Jou nal o Cul u al He i age 71 (2025) 334–345
Con en s lis s a ailable a ScienceDi ec
Jou nal o Cul u al He i age
jou nal homepage: www.else ie .com/loca e/culhe
O iginal a icle
Gene a i e modelling o Monop e os and Tholos emples using
exis ing da a: The case s udy o Ves a emple in Ti oli
Annalau a Vuo o
a
,Ma co F. Funa i
b , ∗, Shaghayegh Ka imzadeh
a
,PauloB. Lou enço
a
a
Depa men o Ci il Enginee ing, ISISE, ARISE, Uni e si y o Minho, Guima ães, Po ugal
b
School o Enginee ing, Uni e si y o Su ey, Guild o d, UK
a i c l e i n o
A icle his o y:
Recei ed 8 Feb ua y 2024
Accep ed 9 Decembe 2024
Keywo ds:
Gene a i e p og amming
Visual p og amming
3D modelling
Seismic assessmen
a b s a c
This pape p esen s a no el me hod o gene a ing geome ic models o a chi ec u al he i age in he ab-
sence o a digi al su ey. The me hod employs a Gene a i e P og amming (GP) algo i hm o geome ic
model gene a ion, wi h he Temple o Ves a in Ti oli chosen as a case s udy. F ancesco Pi anesi’s 18 h-
cen u y e chings a e u ilised as e e ences o iden i y he a chi ec u al layou and modula i y. The e ec-
i eness o he p oposed gene a i e wo kflow is highligh ed h ough i s ime efficiency and he eusabili y
o he algo i hm. The wo kflow includes he capabili y o gene a e an expo file sui able o s uc u al
simula ion so wa e packages. The gene a ed geome ic model is hen used o conduc nonlinea dynamic
analysis using a concu en con inuous/block-based app oach wi hin a Fini e Elemen en i onmen . The
simula ions a e pe o med wi h he s uc u e in i s cu en s a e and do no accoun o e ofi ing in e -
en ions, i.e. ancho ages and ie ods a e no aken in o accoun . The nume ical model e eals how local
ailu e mechanisms o columns and en abla u e a ec he s uc u al sa e y o he Ves a emple.
©2024 The Au ho (s). Published by Else ie Masson SAS.
This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ )
In oduc ion
Today, echnologies o digi al geome ic modelling o exis ing
buildings enable he c ea ion o accu a e ep esen a ions, o en e-
e ed o as Digi al Twins (DTs) [ 1–4 ]. E en i o en used wi hin
ecen li e a u e, his defini ion can be misleading [ 5 , 6 ]; hence, he
e m “Geome ic Digi al Twin” is hus mo e fi ing o emphasising
he geome ic ea u es wi hou encompassing he b oade unc-
ional and da a-d i en dimensions o a comple e DT [ 7 ].
E en hough s a e-o - he-a p ocesses enable high le els o ge-
ome ic fideli y [ 8 ], i emains c ucial o le e age a ailable ools
o s eamline and op imise asks ha would o he wise be com-
plex and ime-consuming. Reali y-based modelling, based on lase
scanning o digi al pho og amme y, is ecommended o a chi-
ec u al he i age whe e s uc u al elemen s canno be accu a ely
ep esen ed using geome ic p imi i es [ 9–14 ]. The mos ad anced
compu a ional ools now enable inc eased au oma ion in bo h
da a acquisi ion and p ocessing phases. These models can be ap-
plied o cap u ing ea u es c ack pa e ns [ 15–17 ], o e en he ull
s uc u al geome ies [ 18 , 19 ]. Howe e , eali y-based app oaches
a e s ill no ully au oma ed, a e challenging o implemen o
la ge buildings, and a e ime-consuming. These limi a ions hinde
∗Co esponding au ho .
E-mail add ess: m. una i@su ey.ac.uk (M.F. Funa i) .
hei widesp ead applica ion in la ge-scale he i age p ese a ion
p ojec s.
The e o e, simplified me hods ha s ill inco po a e ad anced
geome ic modelling echniques can be used [ 20 , 21 ]. Fo ins ance,
mason y mic os uc u e can be gene a ed by algo i hms and hen
used as inpu o nume ical simula ions [ 22–24 ]. A he building
scale, objec -based pa ame ic modelling is pa icula ly e ec i e
o egula s uc u es cha ac e ised by modules, epe i ions, and
symme ies [ 25 ], significan ly accele a ing he modelling p ocess.
Inpu da a can be sou ced om a ailable documen a ion, such as
his o ical eco ds and d awings [ 26 , 27 ], which is especially ad-
an ageous in si ua ions whe e he si e is no accessible [ 28–30 ].
When he geome ical layou pe mi s, isual and ex ual p og am-
ming languages (V/T PL) [ 31 , 32 ] can be employed o gene a e as e
and mo e efficien models. While TPL enables he w i ing o exe-
cu able code o gene a ing geome ic model ou pu s and neces-
si a es a high le el o expe ise, VPL u ilises a flowcha sys em
c ea ed h ough nodes and connec ions, making hem mo e acces-
sible o p ac ising enginee s and a chi ec s [ 31 ]. When combined
wi h he concep o Gene a i e P og amming (GP), VPL pa ame ic
modelling has demons a ed efficiency ac oss a ious enginee ing
fields, hough i s applica ions o his o ical mason y buildings e-
main limi ed in he li e a u e [ 25 , 31 , 33 , 34 ].
In his con ex , a chi ec u es buil du ing he classical e a o -
en comp ise elemen s a anged in he space acco ding o specific
h ps://doi.o g/10.1016/j.culhe .2024.12.005
1296-2074/© 2024 The Au ho (s). Published by Else ie Masson SAS. This is an open access a icle unde he CC BY license ( h p://c ea i ecommons.o g/licenses/by/4.0/ )
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 1. Wo kflow o he p oposed app oach ( he images a e ela ed o he case s udy p esen ed in his wo k and a e in ended o illus a i e pu poses).
modula layou s, acili a ing hei in e p e a ion h ough a me o-
logical app oach. By compa ing he ecu ence o elemen s wi h
he suppo o known ancien uni s o measu emen [ 35 ], i be-
comes easible o analyse he geome ic layou and unco e he
a chi ec u al composi ion ules employed du ing he cons uc ion.
Such an app oach has p o en e ec i e in he s udy o a Roman
b idge da ing o he 2nd cen u y BC, a la e Roman se lemen in
Egyp [ 36–38 ], and a Roman esidence in Cyp us [ 39 ], among o h-
e s.
This wo k explo es he po en ial o 3D pa ame ic modelling
o a chi ec u al he i age using GP in o med by w i en documen s
and exis ing su eying. A modelling wo kflow is de eloped and
alida ed using he Ves a Temple in Ti oli, I aly, as a p oo o con-
cep . The 3D model ob ained is subsequen ly es ed o applicabil-
i y o s uc u al simula ions. Specifically, nonlinea dynamic anal-
yses a e pe o med o assess he s uc u e’s seismic esponse [ 40 ].
The pape is o ganised as ollows: a e add essing he p ob-
lem o geome ical modelling o his o ical mason y buildings and
in oducing he amewo k in Sec ion In oduc ion , he de eloped
gene al me hodology is desc ibed in de ail in Sec ion Me hodology
o e iew . The p oposed amewo k is es ed in Sec ion Applica ion
o he me hodology o a holos emple . Final ema ks and sugges-
ions o ex ending he applica ion o he p oposed amewo k a e
p o ided in Sec ion Conclusion .
Me hodology o e iew
This wo k aims o de elop a me hodology o he 3D pa a-
me ic modelling o a chi ec u al he i age using exis ing da a. Due
o he a chi ec u al ea u es, s a e o p ese a ion, and accessibil-
i y, he di ec acquisi ion o geome ical in o ma ion is no always
easible. Howe e , ob aining geome ical models ha pe o m e -
ficien ly acco ding o hei in ended use has become an impe a-
i e s ep o all conse a ion- ela ed applica ions. The e o e, his
s udy aims o op imise he geome ical modelling phase o a chi-
ec u al he i age, inco po a ing mo phological cha ac e is ics in o
a pa ame ic model in o med by exis ing da a, such as his o ical
pho og aphs, epo s, p e ious su eys, and d awings. A wo kflow
based on gene a i e algo i hms o modelling geome ic compo-
nen s is implemen ed in a VPL, enabling he de elopmen o a p o-
cedu e ha minimises e o s and o e s high eusabili y o mod-
elling simila layou s.
To achie e his ision, his s udy le e ages he po en ial o GP.
In pa ame ic design, he shapes o elemen s a e defined by spe-
cific pa ame e s, wi h geome ic ela ionships algo i hmically ex-
p essed o a icula e he a chi ec u al composi ion [ 41 ]. Specifi-
cally, gene a i e code is de eloped using a ional ules ha define
he dis ibu ion layou o hese elemen s [ 25 , 42 ].
The inpu consis s o geome ical in o ma ion ob ained om ex-
is ing documen s and d awings, whe eas he ou pu is a 3D ge-
ome ical model o he in es iga ed asse . The pipeline s eps a e
ou lined below and schema ised in Fig. 1 :
1. Da a acquisi ion om exis ing sou ces.
2. Geome ical analysis o he s uc u e. I allows o he as-
sessmen o i s sui abili y o a pa ame ic modelling ap-
p oach by iden i ying (i) en i ies, (ii) sub-en i ies, (iii) mod-
ules and epe i ions, and (i ) symme ies o he pa ame ic
disc e isa ion o he s uc u al componen s.
3. Implemen ins ance-based pa ame ic componen s (sub-
en i y, S-E) using a gene a i e modelling pa adigm imple-
men ed in a isual p og amming en i onmen . Once he a-
335
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
ional ules adop ed by he ancien masons a e iden ified in
s ep 2, hey a e ansposed in o a se o coding ules using
Py hon p og amming language o ge he ull geome y o
he s uc u e.
4. Geome ical modelling o he s uc u e. The sub-en i ies a e
mo ed, copied, and assembled using he same sc ip o ob-
ain he en i ies (E) ha make up he emple.
5. In eg a ion o he geome ical ea u es wi h o he da a and
in o ma ion needed o he final use o he model (i.e. ma e-
ials, physical/mechanical/ he mal p ope ies, damage s a e,
a chi ec u al de ails and o namen s, en i onmen al con ex ,
bounda y condi ions, e c.).
6. Impo he geome ical model in a simula ion so wa e pack-
age o he final use, i.e. Building In o ma ion Modelling
(BIM), Ex ended Reali y (XR), clouds, s uc u al modelling,
he mal modelling, e c.
7. Usage o he model o specific pu poses, including a -
chi ec u al o his o ical econs uc ion, digi al p esen a ion
h ough ex ended eali y, he de elopmen o an in o med
model linked o da abases, and s uc u al analyses, e c.
Applica ion o he me hodology o a holos emple
The wo kflow desc ibed in Sec ion Me hodology o e iew has
been applied o he Ves a Temple in Ti oli, I aly. In his ins ance,
he geome ical model has subsequen ly been used o e alua e
he s uc u al beha iou o he asse unde seismic loading condi-
ions. A e comple ing s eps 1–4 o he wo kflow, he geome ical
model has been impo ed in o a s uc u al fini e elemen so wa e
package, whe e he mechanical p ope ies o ma e ials, as well as
bounda y and loading condi ions, we e defined. Nonlinea dynamic
analyses ha e been pe o med using g ound mo ions selec ed and
scaled in acco dance wi h he a ge esponse spec um o Ti oli
as seismic inpu . The analysis esul s p oduced collapse scena ios
ha ha e been in e p e ed o assess he s uc u al sa e y o he
emple and o gain insigh s in o i s s uc u al beha iou .
The Ves a Temple in Ti oli
The Ves a Temple in Ti oli is classified as holos , which is a ype
o ci cula emple ea u ing a colonnade and an inne cella [ 43 ].
Da ing o abou 80 BC, i consis s o a cella and a pe is yle, wi h
eigh een columns, o which only en s ill s and ( Fig. 2 (a), (b)).
The emple s ands on a s yloba e, o ci cula podium ( Fig. 2 (c)),
di ec ly suppo ing he columns wi h an A ic base ( Fig. 2 (d)) [ 44 ].
The Hellenis ic capi al ( Fig. 2 (e), (j)) is he mos s iking and alu-
able elemen o he emple, no able o i s double ow o cu ly-
lea ed acan hus lea es wi h he addi ion o long e n-like lea es
[ 45 ]. The en abla u e ( Fig. 2 ( )) has a plain a chi a e, a co nice
wi h simple mouldings and a ieze deco a ed wi h comple e ox-
heads connec ed by ga lands (see he econs uc ion in Fig. 2 ( i )),
opped by a ceiling wi h a double ow o co e s, ha ing a ose
in hei cen e ( Fig. 2 (g)). T a e ine, a local limes one, is he mos
used ma e ial ac oss he emple, acco ding o he use o he golden
age o Augus us. Only he cella is in opus e icula um , made by i -
egula polygonal u s ones and cemen ( Fig. 2 (j)). The cella o ig-
inally had h ee openings, namely he monumen al a e ine doo
and wo windows on i s le and igh sides.
The Ves a Temple was ex ensi ely s udied and su eyed du ing
he Renaissance. Howe e , hese ep esen a ions o en exhibi in-
consis encies and inaccu acies ega ding he emple’s a chi ec u al
de ails and dimensions. Acco ding o Richa dson [ 46 ], his a iabil-
i y is o be expec ed when di e en indi iduals measu e and in-
e p e an ancien , wea he ed uin using a ious ins umen s, es-
pecially du ing a ime o limi ed echnological esou ces. Some o
he his o ical documen s a e p esen ed in Sec ion Da a acquisi ion .
A c oss-compa ison o hese documen s has been conduc ed o al-
ida e he in o ma ion used o he geome ical modelling. Al hough
some da a may a y sligh ly, he di e en analyses sha e signifi-
can ea u es in common.
Da a acquisi ion
The wo kflow s a s wi h analysing geome ical da a om his-
o ical documen a ion (s ep 1 in he wo kflow o Sec ion Me hodol-
ogy o e iew ). While using exis ing documen s and d awings o e s
significan benefi s, i also has limi a ions, pa icula ly conce ning
buildings ha ha e been subjec ed o modifica ions. To mi iga e
hese issues, i is ad isable o c oss-compa e mul iple sou ces om
di e en pe iods, p io i ising ecu en and consis en in o ma ion.
The eliabili y o documen s also depends on he in ended use o
he geome ical model; in his case, accu acy in he dimensions o
s uc u al elemen s and hei p opo ional ela ionships is essen ial
o c ea ing nume ical models o pe o m simula ions efficien ly.
Se e al sou ces ha e been collec ed and compa ed. The e e -
ence sou ce o he knowledge o he emple has been he anal-
ysis p oposed by Palladio [ 45 ] un il he 17 h cen u y, when An-
oine Desgode z ʼs s udy pa ly supe seded i in 1682 [ 47 ]. F om
he 18 h cen u y onwa ds, he emple became one o he mos
s udied ancien a chaeological si es; he su eys by he English a -
chi ec s Geo ge Dance he Younge and Si John Soane a e wo h
men ioning. In I aly, a ull a chaeological su ey was ca ied ou
by F ancesco Pi anesi in he 1760s and published in 1780 in he
fi s olume o ’ Raccol a de’ empi an ichi’ [ 48 ]. Acco ding o Se-
bas iani [ 49 ], Pi anesi was he fi s o es o e a igo ous econ-
s uc ion o he emple, al hough including mino amends la e e-
mo ed by Ugge i [ 50 ] and Valadie [ 51 ]. In he 1980s, he a chi-
ec Ma k Wilson Jones p o ided an upda ed su ey, whose main
dimensions closely align wi h bo h Dance and Pi anesi’s d awings
[ 46 ]. A e c oss-checking he geome ical in o ma ion con ained in
he sou ces lis ed abo e, Pi anesi’s e chings ha e been chosen as
inpu da a o his s udy. They con ain d awings o he emple’s
plan, on and side ele a ions, and he econs uc ion o nume -
ous a chi ec u al and deco a i e de ails. All d awings we e dimen-
sioned using he Roman palmus maio , i.e. g ea e o majo palm,
equal o 22.34 cm, as a uni o measu emen .
Geome ical analysis
In his subsec ion, he c ea ion o he geome ical model (s eps
2–4 o he wo kflow in Sec ion Me hodology o e iew ) is desc ibed.
In s ep 2, he sui abili y o a pa ame ic app oach o he geome -
ical modelling o he Ves a Temple has been ackled by conduc -
ing a geome ical analysis aimed a iden i ying i) en i ies, ii) sub-
en i ies, iii) ecu ing modula elemen s, and i ) symme ies o
he pa ame ic disc e isa ion o he a chi ec u e o be modelled.
Fou main en i ies ( En
) ha e been iden ified (see Fig. 3 (a)): i) E1
– colonnade, ii) E2 – cella, iii) E3 – co e ed ceiling, and i ) E4 –
en abla u e. These en i ies a e composed o he p ima y a chi ec-
u al elemen s, i.e. sub-en i ies ( S-Eni
), whose s uc u al beha iou
influences he o e all seismic esponse o he emple, as opposed
o he o namen al elemen s, which ha e been neglec ed in his pa-
pe .
Secondly, a sea ch has been conduc ed o find a module o
me ological uni o define he key dimensions o s uc u al ele-
men s and pa ame e ise he emple’s o e all geome y. Conside -
ing ha a he ime o cons uc ion, elemen s’ dimensions we e
es ablished based on modula i y, each dimension has been defined
as a mul iple o he module. One should no e ha a ce ain ole -
ance due o i) ype o ma e ial, ii) p ecision o s onewo k, iii) s a e
o conse a ion, and i ) me hods and ools o measu emen [ 52 ],
336
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 2. The Ves a Temple in Ti oli. Uppe : (a) iew o he emple and he cli , (b) global iew. Middle: a chi ec u al de ails (c) podium, (d) column wi hou plin h, (e)
capi al, ( ) en abla u e, (g) co e ed ceiling, (h) cella in i egula opus e icula um. Bo om: econs uc ion o a chi ec u al de ails (i) Royal Academy lec u e ʼs d awing o he
en abla u e by Si John Soane a Si John Soane Museum wi h he econs uc ion o he ieze’s deco a ion, (j) ull-size eplica o he capi al a Si John Soane ʼs Museum
[
43 ].
mus be accoun ed o . As a as emples a e conce ned, his ba-
sic module is o en he diame e o he column. Indeed, in mos
o he his o ical desc ip ions o he Ves a Temple [ 46 , 53 ], he di-
mensions o he main elemen s we e exp essed as mul iples o
he column diame e and h ough a ios be ween he elemen s.
Fo example, he heigh o he capi al is he same as he diame-
e o he column [ 46 , 53 ]. The in e column is abou wo diame e s
[ 53 ], and he heigh o he column, including he base and capi-
al, is 9.5 diame e s [ 46 , 53 ], e c. ( Fig. 3 ). Some desc ip ions (Dance,
Soane, Wilson Jones [ 46 ]) p o ided he measu emen o he diam-
e e o he column, a ying be ween 74 and 77 cm, co esponding
o en Roman palmus mino , i.e. lesse o mino palm ( Fig. 3 (b)).
One palmus mino measu es 7.35–7.42 cm, oughly one-qua e o
a pes , i.e. oo , which is he basic module o he Roman sys em o
measu emen , equal o 29.4–29.7 cm [ 52 ]. While he palmus maio
seen in Pi anesi’s e chings has been egula ly used, he palmus mi-
no has been used in con ex s equi ing smalle uni s o desc ibe
he geome y modula i y. The e o e, as depic ed in Fig. 3 (a),(c), he
me ological uni o one palmus mino has been chosen as a linea
module ( m ) o pa ame e ise he en i e geome y. Consequen ly, all
he dimensions gi en in majo palms in Pi anesi’s d awings ha e
been con e ed in o mino palms, wi h a mino palm being abou
one- hi d o a majo palm (22.34 cm). An addi ional angula mod-
ule ( i ) co esponding o one in e column (20 °) has been iden ified
and used o he adial disc e isa ion o en abla u e and co e ed
ceiling, isible in Fig. 3 (d).
337
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 3. Geome ical analysis o he Ves a Temple: (a) iden ifica ion o he en i ies ( En ) and plan pa ame isa ion; (b) defini ion o he linea module ( m) equal o 1 Roman
palmus (7.41 cm); (c) ele a ion pa ame isa ion; (d) disc e isa ion o en abla u e and co e ed ceiling by using he angula module (i) equal o he in e column (20 °).
338
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Table 1
Abacus o en i ies (E), sub-en i ies (S-E), a ibu es’ pa ame isa ion and spa ial posi ion.
En i y [E] Pa ame ic model [E] Sub-en i y [S-E] A ibu e Pa ame ic model [S-E] Posi ion in he ull model
Colonnade E1 Column (x10) adius
heigh
5 m
95 m
Cella E2 adius (in )
heigh
hickness
50 m
110 m
5 m
Co e ed ceiling E3 base
heigh
adius (block)
10 m
6 m
i/3.33
En abla u e E4 A chi a e base
heigh
adius (block)
10 m
6 m
i
F ieze base
heigh
adius (block)
10 m
6 m
i
Cu nice base
heigh
adius (block)
10 m
6 m
i/4
Downs eam o he geome ical analysis, a gene a i e algo i hm
has been implemen ed in he Visual P og amming en i onmen
p o ided by Rhinoce os [ 54 ] and G asshoppe [ 55 ] so wa e (s ep
3 o he wo kflow in Sec ion Me hodology o e iew ). The mod-
elling sc ip is a ailable a he ollowing link: Gene a i e Mod-
elling o Monop e os and Tholos Temples: Ves a Temple in Ti oli
( zenodo.o g ) [ 56 ]. Fi s ly, he 3D modelling o he sub-en i ies has
been ca ied ou by ex apola ing he p imi i e geome ies ha
ma ched he sub-en i ies. Va ious a ibu es ha e been selec ed as
inpu a iables o model such geome ies, i.e. adius, heigh , e c.,
and a gene a i e algo i hm has been implemen ed o each sub-
en i y h ough he GHPy hon componen a ailable in G asshop-
pe [ 55 ]. As epo ed in Table 1 , he geome ical a ibu es ha e
been modelled by using bo h linea and angula modules as a uni
o measu emen . Thei dimensions a e exp essed in he able in
e ms o hese modules (see ‘A ibu e’ column). The ob ained sub-
en i ies ha e been collec ed and used o gene a e he ou main
en i ies in he nex s ep o he wo kflow.
The assemblage o he iden ified en i ies has been ca ied ou
by implemen ing he geome ic ela ionships be ween he a chi-
ec u al elemen s ha define he s uc u e ʼs layou (s ep 4 o
Fig. 1 ). This has also been pe o med by using a GHPy hon sc ip ,
which posi ioned he sub-en i ies by mo ing, spacing, and o a ing
hem o ge he en i ies placed in a spa ial a angemen o fi he
o iginal layou o he emple acco ding o he scheme epo ed in
Fig. 3 .
In Fig. 4 , he modelling o he en i y E1 – colonnade is de-
pic ed o p o ide a clea e unde s anding o he p ocedu e. All
he columns comp ising he colonnade ha e been modelled by
s acking hei componen blocks. The ac ual heigh s o he blocks,
339
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 4. Modelling wo kflow o column 1 (S-E11) implemen ed in GHPy hon o G asshoppe .
Table 2
Ma e ial p ope ies o he inne cella.
E0
[MPa] ν ρ [kg/m3
] Dila a ion angle Eccen ici y b0
/ c0 Kc Viscosi y pa ame e
1000 0.2 1450 10 °0.1 1.16 2/3 1e-5
Comp essi e beha io Tensile beha io
S ess [MPa] Inelas ic s ain dc S ess [MPa] Inelas ic s ain d
2.00 0 0 0.15 0 0
2.20 0.004 0 0.001 0.002 0.9
0.2 0.010 0.9
as epo ed in Pi anesi’s e chings (
Fig. 4 (a) and (b)), ha e been
used. The columns ha e been finally indexed and posi ioned
( Fig. 4 (d),(e)) acco ding o he ac ual layou o he emple o ob-
ain he en i e colonnade ( Fig. 4 ( )).
The 3D model o he Ves a Temple is p o ided in Fig. 5 (a–d).
One can no e ha he exis ing lacuna has been in oduced in he
cella h ough Boolean sub ac ion, which allowed o he ep oduc-
ion o i s cu en shape.
One should no e ha sub-en i ies can be s o ed in lib a ies and
u ilised o o he objec s, and en i e sc ip s can be eused o model
simila s uc u es, such as o he monop e os/ holos emples, wi h
mino adjus men s in nea ly no ime. The code ʼs eusabili y has
been es ed o gene a e a geome ical model o he emple’s o ig-
inal configu a ion based on F ancesco Pi anesi ʼs hypo hesis. The
model in Fig. 5 (e) and ( ) has been c ea ed by adjus ing he sc ip ,
inc easing sub-en i ies o comple e he ci cula plan, and adding a
dome as a new en i y. Addi ional capabili ies ha e been coded o
modelling p imi i e geome ies equi ed o he dome.
FE modelling
The s uc u al modelling o he Ves a Temple has been pe -
o med using a concu en con inuous/block-based app oach [ 40 ].
In pa icula , he cella has been modelled ia he mac o-modelling
app oach [ 57 ]. Mason y non-linea i ies ha e been aken in o ac-
coun ia he so-called Conc e e Damage Plas ici y (CDP), which
couples plas ici y wi h a scala -based damage model [ 58 ]. The
quasi-b i le na u e o mason y is ep esen ed by a linea ype
o so ening in ension. In comp ession, a pla eau exis s a e he
comp essi e s eng h, ollowed by a linea ype o so ening. Dam-
age a iables a e adop ed when so ening is ac i e and aim a e-
ducing he ini ial (undamaged) elas ic modulus h ough he ollow-
ing exp essions:
σc
=1 −dc
E0
εc
−εpl
c
σ
=1 −d
E0
ε
−εpl
(1)
whe e E0 is he elas ic modulus o he undamaged mason y, σi
is he e ec i e s ess alue; εi is he o al s ain alue, and εpl
i
is he inelas ic (plas ic) s ain alue. The subsc ip i eads as c
o i associa ed wi h he comp essi e o ensile egime, espec-
i ely. A scala -based damage model desc ibes he damage in en-
sion d (c acking) and comp ession dc (c ushing), which can as-
sume a alue be ween ze o (no damage) and one ( ully damaged).
When cyclic loading is applied, loss o s i ness in he unloading
phase due o c acking and c ushing is likely o happen. CDP as-
sumes a non-associa i e flow ule gi en as a D ucke –P age hy-
pe bolic unc ion and equi es he defini ion o physically based
pa ame e s. Ma e ial p ope ies adop ed in he nume ical analysis
a e epo ed in Table 2 .
T a e ine blocks, o ming he columns, ceiling, and en abla-
u e ( ρ= 2500 [kg/m3
]), ha e been assumed o be de o mable
disc e e blocks ollowing an iso opic and linea elas ic cons i u-
i e law ( E = 63 GPa , ν= 0 . 2 ). The d y-assemblage o blocks has
been ep esen ed by ze o- hickness in e aces, which include a
non-associa i e plas ic flow ule and a classical Moh -Coulomb ail-
u e su ace c i e ion. No mal and angen ial con ac beha iou s as-
sume an infini esimal in e pene a ion be ween blocks. A linea
ela ionship be ween he o e -closu e displacemen s and he ap-
plied s ess has been defined by he no mal and angen ial s i -
ness alues o kn
= 5 ×10
9 Pa / m and ks
= 2 ×10
9 Pa / m , espec-
340
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 5. Final 3D models o he Ves a Temple: ac ual configu a ion (a)–(d); (a) plan, (b) on ele a ion, (c) and (d) 3D iews; econs uc i e hypo hesis acco ding o F. Pi anesi
(e) and ( ).
Fig. 6. FE model: geome y, bounda y condi ions and con ol poin s.
i ely. A ic ion coefficien (
μ= 0 . 70 ) comple ing he shea con-
ac beha iou has been adop ed. No iscous damping has been se
o he con ac in e aces [ 59 ].
The h ee-dimensional FE model ( Fig. 6 ) en o ces he use o
h ee-dimensional (solid) solid elemen s; he e o e, he mesh dis-
c e isa ion has been achie ed using e ahed on FEs o he cella
(TETC3D4) and hexahed al FEs o he emaining s uc u al compo-
nen s (C3D8R) ha ing a cha ac e is ic dimension o 200 mm. Ap-
p op ia e bounda y and loading condi ions ha e been implemen ed
o un he simula ions. Nume ical analyses ha e been pe o med
by applying wo phases ha idealised he load p ocess: a fi s ,
he g adual applica ion o g a i y loads and, subsequen ly, g ound
mo ion eco ds simul aneously in No h-Sou h (NS) (Y) and Eas -
Wes (EW) (X) di ec ions. An explici ime in eg a ion scheme has
been adop ed o in eg a e he equa ion o mo ion, while nonlinea
geome ies ha e been aken in o conside a ion [ 60 ].
G ound mo ion selec ion and scaling
The code-based selec ion o g ound mo ions is a c ucial s ep in
achie ing he seismic assessmen o a his o ic building, as i en-
su es ha s uc u al design and assessmen a e pe o med using
ep esen a i e and ealis ic seismic inpu s. Enginee s u ilise spe-
cific building codes and seismic design s anda ds o guide he se-
lec ion o g ound mo ion eco ds ha eflec he seismic haza d
a a pa icula loca ion. By adhe ing o es ablished seismic design
341
A. Vuo o, M.F. Funa i, S. Ka imzadeh e al. Jou nal o Cul u al He i age 71 (2025) 334–345
Fig. 7. (a) Time his o y displacemen o selec ed con ol poin s (di e en colou s) and ailu e mechanisms (b) Maximum base shea / g a i y loads (BS/GL) in -X ( ed) and
-Y (g een) di ec ions.
342
