion, and bo h o hem
in ol es global bending. Those shapes a e cha ac e ised by a high global
s i ness and a monoli hic beha iou among aul s, cen al co e and walls. The
hi d modal shape displays o sional esponse, and, when highe shapes a e
analysed, weak collabo a ion among he di e en s uc u al pa s is e ealed, and
signi ican ou -o -plane de o ma ions a e obse ed.
The esul s hus ob ained a e consis en wi h he s uc u al ype, as i is
cha ac e ised by wo s i elemen s – pe ime e walls and co e – connec ed by
mo e lexible elemen s –ba el aul s-.
6 Seismic analysis
A numbe o h ee-dimensional linea and non-linea ini e elemen models we e
de eloped, using 3-D solid elemen s o 3-D beams elemen s. All he models
assume ha he mason y s uc u e is homogeneous and in o de o conside he
ma e ial non-linea beha iou – including c ushing and c acking – di e en
cons i u i e models we e used. Fu he mo e, beam models ook in o accoun he
s uc u al esponse unde cyclic loading. These analyses yielded signi ican
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Table 3: E ec i e modal masses.
Figu e 5: Modal shapes.
in o ma ion on he local and global collapse mechanism p edic ions. P e ious
ime-his o y dynamic analyses a e e alua ed o calib a e he non-linea esponse,
and o ake in o accoun ha c ack opening may in oduce nume ical ins abili ies.
S uc u al S udies, Repai s and Main enance o He i age A chi ec u e XI 623
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