Academic Edi o s: Al edo
Reyes-Salaza , Fede ico
Valenzuela-Bel an and Ma io
D. Llanes-Tizoc
Recei ed: 22 Decembe 2024
Re ised: 20 Janua y 2025
Accep ed: 29 Janua y 2025
Published: 2 Feb ua y 2025
Ci a ion: Luge , H.; Rami ez, R.;
Pineda, P.; Lou enço, P.B. Field
In es iga ion and Nume ical
Modeling o he Seismic Assessmen
o he Cas le o Lanja ón, Spain. Appl.
Sci. 2025,15, 1518. h ps://doi.o g/
10.3390/app15031518
Copy igh : © 2025 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
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condi ions o he C ea i e Commons
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(h ps://c ea i ecommons.o g/
licenses/by/4.0/).
A icle
Field In es iga ion and Nume ical Modeling o he Seismic
Assessmen o he Cas le o Lanja ón, Spain
Hayden Luge 1, Ra ael Rami ez 1, Paloma Pineda 2and Paulo B. Lou enço 1,*
1Depa men o Ci il Enginee ing, ISISE, ARISE, Uni e si y o Minho, Campus de Azu ém s/n,
4800-085 Guima aes, Po ugal; [email p o ec ed].ca (H.L.); [email p o ec ed] (R.R.)
2Depa men o Building S uc u es and Geo echnical Enginee ing, Uni e sidad de Se illa, A da. Reina
Me cedes 2, 41012 Se ille, Spain; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : The Cas le o Lanja ón is a 16 h cen u y s onghold loca ed in Andalucía, Spain.
A e losing i s mili a y unc ion, he cas le was abandoned, leading o signi ican decay.
Designa ed a na ional he i age si e in 1985, ecen e o s ha e sough o p ese e i s
his o ical and cul u al alue. This s udy ou lines an inspec ion and diagnosis campaign
ca ied ou on he cas le. Non-des uc i e es s (NDTs) we e employed o cha ac e ize
he p ope ies o he mason y, using bo h mechanical and wa e-based me hods. Dynamic
iden i ica ion was pe o med o de e mine dynamic and modal p ope ies o he s uc u e,
which we e used o de elop and calib a e a h ee-dimensional (3D) ini e elemen model
(FEM) o he wes wall, based on homogenized mason y ma e ial. Limi analysis and
non-linea s a ic (pusho e ) analysis unde a ious bounda y condi ions we e conduc ed o
de e mine he maximum ela i e load ac o in he ou -o -plane di ec ion. The esul s we e
compa ed o he expec ed peak g ound accele a ion (PGA) o he a ea, showing ha he
maximum load capaci y o he wall exceeds local seismic demands wi h a sa e y ac o o
1.39. The s udy highligh s he e icacy o pai ing a homogenized mac o-modeling app oach
wi h wa e-based and dynamic iden i ica ion me hods, pa icula ly o esou ce e iciency.
Finally, ecommenda ions o u u e conse a ion e o s ha e been p o ided.
Keywo ds: his o ical s uc u e; limes one mason y; inspec ion; diagnosis; non-des uc i e
es ing; dynamic iden i ica ion; ini e elemen me hod; ini e elemen analysis; limi analysis;
seismic design
1. In oduc ion
In egions wi h li le ecen seismic ac i i y, he e ec o a seismic e en can o en be
o e looked. Wi h a low seismic haza d, a e u n pe iod o , a imes, hund eds o yea s,
and he e icacy o mode n building ma e ials a mi iga ing isk, seismic isk can be easy o
igno e. Howe e , o asse s o cul u al he i age and his o ical buildings ha ha e exis ed
o cen u ies, hese isks a e ine i able. The seismic e alua ion o he i age s uc u es is
o pa icula in e es since hey a e o en unique and i eplaceable, holding signi ican
his o ical and cul u al alues as buil he i age. These s uc u es a e commonly buil wi h
adi ional building ma e ials such as un ein o ced mason y and we e no designed o
wi hs and he signi ican la e al loading o en accompanying seismic e en s. In addi ion,
hey can be expensi e o main ain and di icul o wo k on. Many o hese buildings a e
cha ac e ized by i egula geome y, massi e size and weigh , and mason y composing
hem ha is b i le and ulne able o ensile and shea loading. These cha ac e is ics
in luence he seismic beha io and ulne abili y o a his o ical s uc u e [1].
Appl. Sci. 2025,15, 1518 h ps://doi.o g/10.3390/app15031518
Appl. Sci. 2025,15, 1518 2 o 24
Nume ical me hods and modeling ha e success ully been employed o he analysis
o he i age s uc u es by allowing he simula ion o an applied loading condi ion [
2
–
5
].
This applica ion is commonly used o simula e he esponse o a s uc u e o ei he a s a ic
loading condi ion, such as a la e al load being applied o a wall, o a dynamic loading
condi ion consis ing o a ime-his o y seismic inpu . The me hods a e also commonly
conside ed in bo h he linea elas ic and non-linea egimes o ma e ials and a e he e-
o e en i ely dependen on he cons i u i e and ma e ial models used in he modeling
app oach. Typical me hods o he modeling o mason y in ol e he di e en ea men o
he mo a –b ick in e ace ha cha ac e izes he ma e ial. Mic o-modeling app oaches a e
mo e compu a ionally demanding and can be used o model indi idual mason y uni s and
he in e aces be ween hem as discon inuous. Mac o-modeling app oaches ep esen he
mason y s uc u e as a homogenized app oxima ion o i s composi ion; hey a e he e o e
less compu a ionally demanding and equi e ewe indi idual p ope ies as inpu s [6].
The need o alida ion and suppo o he model-based app oach is essen ial; expe -
imen ally ob ained da a can complemen a nume ical model by ob aining expe imen al
alues o he mechanical and physical p ope ies o a speci ic si e [
7
]. Howe e , o a
cul u ally signi ican and p o ec ed si e, i is di icul o p ope ly assess hei mechanical
and composi ional p ope ies using ex si u labo a o y se ups o o he means ha would
in ol e he pa ial o o al des uc ion o an elemen . The impo ance o pe o ming non-
des uc i e es s (NDTs) o assess hese pa ame e s becomes immedia ely appa en ; being
able o unde s and he beha io o he s uc u e and i s ma e ials wi hou nega i ely a ec -
ing he exis ing elemen s is pa amoun o assessing i s cu en s a e esponsibly. Physical
p ope ies, such as comp essi e s eng hs o indi idual uni s and mo a s, can be ob ained
using mo e analog me hods such as hose ou lined in his epo (Schmid hamme , Schmid
pendulum hamme , pene ome e , and sc a ch es ing ins umen ). Mo e wholis ic pa am-
e e s ha ep esen mo e global p ope ies can be assessed using wa e-based me hods
and dynamic iden i ica ion, in addi ion o being able o highligh po en ial damage in
he si e [
7
]. Fu he mo e, hese me hods can be used o calib a e a de eloped nume ical
model acco ding o hei modal pa ame e s o ib a ion equencies, mode shapes, and
damping [8].
Lanja ón is in one o he mos seismically ulne able egions in Spain [
9
]. Despi e
local in e es in he p ese a ion o i s his o ical cas le, no inno a i e academic s udies
wi hin he amewo k o seismic e alua ion and his o ical s uc u al conse a ion ha e
been pe o med. Such in es iga ions complemen he use o ini e elemen me hods o
simula e he esponse o a s uc u e o ex e nal loading by p o iding ma e ial p ope ies
ha can be used di ec ly in a ini e elemen (FE) model. Wi hin his con ex , his no el
s udy aims o ou line he esul s o ex ensi e in es iga ions and expe imen al campaigns
o NDTs ha we e pe o med on he si e o cha ac e ize s uc u al elemen s and iden i y
po en ial damage o he cas le. The s udy u he de eloped and calib a ed an FE model
based on a a ie y o modal pa ame e s and using he Modal Assu ance C i e ion (MAC)
o alida ion. Finally, e icien me hods o he sa e y assessmen o his o ical s uc u es
we e used o de e mine he sa e y o he s uc u e, all wi hin a comp ehensi e case s udy.
Fu u e s udies may conside using dynamic non-linea analysis o u he e alua e he es
o he s uc u e.
2. Ma e ials and Me hods
The Cas le o Lanja ón (Figu e 1a) is a 16 h cen u y Ch is ian s onghold ha occupies
a s a egic posi ion upon he sou he n slopes o he Penibae ic Moun ains o he Sie a
Ne ada adjacen o he own o Lanja ón [
10
]. I si s a op a s eep ocky slope and is, oday,
composed o wo main componen s ha ha e la gely allen in o a s a e o decay: a keep, on
Appl. Sci. 2025,15, 1518 3 o 24
he sou he n side o he compound (Figu e 1b), and he ou e enclosu e ha su ounds i
o he no h (Figu e 1c). A ba bican lanks he en ance o he sou h, unning pa allel o
he walls o he keep abo e. In his way, he cas le is e y cha ac e is ic o a s onghold on
he Ibe ian Peninsula om i s ime: he angled app oach c ea ed by he ba bican and he
keep abo e he en ance echo he in luence o he Muslim cul u es ha occupied he egion
be o e [11,12].
Appl. Sci. 2025, 15, x FOR PEER REVIEW 3 o 25
Sie a Ne ada adjacen o he own o Lanja ón [10]. I si s a op a s eep ocky slope and is,
oday, composed o wo main componen s ha ha e la gely allen in o a s a e o decay: a
keep, on he sou he n side o he compound (Figu e 1b), and he ou e enclosu e ha
su ounds i o he no h (Figu e 1c). A ba bican lanks he en ance o he sou h, unning
pa allel o he walls o he keep abo e. In his way, he cas le is e y cha ac e is ic o a
s onghold on he Ibe ian Peninsula om i s ime: he angled app oach c ea ed by he
ba bican and he keep abo e he en ance echo he in luence o he Muslim cul u es ha
occupied he egion be o e [11,12].
The cas le i sel occupies a oo p in o a ound 500 m
2
and does no ha e a egula
polygonal shape. I s cons uc ion is p ima ily o s one ubble mason y, excep o a lime-
based cemen i ious cis e n in he base o he la ge keep on he sou he n side o he
s uc u e. The keep ises o a heigh o 12 m abo e he app oach o he sou h, lanked by
he 1.2 m hick ba bican. A ba el- aul ed passage pe pendicula o his app oach
p o ides access o he ou e enclosu e. The enclosu e is o i ied on all sides by 1.7 m hick
walls ha ise o heigh s o almos 7.5 m a hei alles poin along he long wes e n wall
(Figu e 1d). The e ain inclines s eeply om sou h o no h, ising om he keep o he
apex o he hill he cas le si s upon. A i s no he nmos poin , a massi e wa ch owe looks
ou owa ds he own o he no h.
(a) (b)
(c) (d)
Figu e 1. Visual o e iew o he Cas le o Lanja ón: (a) ae ial iew o he cas le looking wes [13];
(b) iew o he cas le om he sou h showing he ba bican and keep; (c) iew o he inne enclosu e
om he en ance unde he keep; (d) iew showing he long wes wall.
The exis ence o he cas le in i s cu en s a e has i s o igins in he ea ly 16 h cen u y,
sho ly a e he Ch is ian occupa ion o G anada. Ma e ial analysis sugges s ha i is a
Figu e 1. Visual o e iew o he Cas le o Lanja ón: (a) ae ial iew o he cas le looking wes [
13
];
(b) iew o he cas le om he sou h showing he ba bican and keep; (c) iew o he inne enclosu e
om he en ance unde he keep; (d) iew showing he long wes wall.
The cas le i sel occupies a oo p in o a ound 500 m
2
and does no ha e a egula
polygonal shape. I s cons uc ion is p ima ily o s one ubble mason y, excep o a lime-
based cemen i ious cis e n in he base o he la ge keep on he sou he n side o he s uc u e.
The keep ises o a heigh o 12 m abo e he app oach o he sou h, lanked by he 1.2 m
hick ba bican. A ba el- aul ed passage pe pendicula o his app oach p o ides access o
he ou e enclosu e. The enclosu e is o i ied on all sides by 1.7 m hick walls ha ise o
heigh s o almos 7.5 m a hei alles poin along he long wes e n wall (Figu e 1d). The
e ain inclines s eeply om sou h o no h, ising om he keep o he apex o he hill he
cas le si s upon. A i s no he nmos poin , a massi e wa ch owe looks ou owa ds he
own o he no h.
The exis ence o he cas le in i s cu en s a e has i s o igins in he ea ly 16 h cen u y,
sho ly a e he Ch is ian occupa ion o G anada. Ma e ial analysis sugges s ha i is a
Ch is ian mason y cons uc ion buil du ing he annexa ion o he a ea o he Kingdom
Appl. Sci. 2025,15, 1518 4 o 24
o Cas ile [
10
]. The p ima y unc ion o he cas le may ha e been su eillance and con ol
o he a ea and i s inhabi an s du ing ha ini ial pe iod and beyond, un il he e en ual
expulsion o he Muslim popula ion ende ed he cas le obsole e. This led o i s conclu-
si e abandonmen in he cen u ies ollowing. A cheological su eys u he suppo his
conclusion, implying a g adual decline in he s uc u al condi ion o he cas le om i s
his o ical s a e o i s cu en one. The collapsed s a e o he keep is a p oduc o cen u ies o
abandonmen and con inuous exposu e o he elemen s [
14
]. The cas le was added o he
Spanish He i age Monumen Lis ing in 1985; i is p o ec ed and designa ed oday wi h he
s a us o Bien de In e és Cul u al (BIC), o Cul u al He i age Si e.
Conce n o e he collapse o he s uc u e led o a a ie y o es o a i e and p ese -
a i e e o s du ing he 1990s and he 2000s, including he consolida ion o c acks in he
keep. Mason y elemen s we e econs uc ed wi h allen s ones o hei o iginal s a e. O he
mason y uni s we e co e ed wi h a hick mo a whe e i had been emo ed, in addi ion
o deep, medium dep h, and supe icial epoin ing being pe o med. Some deep oids
we e illed and consolida ed; hea ily de e io a ed s one mason y uni s we e eplaced,
and allen masses we e eloca ed o eposi ioned o a oid u he de e io a ion. The mos
ecen in e en ion, comple ed in 2007, also ea u ed he cons uc ion o an ea lie planned
me allic ame in he keep ou lining he his o ical shape o he s uc u e, and he addi ion
o s ai s and sa e y ails [15].
E en wi h he ecency o he in e en ion in 2007, he condi ions o many o he
elemen s con inue o decline. Much o he pain on he me al elemen s has chipped o been
emo ed, exposing hese elemen s o decay. Many o he limes one mason y uni s ha e
been hea ily exposed o al eoliza ion. Two d ainage ubes a e p esen o emo e wa e and
could easily become blocked. Signi ican plan g ow h h ea ens he s a e o he mason y
slowly. Fo an asse o signi ican cul u al in e es such as he Cas le o Lanja ón, he main
elemen s and ma e ials o a si e a e o en agile and o signi ican alue in hei cu en
s a e. Figu e 2demons a es some o hese damages.
An in ensi e in si u expe imen al campaign was ca ied ou o assess and iden i y
p ope ies and condi ions o he elemen s comp ising he cas le. These wo ks included
ock cha ac e iza ion, es ing wi h a ious NDT equipmen (Schmid hamme , Schmid
pendulum hamme , pene ome e , sc a ch es ing ins umen ), a comp ehensi e wa e-
based campaign based on sonic es s, and concluded wi h dynamic iden i ica ion.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 4 o 25
Ch is ian mason y cons uc ion buil du ing he annexa ion o he a ea o he Kingdom o
Cas ile [10]. The p ima y unc ion o he cas le may ha e been su eillance and con ol o
he a ea and i s inhabi an s du ing ha ini ial pe iod and beyond, un il he e en ual
expulsion o he Muslim popula ion ende ed he cas le obsole e. This led o i s conclusi e
abandonmen in he cen u ies ollowing. A cheological su eys u he suppo his
conclusion, implying a g adual decline in he s uc u al condi ion o he cas le om i s
his o ical s a e o i s cu en one. The collapsed s a e o he keep is a p oduc o cen u ies
o abandonmen and con inuous exposu e o he elemen s [14]. The cas le was added o
he Spanish He i age Monumen Lis ing in 1985; i is p o ec ed and designa ed oday wi h
he s a us o Bien de In e és Cul u al (BIC), o Cul u al He i age Si e.
Conce n o e he collapse o he s uc u e led o a a ie y o es o a i e and
p ese a i e effo s du ing he 1990s and he 2000s, including he consolida ion o c acks
in he keep. Mason y elemen s we e econs uc ed wi h allen s ones o hei o iginal s a e.
O he mason y uni s we e co e ed wi h a hick mo a whe e i had been emo ed, in
addi ion o deep, medium dep h, and supe icial epoin ing being pe o med. Some deep
oids we e illed and consolida ed; hea ily de e io a ed s one mason y uni s we e
eplaced, and allen masses we e eloca ed o eposi ioned o a oid u he de e io a ion.
The mos ecen in e en ion, comple ed in 2007, also ea u ed he cons uc ion o an
ea lie planned me allic ame in he keep ou lining he his o ical shape o he s uc u e,
and he addi ion o s ai s and sa e y ails [15]
E en wi h he ecency o he in e en ion in 2007, he condi ions o many o he
elemen s con inue o decline. Much o he pain on he me al elemen s has chipped o been
emo ed, exposing hese elemen s o decay. Many o he limes one mason y uni s ha e
been hea ily exposed o al eoliza ion. Two d ainage ubes a e p esen o emo e wa e
and could easily become blocked. Signi ican plan g ow h h ea ens he s a e o he
mason y slowly. Fo an asse o signi ican cul u al in e es such as he Cas le o Lanja ón,
he main elemen s and ma e ials o a si e a e o en agile and o signi ican alue in hei
cu en s a e. Figu e 2 demons a es some o hese damages.
(a) (b)
Figu e 2. Con .
Appl. Sci. 2025,15, 1518 5 o 24
Appl. Sci. 2025, 15, x FOR PEER REVIEW 5 o 25
(c) (d)
Figu e 2. Cu en conse a ion s a e o he Cas le o Lanja ón: (a) s a e o me allic elemen s in he
cas le; (b) al eolized limes one ashla ; (c) blocked d ainage ube; (d) signi ican plan g ow h on
s uc u al elemen s hides a mason y a ch.
An in ensi e in si u expe imen al campaign was ca ied ou o assess and iden i y
p ope ies and condi ions o he elemen s comp ising he cas le. These wo ks included
ock cha ac e iza ion, es ing wi h a ious NDT equipmen (Schmid hamme , Schmid
pendulum hamme , pene ome e , sc a ch es ing ins umen ), a comp ehensi e wa e-
based campaign based on sonic es s, and concluded wi h dynamic iden i ica ion.
2.1. Rock Tes P ocedu es
The ock es s we e pe o med on isually simila ocks in he a ea su ounding he
cas le and used common geological app oaches o cha ac e ize calca eous ocks in si u
h ough bo h isual means and an acid es . The acid es cha ac e izes ocks con aining
calcium ca bona e acco ding o he eac ion o a weak acid wi h he compound. The
equency and na u e o he gaseous ca bon dioxide bubbles o med by he acid-base
eac ion can se e as an indica ion o whe he limes one o ano he calca eous ock is
p esen [16]. Uni s ha eac ed eadily and bubbled agg essi ely in he p esence o acid
we e labeled as limes one. Uni s i s equi ing he su ace o be sc a ched o a powde
be o e eac ing we e conside ed dolomi ic. Uni s ha did no eadily eac did no con ain
signi ican aces o calcium ca bona e. Based on hese esul s, a Schmid hamme wi h a
ebound ene gy o 2.207 Nm was also used o e alua e he comp essi e s eng hs o he
mason y uni s using 10 consecu i e blows acco ding o s anda d es ing p ocedu es,
ollowed using densi ies and calib a ion ables p o ided in he li e a u e [17–19].
2.2. Mo a Tes P ocedu es
2.2.1. Schmid Hamme
To quan i a i ely assess he comp essi e s eng h o he mo a o he cas le, a
Schmid hamme (PASI SRL Type M) wi h an impac ene gy o 0.169 Nm was used (Figu e
3a). Using his appa a us, a sp ing-loaded mass is p opelled o impac he su ace o a
mo a h ee imes in succession be o e measu ing he ebound numbe . The esul ing
alue was hen con e ed o comp essi e s eng h using he ope a ion ins uc ions [20].
Each loca ion was es ed in acco dance wi h common applica ion me hods om he EN
Eu ocodes o he applica ion o a Schmid hamme [21].
Figu e 2. Cu en conse a ion s a e o he Cas le o Lanja ón: (a) s a e o me allic elemen s in he
cas le; (b) al eolized limes one ashla ; (c) blocked d ainage ube; (d) signi ican plan g ow h on
s uc u al elemen s hides a mason y a ch.
2.1. Rock Tes P ocedu es
The ock es s we e pe o med on isually simila ocks in he a ea su ounding he
cas le and used common geological app oaches o cha ac e ize calca eous ocks in si u
h ough bo h isual means and an acid es . The acid es cha ac e izes ocks con aining
calcium ca bona e acco ding o he eac ion o a weak acid wi h he compound. The
equency and na u e o he gaseous ca bon dioxide bubbles o med by he acid-base
eac ion can se e as an indica ion o whe he limes one o ano he calca eous ock is
p esen [
16
]. Uni s ha eac ed eadily and bubbled agg essi ely in he p esence o acid
we e labeled as limes one. Uni s i s equi ing he su ace o be sc a ched o a powde
be o e eac ing we e conside ed dolomi ic. Uni s ha did no eadily eac did no con ain
signi ican aces o calcium ca bona e. Based on hese esul s, a Schmid hamme wi h
a ebound ene gy o 2.207 Nm was also used o e alua e he comp essi e s eng hs o
he mason y uni s using 10 consecu i e blows acco ding o s anda d es ing p ocedu es,
ollowed using densi ies and calib a ion ables p o ided in he li e a u e [17–19].
2.2. Mo a Tes P ocedu es
2.2.1. Schmid Hamme
To quan i a i ely assess he comp essi e s eng h o he mo a o he cas le, a Schmid
hamme (PASI SRL Type M) wi h an impac ene gy o 0.169 Nm was used (Figu e 3a).
Using his appa a us, a sp ing-loaded mass is p opelled o impac he su ace o a mo a
h ee imes in succession be o e measu ing he ebound numbe . The esul ing alue was
hen con e ed o comp essi e s eng h using he ope a ion ins uc ions [
20
]. Each loca ion
was es ed in acco dance wi h common applica ion me hods om he EN Eu ocodes o
he applica ion o a Schmid hamme [21].
Appl. Sci. 2025,15, 1518 6 o 24
Appl. Sci. 2025, 15, x FOR PEER REVIEW 6 o 25
(a) (b)
(c) (d)
Figu e 3. (a) Schmid hamme ; (b) Schmid pendulum hamme ; (c) pene ome e ; (d) sc a ch es
ins umen .
2.2.2. Schmid Pendulum Hamme
An al e na i e o he Schmid hamme ha uses simila p inciples is he Schmid
pendulum hamme , which ins ead uses g a i y o swing a pendulum and impac a su ace
o e u n a ebound numbe measu emen (Figu e 3b). This p ocess was pe o med using
he ‘measu ing’ ins uc ions ou lined in he de ice’s guidelines o e ical su aces [22].
The hamme was placed upon he su ace o he mo a wi h he head acing downwa ds
as e ically as possible using ligh p essu e, and he head was aised in o he loaded
posi ion. When well posi ioned, his allows he head o all and impac he su ace,
ebounding and e u ning an analog measu emen ha can hen be used o quali a i ely
assess he mo a om he ope a ion manual.
2.2.3. Pene ome e
Wi h he ad an age o no being as es ic ed by he equi ed a ailable su ace a ea
o he Schmid hamme es s, a pene ome e (Diagnos ic Resea ch Company SRL RSM-
15) was also used o quan i a i ely e alua e he comp essi e s eng h o mo a (Figu e
3c). The de ice is based on he same p inciples as he Schmid hamme , using an impac -
d i en accele a ed mass o d i e a small needle in o a mo a . I is conside ed non-
des uc i e. The ‘Type-A—Fas ’ p ocedu e om he use manual was ollowed, in which
en consecu i e blows om he de ice d o e he needle pe pendicula ly in o he mo a .
The needle was hen emo ed, and he dep h o pene a ion was measu ed. The esul ing
dep h can be con e ed in o a comp essi e s eng h alue [23].
Figu e 3. (a) Schmid hamme ; (b) Schmid pendulum hamme ; (c) pene ome e ; (d) sc a ch
es ins umen .
2.2.2. Schmid Pendulum Hamme
An al e na i e o he Schmid hamme ha uses simila p inciples is he Schmid
pendulum hamme , which ins ead uses g a i y o swing a pendulum and impac a su ace
o e u n a ebound numbe measu emen (Figu e 3b). This p ocess was pe o med using
he ‘measu ing’ ins uc ions ou lined in he de ice’s guidelines o e ical su aces [
22
].
The hamme was placed upon he su ace o he mo a wi h he head acing downwa ds as
e ically as possible using ligh p essu e, and he head was aised in o he loaded posi ion.
When well posi ioned, his allows he head o all and impac he su ace, ebounding and
e u ning an analog measu emen ha can hen be used o quali a i ely assess he mo a
om he ope a ion manual.
2.2.3. Pene ome e
Wi h he ad an age o no being as es ic ed by he equi ed a ailable su ace a ea o
he Schmid hamme es s, a pene ome e (Diagnos ic Resea ch Company SRL RSM-15)
was also used o quan i a i ely e alua e he comp essi e s eng h o mo a (Figu e 3c).
The de ice is based on he same p inciples as he Schmid hamme , using an impac -d i en
accele a ed mass o d i e a small needle in o a mo a . I is conside ed non-des uc i e. The
‘Type-A—Fas ’ p ocedu e om he use manual was ollowed, in which en consecu i e
blows om he de ice d o e he needle pe pendicula ly in o he mo a . The needle was
hen emo ed, and he dep h o pene a ion was measu ed. The esul ing dep h can be
con e ed in o a comp essi e s eng h alue [23].
Appl. Sci. 2025,15, 1518 7 o 24
2.2.4. Sc a ch Tes
A sc a ch es ins umen (Ene en P y. L d. Mo a Check II) was used o u he
onsi e e alua ion o he mo a condi ion and s eng h (Figu e 3d) [
24
]. The de ice was
placed upon a la su ace o mo a , and p ope ly o ien ed by placing i s legs on he
su ounding wall. The ab asi e p obe was hen lowe ed on o he su ace wi h he space
s ill a ached and ze oed acco dingly. The de ice was locked in o place, he space was
emo ed, and he o ce o he sp ing d o e he p obe in o he mo a as he yoke was u ned
using wo ull o a ions. Ca e was aken no o apply addi ional p essu e o he p obe while
suppo ing he legs, and he esul ing eading (in inches) was used o quali a i ely e alua e
he mo a sc a ch index.
2.3. Sonic Tes P ocedu es
Tes s based on he p opaga ion o a wa e h ough a medium a e o pa icula in e es
wi hin he con ex o his o ical cons uc ions due o hei non-in asi e cha ac e is ics and
abili y o gain in o ma ion abou wha is below he isible su ace. Examining ma e ial
h ough he beha io o wa e mo emen can e eal se e al cha ac e is ics o he medium,
such as he p esence o c acks o sepa a ion o wy hes wi hin a mason y wall. The speed a
which a wa e p opaga es is he basis o hese me hods, alongside some heo e ical assump-
ions commonly used in ci il enginee ing. Addi ionally, he e is a ela ion be ween he
elas ic modulus, densi y, and speed o he wa e. The equa ions used, p esen ed la e , a e
based p ima ily on he homogenous and iso opic beha io o a linea elas ic ma e ial and
how a wa e p opaga es h ough i . As mason y is no homogeneous i sel , i becomes im-
po an o no e he common homogeniza ion app oaches used o he e ogeneous ma e ials
when s udying hem a a mac o-le el [25].
Tes ing was pe o med using an impac hamme (PCB Piezo onics Model 086D05)
and accele ome e (Model 352B) in combina ion wi h a Na ional Ins umen s (Model NI
USB-4431) Da a Acquisi ion (DAQ) sys em wi h a maximum inpu ange o
±
10 V. This
se up was used o measu e he ime be ween he impac o he hamme and he momen
he accele ome e ecei ed he signal. The hamme had a sensi i i y o 0.23 mV/N and a
signal inpu ange o
±
22,240 N pk. The accele ome e used had a sensi i i y o 1 V/g and
a signal inpu ange om
−
5 g o 5 g. The p og am used in da a acquisi ion was se up o
pe o m con inuous sampling wi h a 100,000 Hz sampling a e, o collec 50,000 samples. A
se ies o six epea ed samples we e collec ed om each poin o ensu e a leas h ee usable
es s we e ga he ed.
A1m
×
1 m a ea was selec ed o es ing in wo di e en loca ions, one o di ec
( h ough he wall) and one o indi ec (ac oss he su ace o he wall) es ing. An app oxi-
ma ely e enly spaced 5 ×5 g id o poin s was used o indi ec es ing (Figu e 4), while a
6
×
6 g id o poin s on opposi e sides o a wall was selec ed o di ec es ing (Figu e 5).
Poin s c ossing a c ack ha was epai ed in a p e ious in e en ion we e also in es iga ed
using he indi ec me hod. Indi ec es s we e pe o med in bo h a e ical and ho izon al
di ec ion by s iking a poin a ei he ex eme o he g id and subsequen ly p og essing
h ough he poin s along he line and epea ing he p ocess.
The collec ed da a we e hen p ocessed, and he modulus o elas ici y o he ma e ials
was calcula ed using he ollowing o mula:
E=V2
pρ(1+ν)(1−2ν)
(1−ν)(1)
whe e
E
[N/m
2
] is he modulus o elas ici y, V
p
[m
2
/s] is he wa e p opaga ion speed,
ρ
[kg/m
3
] is he ma e ial densi y, and
ν
[–] is he Poisson’s a io [
3
,
26
]. Ma e ial p ope ies
om he li e a u e we e used o alues o densi y and Poisson’s a io [6].
Appl. Sci. 2025,15, 1518 8 o 24
Appl. Sci. 2025, 15, x FOR PEER REVIEW 8 o 25
(a) (b) (c)
Figu e 4. (a) Indi ec sonic es loca ion (ex en shown by black ec angle); (b) es g id wi h loca ions
o e ical indi ec sonic es s; (c) es g id wi h loca ions o ho izon al indi ec sonic es s. Hamme
impac poin s a e highligh ed in yellow, accele ome e poin s a e ed, and poin s wi h null eadings
a e whi e.
(a) (b)
Figu e 5. (a) Di ec sonic es loca ion ou side he keep (ex en shown by black ec angle); (b) es
g id wi h loca ions o di ec sonic es s.
The collec ed da a we e hen p ocessed, and he modulus o elas ici y o he
ma e ials was calcula ed using he ollowing o mula:
E=V
ρ1+ν1−2ν
1−ν (1)
whe e E [N/m
2
] is he modulus o elas ici y, V
p
[m
2
/s] is he wa e p opaga ion speed, ρ
[kg/m
3
] is he ma e ial densi y, and ν [–] is he Poisson’s a io [3,26]. Ma e ial p ope ies
om he li e a u e we e used o alues o densi y and Poisson’s a io [6].
2.4. Dynamic Iden i ica ion P ocedu es
Real- ime dynamic iden i ica ion can be used o ob ain a a ie y o dynamic
s uc u al p ope ies ha desc ibe how a s uc u e oscilla es and beha es. The oscilla ion
o a s uc u e is ma hema ically go e ned by i s mass, s iffness, and capaci y o dissipa e
ene gy; hese pa ame e s a e ep esen ed gene ally in dynamic iden i ica ion h ough
modal pa ame e s. Modal pa ame e s a e ypically equencies o ib a ion, he ela i e
shapes o he modes associa ed wi h hese equencies, and damping [8]. The modal
pa ame e s can wholis ically ep esen he esponse o a s uc u e o an inpu , ega dless
o any damage o he e ogenei y in he s uc u e [4]. They can ep esen he cu en s a e
Figu e 4. (a) Indi ec sonic es loca ion (ex en shown by black ec angle); (b) es g id wi h loca ions
o e ical indi ec sonic es s; (c) es g id wi h loca ions o ho izon al indi ec sonic es s. Hamme
impac poin s a e highligh ed in yellow, accele ome e poin s a e ed, and poin s wi h null eadings
a e whi e.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 8 o 25
(a) (b) (c)
Figu e 4. (a) Indi ec sonic es loca ion (ex en shown by black ec angle); (b) es g id wi h loca ions
o e ical indi ec sonic es s; (c) es g id wi h loca ions o ho izon al indi ec sonic es s. Hamme
impac poin s a e highligh ed in yellow, accele ome e poin s a e ed, and poin s wi h null eadings
a e whi e.
(a) (b)
Figu e 5. (a) Di ec sonic es loca ion ou side he keep (ex en shown by black ec angle); (b) es
g id wi h loca ions o di ec sonic es s.
The collec ed da a we e hen p ocessed, and he modulus o elas ici y o he
ma e ials was calcula ed using he ollowing o mula:
E=V
ρ1+ν1−2ν
1−ν (1)
whe e E [N/m
2
] is he modulus o elas ici y, V
p
[m
2
/s] is he wa e p opaga ion speed, ρ
[kg/m
3
] is he ma e ial densi y, and ν [–] is he Poisson’s a io [3,26]. Ma e ial p ope ies
om he li e a u e we e used o alues o densi y and Poisson’s a io [6].
2.4. Dynamic Iden i ica ion P ocedu es
Real- ime dynamic iden i ica ion can be used o ob ain a a ie y o dynamic
s uc u al p ope ies ha desc ibe how a s uc u e oscilla es and beha es. The oscilla ion
o a s uc u e is ma hema ically go e ned by i s mass, s iffness, and capaci y o dissipa e
ene gy; hese pa ame e s a e ep esen ed gene ally in dynamic iden i ica ion h ough
modal pa ame e s. Modal pa ame e s a e ypically equencies o ib a ion, he ela i e
shapes o he modes associa ed wi h hese equencies, and damping [8]. The modal
pa ame e s can wholis ically ep esen he esponse o a s uc u e o an inpu , ega dless
o any damage o he e ogenei y in he s uc u e [4]. They can ep esen he cu en s a e
Figu e 5. (a) Di ec sonic es loca ion ou side he keep (ex en shown by black ec angle); (b) es g id
wi h loca ions o di ec sonic es s.
2.4. Dynamic Iden i ica ion P ocedu es
Real- ime dynamic iden i ica ion can be used o ob ain a a ie y o dynamic s uc u al
p ope ies ha desc ibe how a s uc u e oscilla es and beha es. The oscilla ion o a s uc u e
is ma hema ically go e ned by i s mass, s i ness, and capaci y o dissipa e ene gy; hese
pa ame e s a e ep esen ed gene ally in dynamic iden i ica ion h ough modal pa ame e s.
Modal pa ame e s a e ypically equencies o ib a ion, he ela i e shapes o he modes
associa ed wi h hese equencies, and damping [
8
]. The modal pa ame e s can wholis ically
ep esen he esponse o a s uc u e o an inpu , ega dless o any damage o he e ogenei y
in he s uc u e [
4
]. They can ep esen he cu en s a e o a s uc u e, oge he wi h i s
ma e ial and mechanical p ope ies. Pe iodically pe o ming dynamic iden i ica ion on
a s uc u e, especially o collec da a be o e and a e some damage has occu ed, is an
e ec i e way o con inuously moni o i s heal h non-des uc i ely and wi hou he need
o mo e in asi e es ing [8].
Fo his campaign, 8 piezoelec ic accele ome e s (Model 393B12 PCB Piezo onics)
wi h a sensi i i y o 10,000 mV/g, a measu emen ange o
±
0.5 g pk, and a equency
ange o 0.15 Hz o 1000 Hz we e used wi h a Na ional Ins umen s DAQ (Model NI 9174
wi h wo NI 9234) o da a collec ion. A sampling a e o 200 Hz o 30 min was used o
Appl. Sci. 2025,15, 1518 9 o 24
each acquisi ion; his equency is commonly applied o mason y he i age s uc u es as i
can cap u e equency con en up o 100 Hz [
2
,
7
]. Unde ambien condi ions o exci a ion,
which is conside ed an Ambien Vib a ion Tes (AVT), he se ups a e unlikely o cap u e
any bandwid h abo e 20 Hz. Using a common e e ence poin and accele ome e , mul iple
acquisi ions o da a can be combined. Fo he analysis o he wes wall, wo ins ances
o 30 min acquisi ions wi h wo dis inc se ups we e used o measu e he esponse o
he s uc u e o an unexci ed inpu . This me hod o ou pu -only dynamic iden i ica ion
measu es he ambien ib a ion o he s uc u e, assumed o ollow he inpu o a Gaussian
whi e noise s ochas ic p ocess o Ope a ional Modal Analysis (OMA) [
8
]. Acquisi ions
we e hen p ocessed using ARTeMIS 6.0 modal iden i ica ion so wa e o iden i y modal
pa ame e s acco ding o hei spec al densi ies.
3. Resul s
3.1. Mo a Tes Resul s
A a ie y o NDT equipmen was employed o cha ac e ize he mo a onsi e, and o
iden i y di e ences in he ypes o mo a p esen om p e ious in e en ions. Figu e 6
p esen s he loca ions o he es s pe o med and highligh s he wes wall.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 10 o 25
Figu e 6. Plan iew o si e wi h es loca ions, highligh ing he wes wall.
3.1.1. Schmid Hamme
The Schmid hamme calib a ed o mo a s was used o e alua e he comp essi e
s eng h o he wo es loca ions. Calib a ion ables yielded a comp essi e s eng h o 10.8
MPa o L1 and 2.8 MPa o L2. These alues a e no ably high o mo a s when compa ed
o alues om he li e a u e [6]. This could be explained by he ac ha he es is
pe o med on a supe icial laye o mo a and addi ionally ep esen a i e o he mo a
s eng h om ecen in e en ions on he cas le.
3.1.2. Schmid Pendulum Hamme
Some no able difficul y was obse ed in he applica ion o he Schmid pendulum
hamme ; he appa a us elied mainly on pe pendicula applica ion agains he wall, o en
a signi ican challenge in his o ical s uc u es due o he i egula i y o he mason y. Too
signi ican an inclina ion in ei he di ec ion could a i icially inc ease o dec ease he
measu emen . Ne e heless, nine app op ia e measu emen s o each es ing loca ion
we e ob ained, e u ning ebound alues be ween 25 and 36. These numbe s we e hen
used o quali a i ely assess he mo a condi ion, obse ed as “a e age” o he mo e
in ac loca ion (L1) and “ easonable” o he mo e e oded one (L2).
3.1.3. Pene ome e
Pene ome e measu emen s a e likely o be mo e ep esen a i e o he mo a below
he su ace due o he na u e o he es s and e u ned lowe alues han he supe icial
Figu e 6. Plan iew o si e wi h es loca ions, highligh ing he wes wall.
Two loca ions we e iden i ied and in es iga ed using hese ins umen s, each on he
sou h-wes e n wall o he keep. The i s was a ha de and mo e densely mo a ed sec ion
o he wall, ep esen a i e o much o he mo a ha has been epoin ed in p e ious
Appl. Sci. 2025,15, 1518 16 o 24
Table 4. Linea elas ic and non-linea p ope ies used o mason y.
P ope y Symbol Uni Value
Densi y ρkg/m31900
Elas ic Modulus E GPa 2.0
Poisson’s Ra io ν- 0.2
Comp essi e S eng h cMPa 3.0
Comp essi e F ac u e Ene gy
GcN/mm 7.40
Tensile S eng h MPa 0.1
Tensile F ac u e Ene gy GI
N/mm 0.02
4.4. Model Calib a ion
Calib a ion was necessa y o une he ini ially assumed ma e ial p ope ies o he
model o be e ep esen hose ob ained expe imen ally om dynamic iden i ica ion. An
eigen alue analysis o he FE model was used o iden i y he equencies and mode shapes
o he s uc u e in he model o di ec compa ison wi h hose ob ained expe imen ally.
The equencies de e mined in his me hod a e di ec ly impac ed by bo h he mass and
he s i ness o he s uc u e; he e o e, mass was ixed, while s i ness was adjus ed o
calib a ion. The ele an equencies om DIANA a e ob ained om an eigen alue analysis,
in which he solu ions o he ee ib a ion equa ion (Equa ion (4)) a e ep esen ed by he
eigen alue
λ
(Equa ion (5)) [
32
]. K ep esen s he s i ness ma ix, M he mass ma ix,
ϕ
he
co esponding mode shape ec o , ω he angula equency, and he equency:
Kϕ=ω2Mϕ(4)
λ≡ω2= 4π2 2(5)
Fo he calib a ion, he ini ial elas ic modulus was educed om 2.0 GPa o 1.5 GPa,
which educed he equency e o o simila mode shapes o unde 2.0% o he i s wo
equencies, and unde 9% o he hi d. The a e age absolu e e o was he e o e 3.8% wi h
a maximum e o o 9.0%. Modes we e u he alida ed om he eigen ec o analysis by
selec ing he i s h ee ha mo ed abo e 20% o he mass o he wall each, om an ini ial
analysis ha conside ed up o 70% o he mass mo ed om 20 eigen equencies compu ed.
A isual compa ison be ween he nume ical and expe imen al modes demons a es hei
simila i y (Figu e 11).
4.5. Modal Assu ance C i e ion
Once he elas ic modulus and equencies had been de e mined bo h expe imen ally
and nume ically, i was possible o calcula e he Modal Assu ance C i e ia (MAC) o
compa e he FEA model wi h he expe imen al one. The MAC is he mos commonly
used me hod in he li e a u e o calcula e he co ela ion be ween wo ec o s. In his
case, hese ec o s ep esen he mode shapes ob ained expe imen ally and nume ically.
Ma hema ically, he MAC calcula es he scale p oduc o wo no malized ec o s [
33
].
The MAC compa es he alues o any numbe , n, en ies in wo 1 x n ma ices, and could
he e o e di ec ly be used o compa e he displacemen ec o s be ween he nume ical and
expe imen al esul s o n nodes. O no e is he ac ha he o mula ion o he MAC in
his case is based on he ec o s used ep esen ing only one-dimensional space, since he
accele ome e s a e all placed in an ou -o -plane di ec ion. The displacemen ec o ou pu s
om he nume ical model o each o he ele an nodes we e he e o e exp essed only in
he ou -o -plane di ec ion. One displacemen alue o each node, a each poin ha an
accele ome e was placed, was hen en e ed in o a ec o based on he node’s ID so ha
ele an pai s o nume ical and expe imen al displacemen ec o s could be compa ed.
Appl. Sci. 2025,15, 1518 17 o 24
The ou pu o he MAC is a single numbe anging om 0 o 1 depending on how simila ly
he me hods exp ess he explo ed mode shape; 1 ep esen s comple e co ela ion, while
0 ep esen s comple e disag eemen o he alues and he e o e o he mode shapes. The
o mula ion is w i en wi hou he need o no maliza ion:
MAC(xe, xn)=xT
exn
∥xe∥2∥xn∥2
(6)
whe e x
e
is a ec o o expe imen al displacemen ec o s, and x
n
is a ec o o nume ical
displacemen ec o s [
34
]. These ec o s we e ob ained om DIANA di ec ly a he nodes
speci ied using he mesh by imp in ing and conside ing only he ec o s in he ou -o -
plane di ec ions.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 17 o 25
analysis by selec ing he i s h ee ha mo ed abo e 20% o he mass o he wall each,
om an ini ial analysis ha conside ed up o 70% o he mass mo ed om 20
eigen equencies compu ed. A isual compa ison be ween he nume ical and
expe imen al modes demons a es hei simila i y (Figu e 11).
(a) (b)
Figu e 11. Mode shapes o wes wall: (a) ini ial h ee expe imen ally de e mined mode shapes; (b)
ini ial h ee nume ically de e mined mode shapes.
4.5. Modal Assu ance C i e ion
Once he elas ic modulus and equencies had been de e mined bo h expe imen ally
and nume ically, i was possible o calcula e he Modal Assu ance C i e ia (MAC) o
compa e he FEA model wi h he expe imen al one. The MAC is he mos commonly used
me hod in he li e a u e o calcula e he co ela ion be ween wo ec o s. In his case, hese
ec o s ep esen he mode shapes ob ained expe imen ally and nume ically.
Ma hema ically, he MAC calcula es he scale p oduc o wo no malized ec o s [33].
The MAC compa es he alues o any numbe , n, en ies in wo 1 x n ma ices, and could
he e o e di ec ly be used o compa e he displacemen ec o s be ween he nume ical
and expe imen al esul s o n nodes. O no e is he ac ha he o mula ion o he MAC
in his case is based on he ec o s used ep esen ing only one-dimensional space, since
he accele ome e s a e all placed in an ou -o -plane di ec ion. The displacemen ec o
ou pu s om he nume ical model o each o he ele an nodes we e he e o e exp essed
only in he ou -o -plane di ec ion. One displacemen alue o each node, a each poin
ha an accele ome e was placed, was hen en e ed in o a ec o based on he node’s ID
so ha ele an pai s o nume ical and expe imen al displacemen ec o s could be
compa ed. The ou pu o he MAC is a single numbe anging om 0 o 1 depending on
how simila ly he me hods exp ess he explo ed mode shape; 1 ep esen s comple e
co ela ion, while 0 ep esen s comple e disag eemen o he alues and he e o e o he
mode shapes. The o mula ion is w i en wi hou he need o no maliza ion:
MACx,x=x
x
‖x‖ ‖x‖ (6)
Mode 1 (7.58 Hz)
Mode 2 (10.84 Hz)
Mode 3 (14.13 Hz)
Mode 1 (7.52 Hz)
Mode 2 (11.01 Hz)
Mode 3 (15.40 Hz)
Figu e 11. Mode shapes o wes wall: (a) ini ial h ee expe imen ally de e mined mode shapes; (b)
ini ial h ee nume ically de e mined mode shapes.
Ini ial MAC calcula ions o he sys em e ealed an o e all good ag eemen be ween
he mode shapes ob ained, wi h all alues abo e 0.8. The calcula ed MAC alue was
0.96 o he i s mode, 0.84 o he second mode, and 0.94 o he hi d mode. A g aphical
compa ison be ween he ec o s ob ained h ough bo h me hods e ealed ha he poin s o
maximum displacemen , al hough simila , occu ed in di e en poin s be ween he models.
The expe imen al beha io o he s uc u e did no ma ch he nume ical one a he poin s
closes o he no h owe . This sugges ed he need o educe he s i ness o he owe due
o he p esence o an a ched oom which ep esen ed a signi ican oid in he s uc u e
(Figu e 12). The ul ima ely success ul app oach was he addi ion o an app oxima ion
o he oid oom in he s uc u e, which imp o ed he MAC alues o he i s mode o
0.98 and he second mode o 0.86 while sligh ly educing ha o he hi d mode o 0.91.
This also sligh ly inc eased he equency e o in he i s mode o 1.1% while educing
ha o he second mode o 0.3% and ha o he hi d mode o 8.8% (Table 5).
Appl. Sci. 2025,15, 1518 18 o 24
Appl. Sci. 2025, 15, x FOR PEER REVIEW 18 o 25
whe e x
e
is a ec o o expe imen al displacemen ec o s, and x
n
is a ec o o nume ical
displacemen ec o s[34]. These ec o s we e ob ained om DIANA di ec ly a he nodes
speci ied using he mesh by imp in ing and conside ing only he ec o s in he ou -o -
plane di ec ions.
Ini ial MAC calcula ions o he sys em e ealed an o e all good ag eemen be ween
he mode shapes ob ained, wi h all alues abo e 0.8. The calcula ed MAC alue was 0.96
o he i s mode, 0.84 o he second mode, and 0.94 o he hi d mode. A g aphical
compa ison be ween he ec o s ob ained h ough bo h me hods e ealed ha he poin s
o maximum displacemen , al hough simila , occu ed in diffe en poin s be ween he
models. The expe imen al beha io o he s uc u e did no ma ch he nume ical one a
he poin s closes o he no h owe . This sugges ed he need o educe he s iffness o he
owe due o he p esence o an a ched oom which ep esen ed a signi ican oid in he
s uc u e (Figu e 12). The ul ima ely success ul app oach was he addi ion o an
app oxima ion o he oid oom in he s uc u e, which imp o ed he MAC alues o he
i s mode o 0.98 and he second mode o 0.86 while sligh ly educing ha o he hi d
mode o 0.91. This also sligh ly inc eased he equency e o in he i s mode o 1.1%
while educing ha o he second mode o 0.3% and ha o he hi d mode o 8.8% (Table
5).
(a) (b)
Figu e 12. (a) MAC compa ison be ween nume ical and expe imen al mode shapes o model
conside ing he addi ion o a oid in he no h owe ; (b) model ep esen a ion o he oid in he
no h owe .
Table 5. Compa ison o expe imen ally ob ained equencies wi h calib a ed and uncalib a ed
nume ically ob ained equencies (pe cen diffe ence in pa en heses).
Mode Expe imen al0000F eq
uency (Hz)
Uncalib a ed
0000Nume ical
F equency (Hz)
Ini ial Calib a ed
0000Nume ical
F equency (Hz)
Upda ed Calib a ed
0000Nume ical
F equency (Hz)
1 7.58 8.68 0000(14.58%) 7.52 0000(−0.76%) 7.490000(−1.11%)
2 10.84 12.71 0000(17.29%) 11.01 0000(1.60%) 10.870000(0.34%)
3 14.13 17.79 0000(25.87%) 15.40 0000(8.99) 15.370000(8.80%)
5. Analysis
The s uc u al pe o mance o he cas le was e alua ed using wo me hods o
applying an ou -o -plane o ce o o e u n he s uc u e. The i s o hese me hods was a
simple limi analysis o ou line expec a ions; he second used a non-linea s a ic analysis,
also known as a pusho e analysis in an FEA en i onmen . This me hod o e alua ing he
Figu e 12. (a) MAC compa ison be ween nume ical and expe imen al mode shapes o model
conside ing he addi ion o a oid in he no h owe ; (b) model ep esen a ion o he oid in he
no h owe .
Table 5. Compa ison o expe imen ally ob ained equencies wi h calib a ed and uncalib a ed
nume ically ob ained equencies (pe cen di e ence in pa en heses).
Mode Expe imen al
F equency (Hz)
Uncalib a ed
Nume ical
F equency (Hz)
Ini ial Calib a ed
Nume ical
F equency (Hz)
Upda ed Calib a ed
Nume ical
F equency (Hz)
1 7.58 8.68
(14.58%)
7.52
(−0.76%)
7.49
(−1.11%)
2 10.84 12.71
(17.29%)
11.01
(1.60%)
10.87
(0.34%)
3 14.13 17.79
(25.87%)
15.40
(8.99)
15.37
(8.80%)
5. Analysis
The s uc u al pe o mance o he cas le was e alua ed using wo me hods o applying
an ou -o -plane o ce o o e u n he s uc u e. The i s o hese me hods was a simple
limi analysis o ou line expec a ions; he second used a non-linea s a ic analysis, also
known as a pusho e analysis in an FEA en i onmen . This me hod o e alua ing he
seismic beha io o an i egula his o ical mason y s uc u e has been success ully used
and is well documen ed [
1
]. All me hods we e compa ed o he expec ed peak g ound
accele a ion o he egion acco ding o he local design codes [
9
]. The esul s o hese
analyses ep esen a ac o o g a i a ional accele a ion, equal o 9.81 m/s
2
, applied o he
sel -weigh o he s uc u e uni o mly ac oss i s body.
5.1. Limi Analysis
The b ie analy ical limi analysis was conduc ed o a 1 m long c oss-sec ion o he
wes wall, conside ing a hickness in he ou -o -plane di ec ion o 1.7 m and he a e age o
he minimum and maximum heigh o he wall o 6.4 m. The analysis conside ed a o ce
p opo ional o he sel -weigh being applied a exac ly he mid-heigh , using a ac o (
α
)
o ep esen his o ce. The ac o is de ined as he a io o he o e u ning o he o ce o
he esis ing momen o a s uc u e’s sel -weigh a he poin o equilib ium. The analysis
Appl. Sci. 2025,15, 1518 19 o 24
was pe o med acco ding o a iangula , elas ic dis ibu ion o s ess a he base o he wall
using he ollowing equa ion:
α=W∗ k
2−
W∗h
2
=
k
2−2∗W
3∗ c∗L
h
2
(7)
whe e k [m] is he hickness o he wall, h [m] is he heigh o he wall, W [kN] is he
sel -weigh o he wall se in he geome ic cen oid, c [kN/m
2
] is he comp essi e s eng h
o he mason y, L [m] is he leng h o wall conside ed, and [m] is he dis ance o he
hinge om he side o he wall. The alue o
α
using his me hod was 0.25 g, o 25% o he
sel -weigh applied la e ally o he s uc u e.
5.2. Non-Linea S a ic Analysis
The FE model o he wes wall was u he educed o ep esen only he wall i sel
and no he adjoining s uc u es o he no h owe and he sou he n wall. In his way,
i was possible o explo e ex eme cases o he end condi ions o he adjoining mason y.
The lowes o hese condi ions ep esen s a wo s -case scena io, in he o m o a weak
connec ion o he adjoining mason y. I his minimum condi ion is conside ed sa e, hen
any g ea e s a e o connec ion will be as well. The o he ex eme conside ed he connec ing
su aces as ully ansla ionally ixed wi h he in en o modeling a ailu e pa e n indica i e
o a ching beha io . The eal s a e o he wall should be somewhe e be ween hese wo
ex emes. In each case, he load in he ou -o -plane di ec ion was sequen ially inc eased
using he secan me hod o he con e gence o he bounda y alue p oblem. An ene gy
me hod wi h a con e gence c i e ion o 10
−3
was used, alongside a c-leng h and line sea ch
me hods o assis in con e gence, ollowing me hods ou lined in he li e a u e [
6
]. Each
model was i s loaded e ically unde he sel -weigh o he wall using i e equal load
s eps be o e he sequen ial non-linea s a ic, o pusho e i e a ions we e pe o med.
Ul ima ely, he walls we e able o exhibi non-linea beha io , as e iden by he
app oxima ely bilinea egimes ou lined by he esul ing capaci y cu es o bo h condi ions
(Figu e 13). The capaci y cu e modeled by he pusho e analysis p esen s he di e ences in
he wo u ilized bounda y condi ion models isually. The ully ixed condi ion immedia ely
exhibi s a s eepe ise in load ac o o a gi en displacemen , a ibu ed o he inc eased
s i ness and capaci y p o ided by he s onge bounda y condi ions. The sligh dip in he
load ac o ha appea s jus a e 2 mm could be indica i e o he o ma ion o c acks and
he dissipa ion o ene gy as he slope changes and he model en e s he la e non-linea
egime. The ully ee model exhibi s a less signi ican ise in he ini ial slope, equi ing a
smalle load ac o o achie e a simila amoun o displacemen . As he non-linea beha io
begins a a load ac o sligh ly abo e 0.2, he lack o ene gy dissipa ion capaci y due o he
absence o bounda y cons ain s esul s in a much less signi ican inc ease in displacemen
o a gi en load ac o as he mason y con inues o de o m. The na u e o his de o ma ion
will be discussed la e . The comple ely ee end condi ions exhibi ed a maximum load
ac o o 0.25 g being applied la e ally o he wall, while he ully ixed condi ions con inued
o a alue o almos 0.80 g.
Appl. Sci. 2025,15, 1518 20 o 24
Appl. Sci. 2025, 15, x FOR PEER REVIEW 20 o 25
0.2, he lack o ene gy dissipa ion capaci y due o he absence o bounda y cons ain s
esul s in a much less signi ican inc ease in displacemen o a gi en load ac o as he
mason y con inues o de o m. The na u e o his de o ma ion will be discussed la e . The
comple ely ee end condi ions exhibi ed a maximum load ac o o 0.25 g being applied
la e ally o he wall, while he ully ixed condi ions con inued o a alue o almos 0.80 g.
Figu e 13. Capaci y cu e compa ing ully ixed and ully ee end condi ions o pusho e analysis
o he wes wall.
Fo he e sion o he model conside ing ully ee end condi ions, a o al o 37
con e ged s eps we e able o ou line he de o med shape o he wall as i was sequen ially
loaded h ough he linea elas ic egime, in o non-linea beha io . A maximum
displacemen o 7.8 mm was eached a he highes po ion o he wall, and he s uc u e
was able o wi hs and 0.25 g in he ou -o -plane di ec ion. As he s uc u e eached ailu e,
comp essi e s esses in he ou e oe o he wall inc eased, app oaching he c ushing
s eng h o he mason y, as ou lined by he minimum p incipal s ess in he model (Figu e
14a). A he same ime, a c ack o med on he opposi e side o he wall, consis en wi h he
expec ed beha io o an o e u ning can ile e ed wall (Figu e 14b). C acks began o
appea i s a he uppe base o he wall, indica ed by he maximum p incipal s ain in
he model. Some nuances we e obse ed as a esul o he complexi y o he lowe po ion
o he wall used in modeling; he maximum s ess did no ollow he base ac oss i s leng h
and ins ead jumped o e he mid-po ion o he base ha ex ends downwa d.
(a) (b)
Figu e 14. Resul s om he pusho e analysis o he wes wall wi h ee end condi ion: (a) minimum
p incipal s ess ( iew om he ou side o he wall); (b) maximum p incipal s ain ( iew om he in-
side o he wall).
Figu e 13. Capaci y cu e compa ing ully ixed and ully ee end condi ions o pusho e analysis
o he wes wall.
Fo he e sion o he model conside ing ully ee end condi ions, a o al o 37 con-
e ged s eps we e able o ou line he de o med shape o he wall as i was sequen ially
loaded h ough he linea elas ic egime, in o non-linea beha io . A maximum displace-
men o 7.8 mm was eached a he highes po ion o he wall, and he s uc u e was able o
wi hs and 0.25 g in he ou -o -plane di ec ion. As he s uc u e eached ailu e, comp essi e
s esses in he ou e oe o he wall inc eased, app oaching he c ushing s eng h o he
mason y, as ou lined by he minimum p incipal s ess in he model (Figu e 14a). A he
same ime, a c ack o med on he opposi e side o he wall, consis en wi h he expec ed
beha io o an o e u ning can ile e ed wall (Figu e 14b). C acks began o appea i s a
he uppe base o he wall, indica ed by he maximum p incipal s ain in he model. Some
nuances we e obse ed as a esul o he complexi y o he lowe po ion o he wall used in
modeling; he maximum s ess did no ollow he base ac oss i s leng h and ins ead jumped
o e he mid-po ion o he base ha ex ends downwa d.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 20 o 25
0.2, he lack o ene gy dissipa ion capaci y due o he absence o bounda y cons ain s
esul s in a much less signi ican inc ease in displacemen o a gi en load ac o as he
mason y con inues o de o m. The na u e o his de o ma ion will be discussed la e . The
comple ely ee end condi ions exhibi ed a maximum load ac o o 0.25 g being applied
la e ally o he wall, while he ully ixed condi ions con inued o a alue o almos 0.80 g.
Figu e 13. Capaci y cu e compa ing ully ixed and ully ee end condi ions o pusho e analysis
o he wes wall.
Fo he e sion o he model conside ing ully ee end condi ions, a o al o 37
con e ged s eps we e able o ou line he de o med shape o he wall as i was sequen ially
loaded h ough he linea elas ic egime, in o non-linea beha io . A maximum
displacemen o 7.8 mm was eached a he highes po ion o he wall, and he s uc u e
was able o wi hs and 0.25 g in he ou -o -plane di ec ion. As he s uc u e eached ailu e,
comp essi e s esses in he ou e oe o he wall inc eased, app oaching he c ushing
s eng h o he mason y, as ou lined by he minimum p incipal s ess in he model (Figu e
14a). A he same ime, a c ack o med on he opposi e side o he wall, consis en wi h he
expec ed beha io o an o e u ning can ile e ed wall (Figu e 14b). C acks began o
appea i s a he uppe base o he wall, indica ed by he maximum p incipal s ain in
he model. Some nuances we e obse ed as a esul o he complexi y o he lowe po ion
o he wall used in modeling; he maximum s ess did no ollow he base ac oss i s leng h
and ins ead jumped o e he mid-po ion o he base ha ex ends downwa d.
(a) (b)
Figu e 14. Resul s om he pusho e analysis o he wes wall wi h ee end condi ion: (a) minimum
p incipal s ess ( iew om he ou side o he wall); (b) maximum p incipal s ain ( iew om he in-
side o he wall).
Figu e 14. Resul s om he pusho e analysis o he wes wall wi h ee end condi ion: (a) minimum
p incipal s ess ( iew om he ou side o he wall); (b) maximum p incipal s ain ( iew om he
in-side o he wall).
The second a ia ion o he analysis, which used ully ixed end condi ions, was
s opped a e 144 success ully con e ged load s eps. The model eached a capaci y o 0.76 g,
o e h ee imes highe han he p e ious model. The de o med s uc u e demons a ed an
a ching beha io a he heigh o he wall as he midspan bulged ou wa ds in he di ec ion
he load was applied. F om he poin o maximum displacemen , he displacemen a
Appl. Sci. 2025,15, 1518 21 o 24
a gi en poin dec eased adially un il he ixed end condi ions we e me . Comp essi e
p incipal s esses indica ed c ushing a he base o he wall and along he ou e edges o
he ex e io o he wall (Figu e 15a). Maximum p incipal s ain ou lined he o ma ion o
a cu ed c ack on he in e io o he wall as i begins o ail, consis en wi h he a ching
beha io (Figu e 15b). The c ack ollows he base o he wall a he uppe side o he wall,
which is bo h sho e and mo e ele a ed han he alle , lowe sec ion in which he c ack
p opaga es di ec ly h ough he mason y. The ixed end condi ions allow he wall o beha e
mo e like a beam and less like a can ile e , allowing i o esol e shea o ces and ele an
s esses due o ho izon al loading a he end condi ions.
Appl. Sci. 2025, 15, x FOR PEER REVIEW 21 o 25
The second a ia ion o he analysis, which used ully ixed end condi ions, was
s opped a e 144 success ully con e ged load s eps. The model eached a capaci y o 0.76
g, o e h ee imes highe han he p e ious model. The de o med s uc u e demons a ed
an a ching beha io a he heigh o he wall as he midspan bulged ou wa ds in he
di ec ion he load was applied. F om he poin o maximum displacemen , he
displacemen a a gi en poin dec eased adially un il he ixed end condi ions we e me .
Comp essi e p incipal s esses indica ed c ushing a he base o he wall and along he
ou e edges o he ex e io o he wall (Figu e 15a). Maximum p incipal s ain ou lined he
o ma ion o a cu ed c ack on he in e io o he wall as i begins o ail, consis en wi h
he a ching beha io (Figu e 15b). The c ack ollows he base o he wall a he uppe side
o he wall, which is bo h sho e and mo e ele a ed han he alle , lowe sec ion in which
he c ack p opaga es di ec ly h ough he mason y. The ixed end condi ions allow he
wall o beha e mo e like a beam and less like a can ile e , allowing i o esol e shea
o ces and ele an s esses due o ho izon al loading a he end condi ions.
(a) (b)
Figu e 15. Resul s om he pusho e analysis o he wes wall wi h ully ixed end condi ion: (a)
minimum p incipal s ess ( iew om he ou side o he wall); (b) maximum p incipal s ain ( iew
om he inside o he wall).
5.3. Sa e y E alua ion
The ac ual condi ions o he wall a e likely o exhibi beha io wi h cha ac e is ics o
bo h ailu e pa e ns. The suppo condi ions sugges ed by he model calib a ion a e o
signi ican ly good quali y, hough unlikely o be comple ely ansla ionally ixed. Fo he
pu pose o e alua ing he sa e y o he s uc u e unde seismic loading, howe e , he
analysis in his case is sufficien . Di ec compa isons can be made be ween he expec ed
peak g ound accele a ion (PGA) om local design codes and he alues esul ing om
he analyses. Spanish seismic codes use p obabilis ic seismic haza d analysis o es ima e
he expec ed PGA o a gi en loca ion, in eg a ing da a om his o ical and ins umen al
eco ds o seismici y, which ypically e e ence magni ude in e ms o he momen
magni ude scale (Mw). Spanish seismic codes ou line Lanja ón as one o he mo e
seismically suscep ible egions in Spain, wi h an expec ed PGA alue o 0.18 g [9]. A
minimum, he wall was able o achie e a alue o 0.25 g be o e collapse. This s eng h can
be conside ed sufficien o wi hs and local peak g ound accele a ions acco ding o he
code. A sa e y ac o can be ob ained om he a io o he minimum peak alue achie ed
o he PGA o he a ea, de ined as 0.25 g/0.18 g = 1.39. Howe e , he posi ioning o he
cas le a op a s eep ocky slope and he local aqui e s o he su ounding egion could
des abilize he g ound a ound he s uc u e as sugges ed in [35].
Figu e 15. Resul s om he pusho e analysis o he wes wall wi h ully ixed end condi ion:
(a) minimum p incipal s ess ( iew om he ou side o he wall); (b) maximum p incipal s ain ( iew
om he inside o he wall).
5.3. Sa e y E alua ion
The ac ual condi ions o he wall a e likely o exhibi beha io wi h cha ac e is ics
o bo h ailu e pa e ns. The suppo condi ions sugges ed by he model calib a ion a e
o signi ican ly good quali y, hough unlikely o be comple ely ansla ionally ixed. Fo
he pu pose o e alua ing he sa e y o he s uc u e unde seismic loading, howe e , he
analysis in his case is su icien . Di ec compa isons can be made be ween he expec ed
peak g ound accele a ion (PGA) om local design codes and he alues esul ing om he
analyses. Spanish seismic codes use p obabilis ic seismic haza d analysis o es ima e he
expec ed PGA o a gi en loca ion, in eg a ing da a om his o ical and ins umen al eco ds
o seismici y, which ypically e e ence magni ude in e ms o he momen magni ude scale
(Mw). Spanish seismic codes ou line Lanja ón as one o he mo e seismically suscep ible
egions in Spain, wi h an expec ed PGA alue o 0.18 g [
9
]. A minimum, he wall was
able o achie e a alue o 0.25 g be o e collapse. This s eng h can be conside ed su icien
o wi hs and local peak g ound accele a ions acco ding o he code. A sa e y ac o can
be ob ained om he a io o he minimum peak alue achie ed o he PGA o he a ea,
de ined as 0.25 g/0.18 g = 1.39. Howe e , he posi ioning o he cas le a op a s eep ocky
slope and he local aqui e s o he su ounding egion could des abilize he g ound a ound
he s uc u e as sugges ed in [35].
6. Conclusions
In his wo k, an ex ensi e a ay o non-des uc i e es s o si es o cul u al signi icance
we e p esen ed and pe o med o he Cas le o Lanja ón, Spain. The wo ks explo ed he
applica ion o a Schmid hamme , Schmid pendulum hamme , pene ome e , sc a ch es
Appl. Sci. 2025,15, 1518 22 o 24
de ice, and a se ies o di ec and indi ec sonic es s o wa e-based me hods o cha ac e ize
he ma e ials o he s uc u e and hei mechanical p ope ies. Dynamic iden i ica ion was
employed o egis e ambien ib a ions and ob ain ele an in o ma ion o he nume ical
models. Th ee p ima y modes we e ob ained om he dynamic iden i ica ion p ocess
unde 15 Hz, being 7.58 Hz, 10.84 Hz, and 14.13 Hz. The undamen al equencies o
ib a ion we e selec ed manually and u he alida ed using EFDD and SSI-UPC me hods.
Ope a ional Modal Analysis was used o calib a e and alida e a de eloped homogenized
3D FE model o he wes wall o he cas le. This was used o assess he seismic beha io o
he si e using non-linea s a ic analysis in addi ion o limi analysis. The beha io o he
s uc u e was e alua ed o sa e y in acco dance wi h cu en design codes.
The e icacy o wa e-based me hods and OMA we e highligh ed in he s udy; sonic
es esul s we e able o e ec i ely p edic he ange o he elas ic modulus (1.5–2.0 GPa)
ha esul ed om an eigen ec o analysis o he model, which conside ed an ini ial alue
o 2.0 GPa bu was ul ima ely success ul in calib a ion wi h a alue o 1.5 GPa. The alues
ob ained om indi ec sonic es ing we e wi hin 3% o he calib a ed elas ic modulus o
he wall, while hose om di ec es ing we e a ound 33% highe . The Modal Assu ance
C i e ia we e used o alida e he mo emen o he wes wall in he FE model and he
expe imen ally ga he ed da a om OMA o abo e 85% ag eemen o all modes p esen ed.
The calib a ed equencies o he FE model we e 7.52 Hz, 11.01 Hz, and 15.4 Hz, which
displayed an a e age absolu e e o o 3.8% and maximum absolu e e o o 9.0%.
Limi analysis and FEA allowed o he e alua ion o he seismic beha io o he wall
in he ou -o -plane di ec ion, he mos ulne able o mason y s uc u es. Common ailu e
pa e ns we e explo ed, ul ima ely concluding ha he s uc u e could wi hs and he local
peak g a i a ional accele a ions o 0.18 g as de ined by he Spanish seismic design codes
due o seismic ac i i y. A sa e y ac o o 1.39 was ob ained om he a io o he minimum
peak alue achie ed om non-linea s a ic analysis, 0.25 g, o he PGA o he a ea, 0.18 g.
The no el y o his case s udy p esen s indings ha should be obse ed and consid-
e ed o all u u e wo ks on he Cas le o Lanja ón. The app oach p esen s a amewo k ha
can be adop ed o he e alua ion o egula and i egula his o ical mason y s uc u es
alike. I is especially ele an o si es ha a e o he wise di icul o pe o m common
NDTs on. While mo e adi ional NDTs (Schmid hamme , Schmid pendulum hamme ,
pene ome e , and sc a ch es ing ins umen ) we e less success ul in hei applica ion on
he i egula ly su aced mason y, he wa e-based es s and modal analysis we e ex emely
success ul in hei applica ion. These me hods we e able o wholis ically app oxima e he
mechanical beha io o he s uc u e in e ms o a homogeneous modulus o elas ici y and
modal pa ame e s including mode shapes and equencies o ib a ion. These wholis ic
alues complemen ed he use o he mac o-modeling app oach o mason y and he homog-
eniza ion assump ions ha i en ails. These me hods can s ongly be ecommended o he
p elimina y seismic assessmen o a si e whe e esou ce a ailabili y and he applicabili y o
analog me hods is di icul .
Fu he analyses beyond he scope o he pape o he Cas le o Lanja ón a e ecom-
mended. Ano he non-linea pusho e analysis using mo e accu a e bounda y condi ions
o he wall wi h mo e compu a ional ime could p o ide a mo e accu a e assessmen o he
abili y o he wes wall o esis la e al o ces. A non-linea dynamic analysis o he wall
o a mo e gene al model o he cas le could be e suppo he seismic sa e y conclusions
o his pape [
5
]. Fu he in es iga ions making use o mac o-modeling echniques could
u ilize deep lea ning o AI-based imaging models o de elop hei FE models bu may be
simila ly challenged due o he i egula i y o he mason y in he cas le [36].
Appl. Sci. 2025,15, 1518 23 o 24
Supplemen a y Ma e ials: The ollowing suppo ing in o ma ion can be downloaded a : h ps://www.
mdpi.com/a icle/10.3390/app15031518/s1, Appendix S1: Pho og amme ic su ey and damage
mapping o he Cas le o Lanja ón.
Au ho Con ibu ions: H.L.: concep ualiza ion, me hodology, alida ion, o mal analysis, in es iga-
ion, da a cu a ion, w i ing—o iginal d a p epa a ion, and isualiza ion. R.R.: concep ualiza ion,
me hodology, in es iga ion, da a cu a ion, o mal analysis, w i ing— e iew and edi ing, and isual-
iza ion. P.P.: concep ualiza ion, me hodology, esou ces, w i ing— e iew and edi ing, supe ision,
and p ojec adminis a ion. P.B.L.: concep ualiza ion, me hodology, esou ces, w i ing— e iew and
edi ing, supe ision, p ojec adminis a ion, and unding acquisi ion. All au ho s ha e ead and
ag eed o he published e sion o he manusc ip .
Funding: This wo k was pa ly inanced by FCT/MCTES h ough na ional unds (PIDDAC) unde
he R&D Uni Ins i u e o Sus ainabili y and Inno a ion in S uc u al Enginee ing (ISISE), unde e -
e ence UIDB/04029/2020 (doi.o g/10.54499/UIDB/04029/2020), and unde he Associa e Labo a o y
Ad anced P oduc ion and In elligen Sys ems ARISE unde e e ence LA/P/0112/2020.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : The o iginal con ibu ions p esen ed in he s udy a e included in he
a icle. Fu he inqui ies can be di ec ed o he co esponding au ho .
Acknowledgmen s: This wo k would no ha e been possible wi hou he in ol emen o many
people and pa ies. We would like o hank he Delegación P o incial de Cul u a de G anada, and
he Lanja ón Ci y Hall o allowing his wo k o ake place; Membe s o he Uni e si y o Minho o
hei echnical suppo in modeling and calib a ion; and he esiden s o Lanja ón o hei lo e o he
cas le and pho og aphy, alongside hei hospi ali y and dedica ion.
Con lic s o In e es : The au ho s decla e no con lic s o in e es . The unde s had no ole in he design
o he s udy; in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip ; o
in he decision o publish he esul s.
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Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o
people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
