DYNAMIC IDENTIFICATION AND SEISMIC ANALYSIS
OF THE “SERRA DO PILAR” MONASTERY CHURCH
An ónio A êde1, Celes e Almeida1, Aníbal Cos a1, Jo ge Rod igues2 and Al edo C. Cos a2
(1) FEUP – Facul y o Enginee ing o Po o Uni e si y
Ci il Enginee ing Depa men – S uc u al Di ision
R. D . Robe o F ias, s/n, 4200-465 Po o, Po ugal
E-mail: [email p o ec ed]
(2) LNEC - Na ional Labo a o y o Ci il Enginee ing
S uc u es Depa men (DE)
A . do B asil, 101, 1700-066 Lisboa, Po ugal
E-mail: [email p o ec ed]
ABSTRACT
This pape p esen s pa o he wo k de eloped o he
seismic beha io s udy o an ancien s uc u e, o e 400
yea s old. The chu ch s uc u e was nume ically modeled
ia he ini e elemen me hod, using a h ee dimensional
model wi h pa ame e s calib a ed by expe imen al es ing. In
si u and labo a o y es s on ex ac ed samples we e
pe o med, and dynamic es s we e ca ied ou o modal
iden i ica ion and s uc u al s i ness calib a ion. The seismic
analysis was pe o med in wo calcula ion phases, unde he
ac ion o a i icially gene a ed accele og ams ep esen a i e
o he local seismici y. Resul s o linea elas ic dynamic
calcula ions allowed he global beha io o be analyzed and
p o ided he inpu o mo e de ailed local analyses o
s uc u al pa s whe e he non-linea beha io was
conside ed. Finally, he seismic ulne abili y o he s uc u e
is b ie ly add essed and discussed.
1 INTRODUCTION
The s uc u al beha io and sa e y assessmen o ancien
cons uc ions is becoming a esea ch opic o inc easing
conce n in iew o he alue and amoun o his o ical
he i age o be p ese ed.
Among all he possible loadings ha may be conside ed, he
seismic ac ion is, o su e, one o he mos impo an due o
i s de as a ing e ec s and un o eseeable na u e. Mo eo e ,
he special ea u es o seismic loading, o en equi ing
s uc u al analyses o he whole s uc u e, ende e en mo e
complex he s udy o his ype o cons uc ions.
The as e olu ion o echnological and compu a ional ools
has allowed a signi ican de elopmen o sophis ica ed
beha io models and es ing echniques sui able o he
analysis o ancien s uc u es. No wi hs anding he
conside able scien i ic ad ances in his ield, se e al
di icul ies s ill pe sis mainly ela ed wi h he geome ic
complexi y and la ge dimensions o he p oblem, he
a iabili y o ma e ial p ope ies, he lack o knowledge
abou he o iginal cons uc ion echniques and he possible
subsequen in e en ions in he s uc u e.
In his con ex , he p esen pape deals wi h he dynamic
cha ac e iza ion and seismic analysis o he “Se a do Pila ”
monas e y chu ch loca ed nea by Po o, Po ugal. Fo i s
his o ical impo ance and pa icula ea u es, his 424 yea s
old building is a good example o he use o seismic
analysis models in ancien s uc u es o la ge dimensions.
As desc ibed la e , due he geome ic and s uc u al
complexi y o he monumen , a simpli ied analysis
me hodology was adop ed. A i s linea elas ic calcula ion
o he whole s uc u e allowed he assessmen o he global
beha io , a e which he local esponse o some pa s
(a ches and bea ing columns) was u he analyzed by
ecou se o mo e de ailed calcula ions in ol ing he non-
linea beha io o join s be ween s one blocks.
The s uc u al model was de ined on he basis o he ini e
elemen me hod using he gene al-pu pose compu e code
CASTEM 2000 [1]. De ailed geome ic da a we e a ailable
and gene a ed such ha isible s one blocks could be
simula ed by means o solid elemen s duly indi idualized in
o de o allow he modeling o he join s be ween blocks.
The es ima ion o mechanical and physical p ope ies o
ma e ials was suppo ed by in si u and labo a o y es s on
samples ex ac ed om he s uc u e. In pa icula , dynamic
iden i ica ion es s we e pe o med o e alua e i s dynamic
cha ac e is ics, allowing o calib a ion o he s i ness used
in he global linea analysis. These es s we e pe o med
unde bo h ambien ib a ion and mic o-explosions
p oduced nea by he s uc u e, he modal iden i ica ion o
he s uc u e ha ing been pe o med using wo equency
domain me hods [2] o ou pu only modal iden i ica ion
applied o he measu ed esponses.
In he ollowing sec ions a b ie desc ip ion o he “Se a do
Pila ” monas e y chu ch is i s gi en, along wi h some
commen s on he nume ical modeling. Then he dynamic
es s a e add essed, desc ibing he ins umen a ion, he
es ing sequence and he analysis o es esul s. Nex , he
nume ical modal analysis is p esen ed, he co esponding
esul s being discussed h ough compa ison wi h modal
p ope ies ob ained om expe imen al es s. Finally, he
seismic analysis is add essed, mainly ocusing on he
adop ed me hodology, he esul s being p esen ed and
b ie ly discussed.
2 THE “SERRA DO PILAR” MONASTERY CHURCH
2.1 His o ical backg ound
The “Se a do Pila ” monas e y was ounded back in 1537
and is loca ed in he S. Nicolau hill, in he his o ical cen e o
Vila No a de Gaia. The cons uc ion wo ks de eloped
slowly, such ha only in 1567 he i s monas e y was
ac ually buil . In 1598 i was decided o eplace he chu ch
by a new and la ge one ha inally opened in 1678.
Compa ing o he cu en a chi ec u e by ha ime in he
coun y, his cylind ical chu ch (made ou o local g ani e
s one) was an o iginal op ion, p obably inspi ed in he Rome
Pan heon as e idenced in Figu e 1 whe e ou side and
inside iews o he chu ch a e included.
b)
a)
c)
Figu e 1: The “Se a do Pila ” monas e y chu ch.
(a) Ou side, b) inside and c) he dome s uc u e
Due o i s p i ileged loca ion, igh in he sou h bank o he
Dou o i e and acing he his o ical cen e o Po o, he
monas e y was used as o ess du ing he F ench in asions
and he libe al wa s, leading o a e y deg aded s a e e en
u he agg a a ed du ing he 19 h cen u y. Since 1927,
upon a semi- uin s a e, he Po uguese ins i u ion o
monumen conse a ion (DGEMN – “Di ecção Ge al dos
Edi ícios e Monumen os Nacionais”) has been pe o ming
econs uc ion and ehabili a ion wo ks in he monumen , in
o de o p ese e his ema kable piece o a om he
enaissance.
2.2 S uc u al disc e iza ion and nume ical modeling
The “Se a do Pila ” monas e y chu ch is a 29.6m high
cylind ical shaped building made o s one block mason y,
wi h an ex e nal adius a ying be ween 15.7m and 14.6m,
and co e ed by a 0.60m hick hemi-sphe ical dome o
in e nal diame e 23.0m. On he op o he dome and laying
on i s inne ing, ou columns 4.0m high and sepa a ed by
windows gi e suppo o ano he small dome ha comple es
he oo s uc u e (Figu e 1-c)). Inside he e a e eigh
bu esses (16.8m high) placed in be ween small chapels
(Figu e 1-b)) de ined by a ches suppo ing he windows. In
he main chapel zone he e is a la ge a ch (13.38m high)
adjacen o a aul wi h 14m heigh which co e s he main
al a zone de eloping along a ec angula shaped a ea.
Ou side and la e ally, he e a e some o he small buildings
o negligible impo ance o he p esen s udy. Figu e 2
gi es o e all and schema ic iews o he chu ch and
su ounding cons uc ions.
a)
b)
Figu e 2: Schema ic ep esen a ions o he monas e y.
(a) F on al ele a ion and (b) longi udinal sec ion
The nume ical modeling in ol ed a i s s age o geome ic
de ini ion o he s uc u al elemen s, based on a ailable da a
om DGEMN and on addi ional opog aphic su ey. These
elemen s consis ed o he bu esses, he a ches, he ing
abo e he a ches and he dome, whe e he s one block
pa e n was clea ly isible so as o allow a mo e igo ous
disc e iza ion in o de o espec he exis ing join s be ween
blocks. The emaining zones a e plas e ed and we e ound
o be made o e y i egula s one mason y; o ha eason
hey a e designa ed as ilings.
Based on he geome ic and opog aphic da a, hal mesh o
he chu ch s uc u e was de ined (Figu e 3-a)) using he
compu e code CASTEM 2000 [1], assuming s uc u al
symme y ela i e o he e ical plan c ossing he en ance
and he main al a zone h ough he cen al axis o he
dome. Then, using he symme y ope a o a ailable in he
code, he comple e mesh was ob ained as illus a ed in
Figu e 3-b), whe e bo h he s one blocks and he illing
zones we e simula ed by ou node solid elemen s, wi h due
ca e o isola e each block elemen s. This p ocedu e allowed
join s be ween and abo e blocks in he a ches o be
disc e ized using join elemen s based on h ee node
iangula elemen s [3].
a) b)
Figu e 3: Nume ical modeling o he chu ch. (a) Hal -
mesh (inside iew) and (b) o al mesh (ou side iew)
Conce ning ma e ial p ope ies, se e al labo a o y and in
si u expe imen al es s we e ca ied ou [3], allowing i s
es ima ions o mass densi y and de o mabili y pa ame e s,
such as Young modulus and Poisson a io. Fo he mass
densi y, alues anging om 20 o 25 kN/m3 we e adop ed,
while o he Young modulus a wide ange o alues
be ween 2 GPa (in he illing zones) and 20 GPa (in he
isible s one blocks) was conside ed along wi h an a e age
cons an Poisson a io o 0.2.
3 DYNAMIC TESTS OF THE CHURCH STRUCTURE
3.1 Ins umen a ion
The dynamic es s o he Se a do Pila monas e y chu ch
we e ca ied ou using he ollowing equipmen :
− 12 accele ome e s FBA-11 om Kineme ics;
− 3 a iable capaci ance accele ome e s om Ende co
(model 7290A-2) wi h co esponding powe supply
and signal condi ioning uni s;
− 1 pe sonal compu e wi h a da a acquisi ion ca d AT-
MIO-16XE-10 om Na ional Ins umen s, wi h 16 bi s
A/D con e sion;
− 1 chassis BNC-2090 om Na ional Ins umen s, wi h
16 channels, connec ed o he DAQ ca d by means
o a sui able cable;
− cables o powe and signal ansmission.
The FBA-11 accele ome e s a e uniaxial o ce balance
accele a ion senso s om Kineme ics. Due o hei dynamic
ange o 135 dB, low noise pe o mance and bandwid h ha
goes om DC o 50 Hz, hey a e app op ia e senso s o he
dynamic es ing o ci il enginee ing s uc u es.
In o de o use he FBA-11 accele ome e s, an adequa e
sys em o powe supply and signal condi ioning was
de eloped a LNEC. This sys em comp ises 4 powe supply
and signal condi ioning uni s. Each o hese uni s can be
connec ed o h ee accele ome e s and con ains wo 12V
ba e ies, analog il e s and ampli ie s wi h use selec able
gain ac o s. The uni s a e connec ed o he senso s wi h
ela i ely sho cables (20 m) and o he da a acquisi ion
boa d wi h long cables ha , a he p esen , ange om 50 m
up o 200 m. Be ween hese long cables and he da a
acquisi ion sys em he e is a small box o con e he h ee
pai s long cables o BNC e minals.
In he es s o he Se a do Pila monas e y chu ch, se en o
he FBA-11 accele ome e s had a ac o y con igu ed ull-
scale ange o ±1g and he o he i e had ±4g. The
co esponding gain ac o s a he powe supply and signal
condi ioning uni s we e se -up, espec i ely, o 50 and 200.
The FBA-11 accele ome e s ha e an ou pu o ±2.5V, while
he DAQ Ca d AT-MIO-16X-10 has an inpu o ±10V. Wi h
he selec ed ange and gain ac o s, he minimum
accele a ion ampli ude ha could be measu ed du ing he
es s was 0.0024 mg. The da a acquisi ion was pe o med
wi h so wa e de eloped in LabView [4].
3.2 Tes ing sequence
The es ing campaign [3] consis ed in he measu emen o
accele a ions induced in he chu ch s uc u e by ambien
sou ces o exci a ion (like wind and a ic in nea by oads)
and by explosions o low powe de ona o s bu ied in he
a ea su ounding he chu ch.
Th ee es s we e ca ied ou , co esponding o di e en
loca ions o he accele ome e s h oughou he s uc u e as
ep esen ed in Figu e 4.
n2p7
n2p6
n2p8
n4p4
n4p2
n4p3
c1 n4p3
le el 4
n4p2
Tes se -up 3
n1p6
n1p7
n1p6
n1p8
n1p7
n1p5
n2p6
n4p4
n4p1
n1p5
n1p4
c3
n1p4
n1p3
le el 1
c2
c4
n1p1
n1p1
n1p2
n1p3 n1p2
n2p7
n1p8
n1p1
le el 4
le el 1
n4p4
n4p3
n4p2
c1 n4p3
le el 4
n4p2
Tes se -up 2
c1
n4p4
n4p2
n4p3
n4p3
le el 4
n4p2
Tes se -up 1
n3p7
n3p6
n3p8
n2p5
n3p6
n4p4
n4p1
n2p5
n2p4
n2p4
n2p3
c3
le el 2
c2
c4
n2p1
n2p2
n2p1
n2p3 n2p2
n3p7
n3p5
n3p4
n4p4
n4p1
n3p5
n3p4
n3p3
c3
le el 3
c2
c4
n3p1
n3p2
n3p1
n3p3 n3p2
n2p8
n2p1
le el 4
n3p8
n3p1
le el 4
le el 2
le el 3
E
W
NS
Figu e 4: Ins umen ed poin s o he h ee di e en
es ing con igu a ions
In ac , h ee di e en con igu a ions we e conside ed in
which accele ome e s we e mo ed sequen ially om he
uppe o he lowe le el o he s uc u e as shown in
Figu e 4. Howe e , o any o he h ee con igu a ions, i e
accele ome e s we e kep ixed in he op o he chu ch
dome in o de o ha e e e ence measu emen s allowing o
es ima e he ampli ude and phase ela ions be ween he
ins umen ed poin s. Fou o hese i e accele ome e s
co esponded o wo adial di ec ions, whe eas he
emaining one was posi ioned pe pendicula ly o one o
hose di ec ions.
Fo each es se -up, and due o he limi ed numbe o
a ailable accele ome e s, mainly adial componen s we e
measu ed al hough a leas one angen ial componen was
also ob ained o each le el. Thus, a each s age, eigh
adial componen s we e eco ded, co esponding o he
eigh bu esses o he s uc u e, allowing o measu e bo h
ansla ional and o aliza ion modes o he chu ch.
In each es se -up a o al o abou 9 minu es o ambien
ib a ion measu emen s we e eco ded wi h a sampling
equency o 200 Hz. A e eco ding he ambien ib a ion
da a, a mic o-explosion es was pe o med, and he
co esponding accele a ions in he s uc u e we e eco ded
wi h a sampling equency o 500 Hz.
3.3 Analysis o esul s
Resul s in e ms o eco ded accele a ions ha e shown a
qui e s a iona y esponse unde ambien ib a ion, as
illus a ed in Figu e 5-a). Wi h maximum accele a ion
ampli ude a ound 0.2 mg, his ype o esponse was
somewha unexpec ed o ha kind o exci a ion.
The esponse o bo h he ambien ib a ion and he mic o-
explosions is also shown in Figu e 5-b), wi h an enla ged
ime scale. I is no ewo hy he la ge ampli ude o he signal
due o he mic o-explosion, and also he s a iona y
cha ac e is ic o he eco ded ambien ib a ions.
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
0 5 10 15 20
Time (seg.)
Accele a ion (mg)
a)
-4,0
-3,0
-2,0
-1,0
0,0
1,0
2,0
3,0
4,0
44,5 55,5 6
Time (seg.)
Accele a ion (mg)
b)
Figu e 5: Response o he n1p2 accele ome e due o
(a) ambien ib a ion and (b) explosion
The accele a ions eco ded in he es s we e analyzed o
modal iden i ica ion pu poses using he basic equency
domain me hod [2], implemen ed in a compu e p og am
using Lab iew [4], and he equency domain decomposi ion
me hod [2] implemen ed in he A emis so wa e package [5].
The basic equency domain me hod [2] in ol es, mainly, he
compu a ion o au o-spec a, cohe ence be ween di e en
measu emen poin s and H1 es ima es o he equency
esponse unc ions, also be ween di e en measu emen
poin s. The equency domain decomposi ion me hod [2]
consis s, basically, in a singula alue decomposi ion o he
spec al densi ies ma ix.
Be o e he applica ion o bo h modal iden i ica ion me hods,
he accele a ion eco ds we e p e-p ocessed wi h he
ollowing ope a ions: end emo al; band-pass il e ing
be ween 0.25 Hz and 12.5 Hz, wi h a 8 poles Bu e wo h
il e ; decima ion o he signals om he sampling a es o
200 Hz and 500 Hz o 25 Hz. The decima ion o he signals
implied a Nyquis equency o 12.5 Hz, which, acco ding o
a p elimina y ini e elemen analysis, would be enough o
include he main ib a ion modes o he chu ch in he modal
iden i ica ion analysis.
The a e age no malized powe spec al densi y (ANPSD)
was compu ed aking in o accoun he whole se o eco ds
and is depic ed in Figu e 6, wi h loga i hmic scale in he
o dina es. In he ANPSD p esen ed in Figu e 6, he e a e
wo p edominan peaks o he spec al densi y, o
equencies a ound 4.5 Hz and 6.8 Hz, bu he e a e also
o he less e iden peaks ha we e ca e ully analyzed in
e ms o he cohe ence and H1 equency esponse unc ion
es ima es o he di e en measu emen poin s in ela ion o
he e e ence ones.
0.63 Hz
4.44 Hz
3.52 Hz
3.08 Hz
6.79 Hz
9.52 Hz
8.64 Hz
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
0.0 2.0 4.0 6.0 8.0 10.0
F equency (Hz)
ANPSD
Figu e 6: A e age no malized powe spec al densi y
Figu e 7 shows he cohe ence be ween he esponse
accele a ions eco ded a poin s in he same e ical plan,
bu in wo di e en le els, namely a he op o he dome
(le el 4) and app oxima ely a hal -heigh o he bu esses
(le el 1). F om hese esul s i is e iden ha he cohe ence
alues a e e y close o 1 o equencies a ound 4.5 Hz
and 6.8 Hz, bu i is also possible o see ha , o
equencies o abou 3.1 Hz and 3.5 Hz, he e a e also high
alues o he cohe ence, al hough lowe han 1.
0.68 Hz
3.03 Hz
3.52 Hz 6.79 Hz4.49 Hz
8.64 Hz
0.0
0.2
0.4
0.6
0.8
1.0
0.0 2.0 4.0 6.0 8.0 10.0
F equency (Hz)
Cohe ence
Figu e 7: Cohe ence be ween eco ds a poin s n4p3
(le el 4) and n1p5 (le el 1)
Explosion
Ambien
Ambien
Fo a mo e conclusi e in e p e a ion o he es esul s in
e ms o modal iden i ica ion, i was qui e impo an o ob ain
a g aphical ep esen a ion o he ib a ion mode shapes
(ampli ude and phase ela ions be ween he di e en
measu emen poin s). This was done using bo h me hods
and coinciden esul s we e ob ained.
Figu e 8 shows he modal con igu a ions ha we e ob ained
using he A emis so wa e package [5], o he equencies
o 3.08, 3.52, 4.44 and 6.79 Hz, he i s wo co esponding
o ansla ional modes in he N-S and E-W di ec ions,
whe eas he las wo appea mo e di icul o unde s and.
Howe e , a mo e de ailed inspec ion o mode shape
anima ions sugges s an o aliza ion end in hose
con igu a ions.
a) b)
c) d)
Figu e 8: Plan iews o modal con igu a ions.
a) 3.08 Hz, ansla ion N-S; b) 3.52 Hz, ansla ion E-W;
c) 4.44 Hz, o aliza ion; d) 6.79 Hz, o aliza ion
Al hough wi h some opics equi ing u he in es iga ion,
and possibly addi ional es ing o con i m he conclusions
ha we e d awn om he es s, he abo e desc ibed esul s
show a easonable compliance wi h hose ob ained wi h he
nume ical modal analysis add essed in he nex sec ion.
4. NUMERICAL MODAL ANALYSIS
The nume ical analysis o he compu a ion o equencies
and ib a ion modes was pe o med by ecou se o he
compu e code CASTEM 2000, using he mesh and alues
o ma e ial p ope ies e e ed in sec ion 2.
A i s ial wi h hose p ope ies led o calcula ed alues o
he wo i s equencies no a om hose expe imen ally
ob ained. A e li le adjus men s o he Young modulus, in
pa icula in he in ill zones whe e i is p one o signi ican
a iabili y, good ag eemen was ob ained be ween
nume ical and expe imen al esul s, a leas o he i s wo
modes. Table I includes he equency alues o he i s
i e modes o ib a ion, as ob ained om he nume ical
analysis, and also he expe imen ally es ima ed alues.
Mode F equencies (Hz)
Nume ical Expe imen al
1 3.13
(T ansla ion N-S) 3.08
(T ansla ion N-S)
2 3.54
(T ansla ion E-W) 3.52
(T ansla ion E-W)
3 4.21
(To sion) 4.44
(O aliza ion?)
4 6.07
(O aliza ion) 6.79
(O aliza ion?)
5 6.36
(O aliza ion) ----
Table 1: Na u al equencies: nume ical and
expe imen al
Acco dingly, he i s wo ib a ion modes ob ained om he
analysis a e illus a ed in Figu e 9, whe e a good ag eemen
can be con i med wi h he co esponding modes
expe imen ally eco ded and p esen ed in Figu es 8-a) and
8-b).
N
S
E
W
a) 3.13 Hz b) 3.54 Hz
Figu e 9: 1s and 2nd ib a ion modes, nume ically
ob ained (plan iew)
The o he h ee uppe modes (no illus a ed he ein) we e
ound o co espond essen ially o o sion mo ion (3 d mode)
and o o aliza ion con igu a ions (4 h and 5 h modes), which
seems o be in quali a i e ag eemen wi h he ype o he 3 d
and 4 h modes es ima ed om he expe imen .
5. SEISMIC ANALYSIS
5.1 Seismic ac ion
The seismic analysis o he “Se a do Pila ” monas e y
chu ch was pe o med in he ime domain, using as inpu
ac ion a se o i e a i icial accele og ams (pe di ec ion o
exci a ion) gene a ed o comply wi h he local seismici y o
Po o egion.
The Po uguese seismici y is mainly in luenced by wo ypes
o s ong-g ound mo ions, namely mode a e magni ude wi h
sho ocal dis ance ea hquakes (seismic ac ion ype I,
associa ed wi h in a-pla e e en s) and high magni ude wi h
la ge ocal dis ance ea hquakes (seismic ac ion ype II,

co esponding o in e -pla e e en s). This is e lec ed in he
design esponse spec a (and also powe spec a)
p esc ibed in he na ional s anda ds, which a e cu en ly
being adap ed o i he o hcoming Eu opean S anda d o
seismic design, he Eu ocode 8 (EC8) [6], by means o he
Na ional Applica ion Documen (DNA) [7].
A i icial accele og ams we e ob ained wi h 10s du a ion, in
compliance wi h he basic shape o he esponse spec a
p esc ibed in he e e ed documen (DNA) o he seismic
ac ion ype I (mo e demanding o he p esen s uc u e).
The peak g ound accele a ion o 0.1g ( o ha d soil) was
chosen acco ding o p e ious s udies [8] o a e u n pe iod
o 10000 yea s, which was conside ed app op ia e o an
ancien (o e 400 yea s old) s uc u e ha mus s and he e
o he nex gene a ions.
5.2 Analysis me hodology
Fo he en isaged analysis and due o he la ge dimensions
and complexi y o he chu ch s uc u e, a simpli ied analysis
me hodology was adop ed. This s a egy in ol ed wo
sepa a e bu dependen calcula ion phases in o de o
assess bo h he global s uc u al esponse and he local
beha io o some pa s o he s uc u e. Acco ding o his
objec i es, he wo calcula ion phases de eloped as ollows:
− 1s Phase – Linea Elas ic Global Calcula ion
The whole s uc u e was elas ically analyzed unde
he ac ion o sel -weigh and o h ee o hogonal
di ec ion accele og ams. The Newma k me hod was
used o in eg a e he dynamic equilib ium equa ions.
S esses in all s uc u al elemen s we e ob ained
and, pa icula ly o he blocks o he a ches and hei
columns, he equi alen nodal o ces we e calcula ed
and s o ed as a ime- a ying ec o ield.
− 2nd Phase – Non-Linea Local Analysis
The so-ob ained o ce ec o ield was hen applied
in he subs uc u e o a ches and columns, in o de
o pe o m non-linea s a ic calcula ions o each s ep
o load a ia ion. The solid elemen s o his educed
mesh we e s ill assumed beha ing linea elas ically,
whe eas he in e aces be ween s one blocks we e
simula ed by ze o hickness join elemen s wi h non-
linea beha io [3].
Fo seismic ulne abili y assessmen pu poses, se e al
non-linea s a ic calcula ions we e pe o med in he 2nd
phase co esponding o inc easing in ensi ies o he seismic
ac ion. This was done by mul iplying he ime- a ying ec o
ield ob ained om he 1s calcula ion phase by he ollowing
sequence o ac o s 0.5, 1.0, 1.5, 2.0 and 2.4, he la e
ha ing been condi ioned by con e gence p oblems possibly
e lec ing loss o s uc u al equilib ium.
5.3 Resul s
A la ge amoun o esul s was ob ained, some o which a e
e y b ie ly e e ed nex in e ms o a e age peak alues o
p incipal ( ensile and comp essi e) s esses and o adial,
angen ial and e ical displacemen s. A e age alues we e
aken om he maximum esul s co esponding o he i e
accele og ams conside ed.
The linea elas ic calcula ion allowed a i s insigh in o he
s ess s a e unde he p esc ibed seismic load. The a e age
peak alues o maximum p incipal ensile and comp ession
s esses we e ound o be 2.30 MPa and 3.33 MPa,
espec i ely, occu ing e y localized nea he window
openings. In he emaining pa s o he s uc u e signi ican ly
lowe p incipal ensile s esses a e ound, no exceeding
0.37 MPa in he subs uc u e o he a ches and columns
(app oxima ely a mid-heigh o he columns), whe eas he
p incipal comp essi e s esses show peak alues o
2.52 MPa in he a ches and columns.
The maximum de o med shape was mainly in luenced by
he 1s and 2nd modes o ib a ion as e idenced by he peak
displacemen en elopes shown in Figu e 10. The maximum
displacemen s o he op o he dome (no including he
small uppe dome) we e ound o be abou 1.0 cm in bo h
adial and angen ial di ec ions and 0.7 cm downwa ds in
he e ical di ec ion. These a e a he small displacemen s,
which co espond o a o al ho izon al d i o 0.034% and
e lec he e y la ge s i ness o his s uc u e.
Figu e 10: Peak displacemen en elopes om linea
elas ic analysis
F om he non-linea calcula ions, a mo e de ailed analysis
was ca ied ou o he a ches and espec i e columns,
pa icula ly in e ms o p incipal s esses and displacemen s.
Al hough calcula ions we e made o i e inc easing
in ensi ies, esul s jus ocus on in ensi y 1.0 and 2.4.
Conce ning p incipal s esses, he maximum ensions o
0.38 MPa and 1.15 MPa we e ound in he columns,
espec i ely o 1.0 and 2.4 in ensi y; Figu e 11 e e s o he
ensile s ess dis ibu ion o he highe in ensi y. Simila ly,
comp essi e s esses, occu ing nea he column bases,
ange om 2.52 MPa and 4.42 MPa, o he same seismic
in ensi ies. The s one blocks o he a ches exhibi much
lowe ensile and comp essi e s esses.
I is wo h men ioning ha comp essions s ay a bellow he
s one s eng h (ac ually, s eng h alues abo e 70 MPa
we e ound in comp ession es s) bu ensile s esses in he
blocks, al hough s ill compa ible wi h he s one ensile
s eng h (abou 3 MPa), sugges ha inc easing non-
linea i y occu ed in he join s be ween blocks as he
seismic in ensi y was inc eased. Ac ually, he 0.38 MPa
ensile s ess in he blocks means ha sligh non-linea i y
occu s in he adjacen join s bu , o he seismic in ensi y
2.4, he block ensile s ess o 1.15 MPa equi es in ense
non-linea i y and opening o join s.
Figu e 11: Maximum ensile s esses (1.15 MPa) in
blocks o a ches and columns (in ensi y 2.4)
The abo e men ioned non-linea i y was con i med by he
inspec ion o de o med shapes o he a ches as he seismic
in ensi y is inc easing, as shown in Figu e 12-a).
-80,0
-60,0
-40,0
-20,0
0,0
20,0
40,0
60,0
80,0
00,5 11,5 22,5 3
In ensi y
Displacemen s (mm)
adial
angencial
e ical
e ical
angencial
adial
Figu e 12: a) Maximum de o med shape o a ches and
columns; b) Vulne abili y unc ions o a ch
displacemen s
Vulne abili y unc ions o a ches displacemen s we e plo ed
o adial, angen ial and e ical di ec ions, leading o he
cu es shown in Figu e 12-b). These ela ions be ween
peak esponse alues and he seismic in ensi y clea ly show
a p onounced non-linea s uc u al esponse o in ensi y
alues abo e 1.5. Mo eo e , he maximum in ensi y (2.4)
ha was allowed un il con e gence p oblems a ose (mos
likely due o loss o equilib ium), led o a peak adial
displacemen o 8 cm o he a ch key s one. This means
abou 0.98% adial d i , which is al eady a conside able
alue o his kind o s uc u es, bu p oduced by a seismic
ac ion mo e han wice he in ensi y o seismic e en s o
10.000 yea s e u n pe iod!!
The e o e he seismic sa e y o his s uc u e seems o be
qui e assu ed, which p obably migh ha e been al eady
p o ed by his o y. Ac ually, i has su i ed, appa en ly
wi hou signi ican damages, he s ong Lisbon ea hquake
in 1755 ha was clea ly el and p oduced hea y damages
in he a no h o Po ugal.
6. CONCLUSIONS
The p esen wo k has shown he possibili ies o combining
nume ical analysis based on pa ame e s calib a ed by c oss
in o ma ion om labo a o y and/o in si u es ing and om
dynamic iden i ica ion es s in la ge and old s uc u es.
S a ing om a ca e ully chosen nume ical model whe e
dis inc beha io zones a e duly indi idualized and using
ma e ial p ope ies adequa ely selec ed om local es ing, i
is possible o compa e compu ed modal cha ac e is ics wi h
hose ob ained in dynamic es ing. The compa ison allows
s i ness pa ame e uning which, o he p esen case, led
o e y good ag eemen o nume ical and expe imen al
p edic ions.
Despi e he high s i ness o he s uc u e, dynamic es s
unde ambien ib a ion and mic o-explosions allowed he
i s equencies and mode shapes o be de e mined
h ough bo h he basic equency domain me hod and he
equency domain decomposi ion echnique. Howe e ,
some opics emain o be u he cla i ied, pa icula ly
ela ed wi h wo highe and e y exci ed equencies.
The adop ed me hodology o seismic analysis is pa icula ly
app op ia e as a simpli ied and app oxima e echnique o
la ge s uc u es whe e ull con ol o he non-linea beha io
emains a qui e hea y (may be s ill impossible!!) ask o be
pu sued. A easonable comp omise is he e o e ob ained
be ween compu a ional e o and le el o esul s achie ed.
In his con ex , he global beha io o he chu ch s uc u e
was assessed o he si e seismic ac ion and a mo e
de ailed local analysis allowed o con i m i s obus ness and
capaci y o wi hs and s ong g ound mo ions.
ACKNOWLEDGEMENTS
The au ho s wish o acknowledge he Po uguese ins i u ion
o monumen s and na ional buildings (DGEMN) o all he
suppo gi en du ing his wo k.
REFERENCES
[1] CEA, Cas em 2000 – Guide d’u ilisa ion, CEA, F ance,
1990.
[2] Ven u a, C. and B incke , R., Modal Iden i ica ion o
Ou pu Only Sys ems – Cou se No es, Sho Cou se,
Uni e sidad Poli ecnica de Mad id, June 5-6, 2000.
[3] Almeida, C., Análise do Compo amen o da Ig eja do
Mos ei o da Se a do Pila sob a Acção dos Sismos,
Mas e Thesis, Faculdade de Engenha ia da
Uni e sidade do Po o, Po o, 2000. (in Po uguese)
[4] Na ional Ins umen s, LabView 6i Re e ence
Manuals, 2000.
[5] S uc u al Vib a ion Solu ions, ARTeMIS Ex ac o –
Ambien Response Tes ing Modal Iden i ica ion
So wa e, S uc u al Vib a ion Solu ions (SVS) ApS,
Aalbo g, Denma k, 2000.
[6] Eu ocode N. 8, Design o P o isions o Ea hquake
Resis an S uc u es, Pa 1-1, 1-2, 1-3, p ENV 1998-
1-1, 1-2, 1-3 – CEN/TC250/SC8, 1994.
[7] DNA, Na ional Applica ion Documen , p o isional
e sion o CT115 app o al, LNEC, Lisbon, 1998.
[8] Campos Cos a, A. P. N., A Acção dos Sismos e o
Compo amen o de Es u u as, Phd Thesis, Faculdade
de Engenha ia da Uni e sidade do Po o, Po o, 1993.
(in Po uguese).