NSIE#1857795, VOL 0, ISS 0
Value o addi ional a ic da a in he con ex o b idge se ice-
li e managemen
Dominik Skokandi
c and Ana Mandi
c I anko i
c
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PROOFONLY
Value o addi ional a ic da a in he con ex o b idge se ice-li e managemen
Dominik Skokandi
c and Ana Mandi
c I anko i
c
Depa men o S uc u es, Facul y o Ci il Enginee ing, Uni e si y o Zag eb, Zag eb, C oa ia
ABSTRACT
The assessmen o exis ing oad b idges as pa s o in as uc u e ne wo ks is equi ed in conside a ion
o hei de e io a ion and age. Ad anced moni o ing and managemen ools a e mainly used o land-
ma k b idges while he decision making p ocess o small o medium b idges, which cons i u e he
majo i y o he b idge ne wo k, mainly elies on condi ion assessmen based on expe ience and con-
se a i e analysis ela ed o design codes. In he analysis o he load-ca ying capaci y o heses
b idges, loads imposed by he passing a ic a e p edominan due o hei a iable na u e and le el
o unce ain ies. The esea ch p esen ed in his pape ou lines he alue o addi ional a ic da a, col-
lec ed wi h bo h a ic coun e s and Weigh-in-Mo ion (WIM) me hod in he scope o assessmen p o-
cedu es o hese b idges. Adequa e p ocessing o collec ed a ic da a is c ucial o subsequen
ex apola ion o maximum load e ec s on a pa icula b idge o e a ce ain pe iod in ime. By aking
in o accoun all ela ed cos s, he pu pose o his pape is o p o e he bene i s o employing a ic
load moni o ing da a in s uc u al assessmen and subsequen decision-making p ocess in se ice li e
managemen o b idges.
ARTICLE HISTORY
Recei ed 27 Ap il 2020
Re ised 22 Sep embe 2020
Accep ed 29 Sep embe 2020
KEYWORDS
Assessmen ; decision-
making; exis ing b idges;
se ice-li e managemen ;
Value o in o ma ion;
weigh-in-mo ion
1. In oduc ion
Vas majo i y o ci il in as uc u e in he USA and
Wes e n Eu ope has been cons uc ed in he 1960s and
1970s and is cu en ly a he isk o ageing and in di e need
o assessmen and ehabili a ion. The de e io a ion and age-
ing p ocess is especially e iden on he exis ing oad b idges,
which ep esen a c i ical pa o global anspo a ion ne -
wo ks, as he consequences o hei po en ial ailu e would
be se e e, om bo h social and economic aspec s.
The e o e, he sa e y assessmen o hese b idges is equi ed
o he e alua ion o hei eliabili y le els, as hey ha e
been designed and cons uc ed acco ding o old codes,
which we e no as s ic as cu en s anda ds, in e ms o
loading and esis ance modelling (Skokandi
c, 2020).
One o key s eps in he design o assessmen p ocess o
new o exis ing b idges is he de e mina ion o o al load
e ec s a c i ical sec ions o he b idge. Due o hei a iable
na u e, mos signi ican e ec s a e induced by he a ic
passing o e he b idge i sel (O’Conno & O’B ien, 2005).
P ac ical applica ion o a ic load models om cu en
design codes o new b idges (Eu ocode, 2005) in he assess-
men p ocedu e o exis ing ones may p o ide conse a i e
esul s sugges ing ha majo i y o hese b idges need o be
s eng hened o e en eplaced. On he o he hand, mo e
ecen esea ch has p o en ha he applica ion o si e-spe-
ci ic a ic load models, de i ed om S uc u al Heal h
Moni o ing (SHM) da a, esul s in inc eased eliabili y le els
and, consequen ly, in an un es ic ed use o he b idge o e
a much longe emaining se ice li e (Skokandi
c, 2020). In
addi ion, ex eme a ic loads can be quan i ied om
collec ed da a so as o nume ically e alua e b idge esponse
unde ex eme load scena ios and compa e hem wi h ala m
le els es ablished by b idge designe s (Sousa, Cos a,
Hen iques, Ben o, & Figuei as, 2015). These load models a e
de eloped om he collec ed eal-li e a ic da a ob ained
using he Weigh -in-Mo ion (WIM) echnology, a measu e-
men p ocedu e o he collec ion o a ic da a as a pa o
SHM ools. WIM de ices ins alled ou side he b idge leng h
a e pa icula ly in e es ing om he ne wo k-le el pe spec-
i e since, i well designed, hey allow cha ac e isa ion o
a ic load pa e ns o a se o b idges wi hin a oadway
ne wo k (Mandi
c I anko i
c, S auss, & Sousa, 2020).
In addi ion o hese s udies, a numbe o esea ch p oj-
ec s, bo h in Eu ope and wo ldwide, ha e ocused o e he
las wo decades on he opics o b idge assessmen , inspec-
ion, and S uc u al Heal h Moni o ing (SHM) in he con-
ex o he b idge managemen p ocess. One o hese
p ojec s is he ecen ly concluded COST Ac ion TU1402
“Quan i ying he Value o S uc u al Heal h Moni o ing”.
The p ojec was ini ia ed o add ess he challenges o alid-
a ion and quan i ica ion o he SHM da a om he pe spec-
i e o s akeholde s and in as uc u e owne s (Th€
ons e al.,
2017) and i esul ed in he decision-suppo ing guidelines
o ope a o s, p ac icing enginee s and scien is s
(Diaman idis, Syko a, & Sousa, 2019; Helde Sousa, Wenzel,
&Th
€
ons, 2019;Th
€
ons, 2019). The heo e ical amewo k
de eloped wi hin he TU1402 ac ion is based on implemen-
a ion o he Value o In o ma ion (VoI) analysis and deci-
sion ee me hod in he decision-making p ocess ega ding
he u iliza ion o SHM da a. In he cu en s a e o p ac ice,
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CONTACT Dominik Skokandi
c[email p o ec ed] Depa men o S uc u es, Facul y o Ci il Enginee ing, Uni e si y o Zag eb, Zag eb, C oa ia
ß2020 In o ma UK Limi ed, ading as Taylo & F ancis G oup
STRUCTURE AND INFRASTRUCTURE ENGINEERING
h ps://doi.o g/10.1080/15732479.2020.1857795
PROOFONLY
SHM is mo e used o esea ch pu poses han o eal s uc-
u es. This is mainly due o he lack o unde s anding o he
alue o addi ional in o ma ion ha is gained using SHM
ools, as e en in he cases when SHM is implemen ed, i s
in o ma ion is o en dis ega ded by b idge owne s and engi-
nee s in cha ge, and he decisions a e based on expe ience,
equen ly wi h conse a i e assump ions (Zon a, Glisic, &
Ad iaenssens, 2014). Un o una ely, such p ac ices can esul
in unnecessa ily high main enance and ehabili a ion cos s
o b idges and iaduc s, which a e he e o e deemed c i ical
elemen s o he anspo in as uc u e ne wo ks.
Fu he mo e, e e y pa ial o comple e closu e o hese
b idges leads o bo h di ec losses incu ed by b idge owne s
and indi ec losses o b idge use s, no o men ion socio-
economic cos s o he local communi y. These indi ec
cos s can be signi ican and, o impo an b idges, hey can
e en be highe han he di ec ones (Tho -Ch is ensen,
2009, Tho -Ch is ensen, 2012).
None heless, i b idge moni o ing could be designed and
implemen ed as a complemen o isual inspec ion, o
enhance i s e ec i eness and imp o e on i s sho comings,
b idge owne s could decide o ecognise i s ad an age
(Mandi
c I anko i
c e al., 2020). In o de o add ess hese
issues in he con ex o b idge managemen p ocess, a
de ailed algo i hm o alida ion o addi ional SHM da a in
b idge assessmen p ocedu es has been de eloped in
(Skokandi
c, 2020), based on heo e ical amewo k de ined
in he COST TU1402 Ac ion.
The wo k p esen ed in his pape aims o quan i y he
alue o inco po a ing b idge assessmen esul s based on
a ic load moni o ing da a in o he decision-making p o-
cess o b idge main enance and managemen , using he
VoI me hodology de eloped in (Skokandi
c, 2020). Al hough
a ic measu emen s discussed in he pape a e eco ded
egula ly, hey a e cu en ly only used o a ic analysis
and selec ion o o e loaded ehicles. In his esea ch, hey
a e implemen ed in he p ocedu e o b idge assessmen .
The bene i s o he assessmen esul s om he owne ’s
poin o iew in e ms o educed o e all main enance cos s
a e also in es iga ed. By doing so, esul s o pos e io VoI
(based on a ailable da a om a ic coun e s in he coun y
and WIM measu emen s on a oad leading o a ce ain
b idge) could con ince he ope a o o in es in mo e a ic
load analysis and WIM measu emen s (a di e en loca-
ions) and o use he exis ing and subsequen ly collec ed
a ic load and WIM da a in b idge managemen , and no
only o a ic coun ing and weigh limi a ions as i has
been done so a .
In he i s pa o he pape , he emphasis is placed on
he WIM echnology, de elopmen o a ic load models,
and eliabili y analysis o he Case S udy b idge. Th ee dis-
inc assessmen le els (s a egies) will be conside ed: a he
ini ial le el, he assessmen is pe o med wi hou any add-
i ional a ic in o ma ion, using he codi ied Load model 1.
A he second le el, he assessmen is conduc ed based on
Load model 1 adjus ed in espec o hea ies a ic meas-
u emen s in he coun y and, a he hi d le el, he assess-
men is based on speci ic a ic load ela ed o con inuous
WIM measu emen s on a oad leading o a b idge.
De elopmen o he pos e io VoI analysis algo i hm and
es ima ion o all ela ed cos s and bene i s a e p o ided in
he second pa o he pape o he h ee assessmen s a -
egies (S0 ela ed o le el 1 assessmen , S1 ela ed o le el 2
assessmen , and S2 ela ed o le el 3 assessmen ). The ana-
lysis o VoI esul s, and ecommenda ions o u u e
esea ch, a e gi en in he concluding sec ion ha p esen s
bene i s o employing a ic load moni o ing da a in s uc-
u al assessmen and subsequen decision-making p ocess
wi hin he se ice li e managemen o b idges.
2. Impo ance o a ic load modelling in
assessmen o exis ing b idges
2.1. O e iew
Reliabili y analysis o bo h new and exis ing s uc u es is a
p ocedu e in which s uc u al esis ance is e alua ed in ela-
ion o he o al e ec o he applied loads, in o de o
quan i y he sa e y le el o eliabili y o he s uc u e. Fo
b idges, dominan loads a e desc ibed as pe manen loads,
consis ing o he s uc u e sel -weigh and addi ional dead
loads ( oad su acing, ailings, e c.), and li e loads induced
by he passing a ic. Rega dless o he eliabili y analysis
me hod (de e minis ic, semi-p obabilis ic, p obabilis ic),
a ic loads a e associa ed wi h he highes le el o unce -
ain ies, due o hei a iable and unp edic able na u e.
Addi ionally, o exis ing b idges, which ha e educed eli-
abili y le els when compa ed o new b idges, pe manen
loads can be accu a ely calcula ed based on he on-si e
geome y measu emen s and ma e ial es ing, hus u he
educing hei unce ain y le els. On he o he hand, loads
induced by he passing a ic can be ei he es ima ed using
codi ied load models o he design o new b idges, o
de eloped using he eco ded a ic da a. Some coun ies,
such as Ne he lands, Denma k, Swi ze land, and Slo enia,
ha e de eloped speci ic b idge assessmen codes based on
he educed a ic load models o si e-speci ic models
(Skokandi
c, 2020;Wi
sniewski, Casas, & Ghosn, 2012).
P inciples o weighing ehicles in mo ion using b idges,
which a e alid o his day, we e i s es ablished by Moses
in he USA (Moses, 1979). In he la e 1990s, esea ch in e -
es in B-WIM in ensi ied as wo esea ch p ojec s suppo ed
by he Eu opean Commission we e ini ia ed based on he B-
WIM wo k om Slo enia and s udies om I eland: COST
Ac ion 323 –Weigh in Mo ion o Road ehicles (Jacob,
2002) and FP4 p ojec WAVE –Weighing o Axles and
Vehicles (Jacob, 2002) in Eu ope. Mo e ecen imp o e-
men s in B-WIM echnology we e achie ed as a pa o wo
FP7 esea ch p ojec s, TRIMM (Ralbo sky e al., 2014) and
BRIDGEMON (Co baly,
Znida i
c, Leahy, Hajializadeh, &
Zupan, 2014; Fa ai e al., 2014).
In C oa ia, he e a e s ill no o icial codes o guidelines
o modelling a ic loads in he assessmen p ocess o he
exis ing oad b idges, and his modelling is also no
included in o icial EU s anda ds Eu ocodes. On he o he
hand, a ic da a measu emen s ha e been conduc ed egu-
la ly on C oa ian s a e oads o o e wo decades, using
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2 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
bo h WIM and B-WIM echnology (Skokandi
c, Mandi
c
I anko i
c,
Znida i
c, & S bi
c, 2019). Resea ch ocusing on
he use o eco ded a ic da a in he assessmen p ocedu es
o oad b idges in C oa ia has been conduc ed a he
Uni e si y o Zag eb o e he las decade, as epo ed in
se e al pape s (Mandi
c I anko i
c, Skokandi
c,
Znida i
c, &
K eslin, 2019; Mandi
c, Radi
c, &
Sa o , 2009; Skokandi
c,
Mandi
c I anko i
c, & D
zeba, 2016) and PhD hesis (Mandi
c
I anko i
c, 2008; Skokandi
c, 2020). This pape ocuses on
he quan i ica ion o measu ed a ic da a om he pe spec-
i e o b idge owne s and b idge use s.
In gene al, a ic load on oad b idges can be di ided
in o conges ed a ic, basically a a ic jam si ua ion, and
ee- low a ic, which is a s eady a ic low o 60-100 km/
h. Fu he mo e, om he enginee ing poin o iew, he
a ic load is di ided in o he s a ic and dynamic compo-
nen s. Mos o he cu en design codes ha e he dynamic
pa al eady in eg a ed wi h he speci ied load models bu ,
in olde codes, dynamic ac o was calcula ed manually
depending on b idge cha ac e is ics (B uls, C oce, &
Sanpaolesi, 1996; B uls, Ma hieu, Calga o, & P a , 1996;
Dawe, 2003; Eu ocode, 2005; Skokandi
c e al., 2019). Mo e
de ailed his o ical e iew o a ic load models de eloped
o e he yea s can be ound in he book by Dawe (2003). In
C oa ia, a majo i y o exis ing s a e oad b idges ha e been
designed acco ding o olde codes, mainly PTP-5 ( alid un il
1973) and he codes based on he Ge man DIN 1072 ( alid
un il 2002). The Case S udy b idge analysed in his pape
was buil in he 1960s acco ding o PTP-5 code. Signi ican
inc ease in he a e age annual daily a ic (AADT) o e he
las wo decades o he pas cen u y caused he e ision o
design codes and accep ance o Eu opean s anda ds in he
2000s (Mandi
c & Radi
c, 2004; Skokandi
c e al., 2019).
The basic app oach o he de elopmen o a ic loads,
bo h si e-speci ic and mode n codi ied ones, is o collec a
ce ain amoun o a ic da a, including axle loads and
spacings, and o apply one o s a is ical me hods o ex apo-
la e he collec ed da a and es ima e he maximum expec ed
load e ec s. The e is a numbe o a ic da a collec ion
me hods a ailable, bu mos widely accep ed ones a e based
on he WIM and B-WIM me hods (
Znida i
c, K eslin,
La i
c, & Kalin, 2012). Codi ied a ic load models ha e
been de eloped o he design o new b idges and, he e o e,
hey may p o ide conse a i e esul s in he assessmen p o-
cedu e o exis ing b idges. The applica ion o localised,
adjus ed o si e-speci ic a ic load models in he assess-
men o exis ing b idges is c ucial o making op imum
managemen decisions.
2.2. Cu en a ic load models o he design o
new b idges
The Eu opean code EN 1991-2:2003 (Eu ocode, 2005)
de ines imposed loads, bo h models and ep esen a i e al-
ues, associa ed wi h oad a ic, which includes dynamic
e ec s, cen i ugal, b aking, and accele a ion ac ions o be
used o he design o new b idges. These load models we e
de eloped based on a ic da a collec ed wi h WIM
echnology on a mo o way in F ance in he 1980s. The da a
we e used o calcula ing load e ec s using in luence lines
and a eas, and ex apola ions we e made o e alua e e e -
ence alues o ep esen a i e a ic loads. A mo e de ailed
e iew on he backg ound and de elopmen o EN 1991-2
codes can be ound in (B uls, C oce, e al., 1996; B uls,
Ma hieu, e al., 1996).
The Load Model 1 (LM1), de ined as a gene al a ic
model ha al eady akes in o accoun dynamic ampli ica ion
due o ehicle-b idge in e ac ion, is used in he majo i y o
b idge designs o e e y oad and b idge ype and is he e-
o e implemen ed in he assessmen p ocedu e o he Case
S udy b idge in his pape . I is comp ised o wo andem
sys ems (TS) ep esen ing concen a ed axle loads and uni-
o mly dis ibu ed load (UDL) ac oss he en i e wid h o he
ca iageway. G aphical ep esen a ion o LM1 o s a e oad
b idges (wi h he o al wid h wunde 9.0 m) is gi en in
Figu e 1 (Skokandi
c e al., 2019).
Adjus men ac o s (Figu e 1)aQ,i,aq,iand aq, a e
used o he adjus men o o al a ic loads depending on
he oad ca ego y and expec ed a ic densi y and weigh .
Values o hese ac o s a e de ined in Na ional Annex o
each coun y, o i no speci ically indica ed, hey can be
aken equal o 1.0 o all new b idges, as i is he case in he
majo i y o EU coun ies. Ne e heless, some coun ies,
such as F ance, Ge many, and Ne he lands apply inc eased
alues o adjus men ac o s o ake in o accoun p edic ed
inc ease in a ic g ow h. A de ailed lis wi h alues o hese
speci ic adjus men ac o s o selec ed EU coun ies can be
ound in (Skokandi
c e al., 2019).
Adjus men ac o s om Figu e 1 can also be used o
he educ ion o o al a ic load e ec s in he assessmen
p ocedu e o exis ing oad b idges, by educing hei ini ial
alue o 1.0 based on he measu ed a ic da a. Fo
example, Swi ze land de ined na ional assessmen codes o
exis ing b idges and implemen ed educed adjus men ac-
o s based on b idge ype and span leng h (SIA, 2011). The
p ocedu e o calib a ion o adjus men ac o s based on
WIM da a, de ined by O’B ien e al. (2012), can be used o
a single b idge o he local anspo ne wo k. In C oa ia,
he a ic load e ec s calib a ion based on measu ed a ic
da a was conduc ed by Mandi
c I anko i
c(2008, 2009),
h ough analysis o na ional a ic eco ds. As a esul ,
educed alues o adjus men ac o s a e calib a ed and will
be used in his pape as one o assessmen s a egies in he
analysis o he Case S udy b idge. Reduced ac o alues,
depending on b idge ype and span leng h, a e gi en in
Table 1.
2.3. WIM and B-WIM as a pa o s uc u al
heal h moni o ing
T a ic da a collec ed using bo h WIM and B-WIM sys ems
cons i u e an unbiased a ic sample as he measu emen is
conduc ed in uncon olled condi ions and wi hou he need
o ehicle o slow down o s op. The da a se ob ained o
each ehicle passing o e he measu emen si e includes i s
g oss weigh (GVW), axle load, numbe and spacing, ehicle
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STRUCTURE AND INFRASTRUCTURE ENGINEERING 3
PROOFONLY
speed, and imes amp o he passage. Pos -p ocessing o col-
lec ed a ic da a is equi ed o hei ex apola ion and subse-
quen es ima ion o maximal load e ec s on he selec ed
b idge o e a ce ain ime pe iod, as i was done based on col-
lec ed WIM da a o he Case S udy b idge in his pape .
Addi ionally, B-WIM sys ems also p o ide supplemen al s uc-
u al da a on b idge esponse o he e ec o he passing a -
ic, such as measu ed in luence lines, load dis ibu ion, and
dynamic ac o s. This addi ional in o ma ion can be used as a
key inpu in assessmen p ocedu es o exis ing oad b idges,
applied o calib a ion o nume ical models, as p esen ed in
(Mandi
c I anko i
c, Skokandi
c, e al., 2019;
Znida i
c, Kalin, &
K eslin, 2018). Fo he p esen ed Case S udy b idge, con inu-
ous a ic da a measu emen s we e conduc ed using he pa e-
men WIM sys em on he oad leading o he b idge.
The e o e, he VoI analysis p esen ed in he second pa o he
pape willbeconduc edino de oquan i ybene i s esul ing
om inco po a ion o eco ded a ic da a in he assessmen
o exis ing oad b idges.
In gene al, he e a e wo main app oaches o he pos -
p ocessing o collec ed a ic da a, ei he using s a is ical
me hods, i.e. ex apola ing he da a by i ing i o a ce ain
dis ibu ion, o using a e y la ge numbe o long- un
simula ions like he Mon e Ca lo me hod. Fo example, in
he de elopmen p ocess o cu en design load models
om EN 1991-2, he pos -p ocessing was conduc ed using
h ee dis inc me hods, wo based on s a is ical app oach
( i ing he uppe da a ail o a hal -no mal and a Gumbel
dis ibu ion) and Mon e Ca lo (MC) simula ion o he al-
ida ion o ob ained esul s (B uls, C oce, e al., 1996). O he
commonly used me hods include Block Maxima, Peaks o e
Th eshold (POT), Box-Cox app oach (O’B ien e al., 2015),
and con olu ion me hod (
Znida i
c, 2017).
While s a is ical me hods a e subjec o a ce ain le el o
subjec i i y and can, he e o e, ha e a conside able ma gin
o e o , MC simula ions a e no p ac ical o gene al use,
as hey equi e a ce ain le el o knowledge and high com-
pu a ional powe . Fu he de ails on he mos widely used
pos -p ocessing me hods o he ex apola ion o a ic da a
can be ound in he e iew pape by O’B ien e al. (2015).
Along wi h he selec ion o a s a is ical ex apola ion
me hod, he selec ion o a e e ence ime pe iod is essen ial
in he pos -p ocessing o a ic da a and subsequen calcula-
ion o maximum expec ed a ic load e ec s. Fo example,
cha ac e is ic alues o LM1 (Figu e 1) we e ex apola ed o
a 50-yea e e ence pe iod du ing he de elopmen o EN
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
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404
405
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410
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413
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419
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423
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425
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427
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429
430
431
432
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435
436
437
438
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442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
Figu e 1. Example o LM1 on a wo-lane s a e oad b idge.
Table 1. Reduced adjus men ac o s o assessmen o s a e oad b idges in C oa ia - esea ch-based p oposal (Mandi
c e al., 2009).
Span [m] 10 10 –20 20 –30 30 –40 40 –50
Simply suppo ed b idge
aq,2¼aq, ¼1,0
aQ,10,80 0,80 0,80 0,80 0,80
aQ,2;aQ,3;aq,10,30 0,38 0,51 0,58 0,62
Con inuous b idge
aq,2¼aq, ¼1,0
aQ,10,80 0,80 0,80 0,80 0,80
aQ,2;aQ,3;aq,10,48 0,72 0,78 0,81 0,82
4 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
1991-2 (B uls, Ma hieu, e al., 1996). In o de o apply he
LM1 o sho e ime pe iods, wo app oaches can be used.
The i s one is o shi he Gumbel dis ibu ion o lowe
e e ence pe iods in o de o ob ain a lowe mean alue o
a ic load e ec s. Addi ionally, EN 1990 (Eu ocode, 2002)
p o ides simpli ica ion o educ ion o cha ac e is ic alues
o LM1 o a one-yea pe iod by simply educing ini ial al-
ues (Figu e 1) by 20%. The i s app oach is used o he
eliabili y analysis o he Case S udy B idge as he simpli i-
ca ion p o ided by EN 1990 is ela i ely conse a i e.
Chosen app oach u ilizes he p ope y o he Gumbel dis i-
bu ion ha he s anda d de ia ion is independen o he
conside ed e e ence pe iod and ha he mean alue
depends on he pe iod Tin he ollowing way (Fabe , 2012):
l50 ¼l1þ0, 78 1lnðT50Þ(1)
whe e:
l50,l1–a e he a ic load e ec s mean alues o 50-
and 1- yea e e ence pe iods;
1–is he a ic load s anda d de ia ion o 1- yea e e -
ence pe iod ( 1¼ 50Þ;
T–is he chosen e e ence pe iod.
The ex apola ion me hod chosen o his esea ch, called
con olu ion me hod, has p o en o p o ide simila esul s like
long- un simula ions and, a he same ime, i is compu a ion-
ally less complex and mo e sui able o p ac ical applica ion. I
was i s p oposed by Moses and Ve ma (1987), and has been
used and cons an ly imp o ed in Slo enia (
Znida i
ce al.,
2012) o o e wo decades wi h da a eco ded om SiWIMV
R
B-WIM sys em (
Znida i
c, 2017). The con olu ion me hod is
based on assump ions ha he a ic in wo adjacen lanes on
he b idge is independen and ha he highes load e ec s a e
achie ed when wo ehicles in each lane mee side by side a a
c i ical sec ion o he selec ed b idge. The desc ibed me hod
was de eloped a ound he ac ha , due o he ypical leng h
o hea y ehicles, c i ical loading scena ios o sho o
medium size b idges occu in he ee low a ic (while he
a ic jam si ua ions ypically ep esen c i ical loading scen-
a ios o long b idges). Such an app oach is jus i ied on a
majo i y o simply suppo ed con inuous b idges whose in lu-
ence-line leng hs be ween suppo s a e up o 30 me e s, and
has he e o e been chosen o he Case S udy b idge analysed
in his pape .
The con olu ion me hod applies he in luence line heo y
o he calcula ion o a ic load e ec o each ehicle, ol-
lowed by gene a ion o load e ec s his og ams o each
independen lane, he con olu ion o hese his og ams o
simula e he p esence o ehicles in bo h acks simul an-
eously, and subsequen ex apola ion o maximum alues o
ce ain ime pe iods. Fo u he de ails, his can be ound
elsewhe e (Skokandi
c,
Znida i
c, Mandi
c I anko i
c, &
K eslin, 2017;
Znida i
c, 2017).
3. Case s udy b idge
3.1. O e iew
The Case S udy b idge used in his esea ch was buil in
1961 as a con inuously ein o ced conc e e (RC) slab b idge
o e h ee spans. I is loca ed on a C oa ian s a e oad, nea
he own o Poseda je, and ea u es a o al deck wid h o 8.50
me e s, and wo a ic lanes, one o each di ec ion o a el.
Theb idgeiscon inuousac oss h eespans,9.0þ15.0 þ9.0
m, di ided wi h RC pie s and abu men s, and suppo ed on
RC ounda ions and wooden piles. The b idge se up in ol ing
a la ge cen al span has been selec ed due o hea y ain all,
which caused he collapse o he old conc e e a ch b idge ha
had been buil on he same loca ion in he 1960s. The o iginal
documen a ion and design plans, along wi h he buil -in
ein o cemen , a e a ailable om he a chi es (
S am, 2002).
The longi udinal and ans e se sec ions o he b idge a e p e-
sen ed in Figu es 2 and 3.
The nume ical FE model o he b idge was used o cal-
cula ion o o al load e ec s o he load-ca ying capaci y
assessmen . I was de eloped using So is ik so wa e
(So is ik & So is ik, 2014) o s uc u al analysis, using 2D
quad elemen s, wi h ini e elemen size o 0.2 0.2 m, p e-
sen ed in Figu e 4. Ma e ial cha ac e is ics and addi ional
pe manen load alues ( oad su acing, ailings e c.) we e
ob ained om he o iginal documen a ion, as p esen ed in
Tables 2 and 3. In addi ion o sel -weigh and addi ional
pe manen load, only a ic load e ec s we e aken in o
accoun in s uc u al analysis, as dominan a iable loads on
oad b idges. Based on he p elimina y isual inspec ion,
documen a ion e iew and linea analysis, he c i ical ailu e
mode o he selec ed b idge was de ined as a lexu al ailu e
due o bending momen in he middle o he cen al span
( esis ance o load a io 0,836 –sec ion 2-2 in Figu e 4),
and ailu e a in e nal b idge suppo s due o hogging
momen ( esis ance o load a io 0,742 –sec ion 1-1 in
Figu e 4). The limi s a e equa ion (LSE) o he c oss-sec-
ional bending capaci y was de ined o bo h c i ical sec ions
based on he geome y, ma e ial cha ac e is ics, and buil -in
ein o cemen .
3.2. Assessmen s a egies
The mul i-le el assessmen o he Case S udy b idge was
conduc ed in o de o quan i y he alue o addi ional a ic
da a ob ained using he p e iously desc ibed WIM measu e-
men s, wi h each le el ep esen ing one o he de ined
assessmen s a egies. Mul i-le el assessmen p ocedu es a e
sui able o exis ing b idges as he complexi y and accu acy
inc ease consecu i ely h oughou he le els. A he ini ial
le el, he assessmen p ocedu e is pe o med wi hou any
addi ional in o ma ion, using he codi ied p ocedu e and
Load model 1 o he design o new b idges om EN 1991-
2. The esul s ob ained a his le el a e conside ed as a e -
e ence alue, which will be used o compa ison and quan i-
ica ion o addi ional a ic da a implemen ed a subsequen
le els. The e-assessmen o he Case S udy b idge is pe -
o med a he second le el o he de ined p ocedu e, using
educed alues o adjus men ac o s o codi ied LM1, as
based on a ic measu emen s conduc ed on he hea ies
loaded oad in C oa ia and p esen ed in Table 1 (Mandi
c
e al., 2009). T a ic load e ec s a e de eloped in he inal
s ep o he assessmen p ocedu e using he con olu ion
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
STRUCTURE AND INFRASTRUCTURE ENGINEERING 5
PROOFONLY
me hod based on con inuous WIM measu emen s on he
oad leading o he Case S udy b idge.
The eliabili y analysis o he Case S udy b idge is con-
duc ed o each le el using a ully p obabilis ic app oach, as
ecommended in he P obabilis ic Model Code (JCSS, 2002),
and he esul s a e p esen ed in e ms o calcula ed p oba-
bili ies o ailu e p
and he co esponding eliabili y indices
b. The basic limi s a e equa ion o eliabili y analysis is
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
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645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
Figu e 2. Longi udinal sec ion o Case S udy b idge (uni s in m).
Figu e 3. C oss-sec ion o Case S udy b idge (uni s in m).
Figu e 4. FE nume ical model o Case S udy b idge –de o ma ion unde pe manen load (de eloped in he So is ik so wa e o s uc u al analysis).
Table 2. Pa ame e s o modelling c oss-sec ional esis ance –s a is ical cha ac e isa ion.
Va iable Symbol [Uni s] Dis ibu ion Nominal Value Mean Value (m) S .De . ( ) Sou ce
E ec i e dep h o ba s d[m] No mal 0.56 0.56 0.10 m(JCSS, 2001b)
Numbe o ba s pe slab sec ion n
b
De e minis ic 14 14 /
Yield s eng h o ein o cing s eel
y
[kN/cm
2
] No mal 22.0 24.46 0.05 m
A ea o eba A
s
[cm
2
] No mal 3.14 3.14 0.02 m
Resis ance unce ain y hRLogno mal / 1.00 0.06 m(Fib, 2016)
6 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
de eloped based on he de ined c i ical ailu e mode and
JCSS ecommenda ions (JCSS, 2001b). Design codes o new
b idges (Eu ocode, 2002) p opose a semi-p obabilis ic p o-
cedu e based on he pa ial sa e y ac o s me hod (PSFM),
bu i has been p o en ha p obabilis ic app oach p o ides
imp o ed assessmen esul s in e ms o load-ca ying cap-
aci y (Lau idsen, Jensen, & Ene oldsen, 2007). The low
cha o he mul i-le el assessmen p ocedu e de ined o
he Case S udy b idge, as based on he one de eloped in
(Skokandi
c, 2020), is gi en in Figu e 5.
3.3. Assessmen p ocedu e and esul s
The basic limi s a e equa ion (LSE) o he eliabili y ana-
lysis o he Case S udy b idge is de ined as:
Z¼hRRhEE(2)
whe e:
R–is he c oss-sec ional esis ance o selec ed load e ec
(bending momen , shea o ce, e c.);
E–is he alue o he co esponding load e ec a c i ical
c oss-sec ion;
hR;hE–a e addi ional model unce ain y dis ibu ions
accoun ing o de ia ions be ween he model and eali y
(JCSS, 2002).
Fu he de i a ion o Equa ion (2) is conduc ed based on
he selec ed c i ical ailu e mode o which he assessmen
p ocedu e is pe o med. Fo he Case S udy b idge, based
on he p elimina y condi ion assessmen he c oss-sec ional
lexu al ailu e due o nega i e bending momen on bo h
inne suppo s is de ined as he c i ical ailu e mode.
Fu he mo e, as he Case S udy b idge is a con inuous sys-
em, lexu al ailu e in he middle o he cen al span is also
conside ed in he assessmen . The e o e, Equa ion (2) can
be e-w i en as:
Z¼hRMRhEME(3)
whe e:
MR–is he c oss-sec ional bending momen esis ance;
ME–is he o al bending momen load e ec a a c i ical
c oss-sec ion;
The c oss-sec ional bending esis ance o he Case S udy
b idge M
R
can be calcula ed based on o iginal documen a-
ion and buil -in ein o cemen , as ollows:
hRMR¼hR0:9dnbAs y(4)
whe e:
d–is he e ec i e dep h o ein o cing ba s;
nb–is he o al numbe o ein o cing ba s in he c i ical
c oss-sec ion;
As–is he c oss-sec ional a ea o a single ein o cing ba ;
y–is he yield s eng h o ein o cing s eel, a ailable om
o iginal documen a ion.
Bending momen alues as he o al load e ec in c i ical
c oss-sec ions M
E
can be de ined as:
hEME¼hE,GðMGþMDGÞþhE,QMQ(5)
whe e:
MG–is he po ion o o al bending momen induced by
sel -weigh o he b idge;
MDG–is he po ion o o al bending momen induced by
addi ional dead load (e.g., oad su acing, ailings, e c.);
MQ–is he po ion o he o al bending momen induced by
a ic load;
hE,G–is he pe manen load model unce ain y unc ion;
hE,Q–is he a ic load model unce ain y unc ion.
Finally, he ully de i ed LSE o he Case S udy b idge can
be de ined as:
Z¼hR0:9dnbAs yhE,GðMGþMDGÞhE,QMQ
(6)
All pa ame e s in Equa ions (2)–(6) a e modelled as s o-
chas ic a iables (o andom a iables –i.e., pa ame e s
whose alues depend on ce ain unce ain y o an ou come
in hei quan i ica ions) wi h he co esponding s a is ical
pa ame e s and dis ibu ion ypes, as p esen ed in Tables 2
and 3. Values o s a is ical pa ame e s and ecommended
dis ibu ion ypes a e aken om he P obabilis ic Model
Code (JCSS, 2002) and ib guidelines (Fib, 2016), while
nominal alues o esis ance a iables a e ob ained om
o iginal documen a ion (
S am, 2002) and om he nume -
ical model analysis o load e ec a iables. Bo h load e ec s
and c oss-sec ional esis ance a e calcula ed in he middle o
he middle span (sec ion 2-2, Figu e 4) and a inne sup-
po s (sec ion 1-1, Figu e 4). Based on s uc u al analysis o
he Case S udy b idge nume ical model (Figu e 4), he c i -
ical ailu e mode is de ined as lexu al ailu e due o he
nega i e bending momen on he suppo s abo e he pie s.
The co esponding alues a e shown in Tables 2 and 3.
The o al a ic load e ec M
Q
is calcula ed sepa a ely
o each o he h ee assessmen s a egies as explained in
he lowcha shown in Figu e 5. Fo he i s wo assess-
men le els, i is de i ed om he nume ical model o a
educed LM1 compa ible wi h he one-yea e e ence pe iod
based on Equa ion (1). As o he inal le el, M
Q
is de i ed
di ec ly om WIM measu emen s o a ious ime pe iods
using he con olu ion me hod. Mean alues o WIM a ic
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
Table 3. Pa ame e s o modelling o al load e ec s o a e e ence pe iod o one yea –s a is ical cha ac e isa ion.
Va iable Symbol [Uni s] Dis ibu ion Nominal Value Mean Value (m) S .De . ( ) Sou ce
Sel -weigh load e ec M
G
[kNm/m] No mal / 253.60 0.04 m(JCSS, 2001a)
Addi ional dead load e ec M
DG
[kNm/m] No mal / 51.70 0.05 m
T a ic load e ec –le el 1 M
Q,1
[kNm/m] Gumbel / 216.10 0.14 m(Eu ocode, 2005)
T a ic load e ec –le el 2 M
Q,2
[kNm/m] Gumbel / 163.97 0.14 m
T a ic load e ec –le el 3 M
Q,3
[kNm/m] GEV / 67.10 0.13 m(ARCHES D10,10,2009)
Dynamic ampli ica ion ac o DAF Gumbel / 1.25 0.10 m
Dead load unce ain y hE,GNo mal / 1.00 0.05 l(JCSS, 2001b)
T a ic load unce ain y hE,QNo mal / 1.0 0.10 l
STRUCTURE AND INFRASTRUCTURE ENGINEERING 7
PROOFONLY
load e ec s a e de ined as median alues o cumula i e dis-
ibu ion unc ions (CDFs) o a ious ime pe iods, as p e-
sen ed in Figu e 6. The ini ial CDF o a ic load e ec s
(x) (Figu e 6a) is de eloped wi h he con olu ion me hod
om ac ual WIM measu emen s eco ded o a pe iod o
o e wo mon hs, in bo h summe and win e seasons.
CDFs o o he ime pe iods a e ex apola ed using he
ex eme alue heo y (Ang & Tang, 1975) by exponen ia ing
he ini ial dis ibu ion (x) o a ce ain powe .
Znida i
c
(2017) p oposes he a iable N o exponen ia ion, whose
alue is based on h ee pa ame e s: numbe o days aken
in o conside a ion (e.g. numbe o wo king days pe yea ),
selec ed ime pe iods o ex apola ion, and he numbe o
mul iple p esence e en s on he b idge expec ed in a chosen
ime pe iod. The las o hese pa ame e s p esen s he mos
in luencing pa ame e o he alue o Nand is explained in
mo e de ail in (
Znida i
c, 2017).
Fo he eliabili y analysis o he Case S udy b idge, he
maximum expec ed a ic load e ec s om WIM measu e-
men s a e ex apola ed o a e e ence pe iod o one yea
only, o be compa ible wi h he a ge eliabili y index. The
alue o Nis calcula ed di ec ly om he ob ained da a and
he CDF is p esen ed in Figu e 6b.
I is clea om Figu e 6 ha he CDF o he ime pe iod
o 1 yea has shi ed o he igh compa ed o he ini ial one,
esul ing in inc eased mean and cha ac e is ic alues, bu is
also s eepe , meaning ha he a iabili y is dec easing. Fo
longe ime pe iods, he a iabili y dec ease e en mo e, as
he pa ame e Ninc eases exponen ially and he CDFs will
be mo e and mo e s eepe , as desc ibed in (
Znida i
c
e al., 2012).
Expec ed bending momen alues shown in Figu e 6 a e
de i ed om WIM measu emen s o he o al wid h o he
b idge c oss-sec ion and a e he e o e exp essed in kNm.
The absolu e alue om Figu e 6 mus be modi ied as he
LSE in Equa ion (5) is de ined o he eliabili y analysis o
he c i ical b idge-deck sec ion, wi h he o al wid h o
100 cm, based on ecommenda ions gi en in design codes
(Eu ocode, 2004). Be o e hei implemen a ion in Equa ion
(6) hei absolu e alue is mul iplied wi h he ac o (LDF),
which de ines he p opo ion o o al load ans e ed o he
c i ical slab sec ion. Fo he Case S udy b idge, he LDF ac-
o is de i ed di ec ly om he nume ical model, as a a io
o absolu e alue o o al load e ec s [kNm] o hei p opo -
ion ans e ed on he c i ical sec ion [kNm/m] is equal o
0.167. Fu he mo e, o ake in o accoun he dynamic p o-
po ion o load e ec s due o b idge- ehicle in e ac ion, he
alues om Figu e 6 need o be mul iplied wi h he
dynamic ampli ica ion ac o (DAF). In he absence o add-
i ional a ic da a, he alue om design codes o new
b idges is used o he DAF (B uls, Ma hieu, e al., 1996;
Eu ocode, 2005). I s alue depends on he b idge ype, span
and selec ed load e ec , and o he Case S udy B idge, i is
equal o 1.25. The a ic load e ec s p esen ed in he Table
3a e calcula ed o one-yea e e ence pe iod, using
Equa ion (1) o le els 1 and 2, while n le el h ee hey a e
de i ed di ec ly om WIM measu emen s (Figu e 6).
The eliabili y analysis o he Case S udy b idge is con-
duc ed o each o he h ee de ined assessmen s a egies
using Mon e Ca lo simula ion wi h 10
8
uns, based on he
de ined LSE (6) and he alues om Tables 2 and 3. The
numbe o simula ions is calcula ed om he ecommenda-
ions gi en by Nowak and Collins (2007) based on he
expec ed p obabili y o ailu e (10
5
) and he coe icien o
a iance (0.05). The p obabili y o ailu e is selec ed
app oxima ely based on ecommenda ions o new s uc-
u es while he coe icien o a iance is app oxima ed o
ake s a is ical e o in o accoun . Resul s in e ms o calcu-
la ed p obabili ies o ailu e, and he co esponding eliabil-
i y indices, a e p esen ed in Table 4.
Resul s p esen ed in Table 4, on one hand, clea ly poin
o he bene i s o addi ional da a in bo h second and hi d
assessmen le els, alida ing he addi ional da a wi h he
educ ion o p obabili y o ailu e and inc ease in he co e-
sponding eliabili y index. Howe e , on he o he hand,
ob ained eliabili y indices a e oo low compa ed o he
minimum equi ed alue o 3.3, based on he consequence
class and ela i e cos o sa e y measu es (JCSS, 2002).
The e o e, he conclusion can be made ha he Case S udy
b idge is no sui able o a ic loads p esc ibed in he
820
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Figu e 5. Mul i-le el assessmen s a egy suppo ed by ull-p obabilis ic analysis.
8 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
ime is a ound 5 minu es, based on a ailable al e na e
ou es. The same pa ame e s a e used o he b idge epai
pe iod when cos s o b idge epai a e o e 200% o he
b idge alue (Equa ion (17)).
Cos s in he e en o o al b idge ailu e C
FAIL
a e aken
as 400% o he b idge o al alue C
BV
(sec ion 4.2.2.). Cos s
o una ailabili y in cases when b idge epai o ailu e
occu s a e calcula ed using Equa ion (18) and Eu os a da a.
The a e age cos pe weekend days is es ima ed a 50% o
he wo kday cos , while he o al cos pe ehicle pe mon h
o e e y minu e o p olonged ime is calcula ed as 12.75
EUR. Wi h an a e age AADT o 9500 ( aking in o accoun
bo h summe and win e seasons) ob ained by b idge owne ,
cos s a e calcula ed as ollows:
CN
AREP
ðÞ
¼NCN
A, ehicle N
A
¼9500 12, 75 1:5min 3mon hs
¼545:062, 00 EUR
CN
AFAIL
ðÞ
¼NCN
A, ehicle N
A
¼9500 12, 75 5:0min 12mon hs
¼7:267:500, 00 EUR
VoI analysis is conduc ed using he algo i hm de eloped
in he Excel sp eadshee so wa e o he assessmen esul s
gi en in Table 4. Summa ized inpu da a o VoI analysis
o 1-yea e e ence pe iod a e p esen ed in Table 7, wi h
bene i s o each ou come Bi calcula ed using Equa ion (7)
as nega i e o al cos s C
TOT, assessmen
using Equa ion (14).
The VoI analysis is pe o med by means o da a om
Table 8 and he decision ee concep p esen ed in Figu e 7,
using nume ical model de eloped in he Excel sp eadshee
so wa e. The esul s a e p esen ed in Figu es 9 and 10. The
op imum assessmen s a egy b anch is p esen ed wi h a
hick dashed line, as he one esul ing in maximized bene i s
B
i
(nega i e cos s C
TOT,assessmen
which a e p esen ed as pe -
cen age o he o al b idge alue C
BV
).
4.3.2. Voi analysis including bo h b idge owne and
use ’s cos s
Resul s o VoI analysis gi en in Figu e 9 show ha he
assessmen s a egy S2 a le el 3 (da k shaded cell on Figu e
9), using si e-speci ic a ic load model de eloped om
WIM da a, is an op imum s a egy o assessmen o he
Case S udy b idge, in e ms o cos s and bene i s o bo h
b idge owne and use . Fu he mo e, s a egy S
1
, based on
educed codi ied a ic load model using he eco ded a -
ic da a, is also easible, compa ed o he ini ial s a egy S
0
in which no addi ional da a is used in he assessmen . The
ela i e alue o addi ional in o ma ion in bo h s a egies
using addi ional da a, S
1
and S
2
is calcula ed wi h Equa ion
(12) and (13), and o al bene i s o each s a egy (ligh
shaded cells on Figu e 9):
VS1, ela i e ¼B1S1
ðÞ
B0S0
ðÞ
B0S0
ðÞ
jj
¼1:3188ð3:7849Þ
3:7849
jj
¼0:6515
¼65:15 %
VS2, ela i e ¼B2S2
ðÞ
B0S0
ðÞ
B0S0
ðÞ
jj
¼0:1340ð3:7849Þ
3:7849
jj
¼0:9646
¼96:46 %
The di e ence be ween s a egies S1 and S2 is no la ge
as i is be ween S1 and he p io s a egy S0, which is
mainly due o he di e ence in he mean alue and s anda d
de ia ion o he bending momen s ela ed o a ic ac ion
a le el 2 and le el 3, espec i ely. Bu he di e ence could
ge la ge o b idges wi h lowe speci ic a ic loads.
Resul s o he S a egy S1 wi h he adjus ed Load model 1
a e also e y impo an as hese adjus men ac o s a e
based on a ic coun in he coun y in gene al, al hough a
mo e localised a ic load could be o g ea e impo ance
o a speci ic b idge.
Fu he mo e, as i is clea om esul s gi en in Figu e 9
and sepa a e C
REP
cos alues om Table 7, he esul s o
each b anch show ha he epai o he Case S udy b idge
is no op imum main enance app oach due o high cos s o
b idge epai as he eliabili y indices a e e y low (choice
a
0
–do no hing alues a e close o 0 han a
i
– epai b idge
alues). Howe e , i is also isible om Figu e 9 ha he
VoI esul s s ongly depend on calcula ed use cos s a ising
om b idge una ailabili y (C
N/A
speci ied in Table 7)in
case o epai wo ks o i s ailu e. This p o es he assump-
ions made in p e ious esea ch (Koch e al., 2002;
Skokandi
c, 2020; Tho -Ch is ensen, 2009) ha use cos s
quickly become dominan in he global cos unc ion e en
o smalle b idges when he una ailabili y pe iod
is p olonged.
These esul s could be o key in e es o decision make s
a he go e nmen le el. Ne e heless, as hese cos s a e
commonly no aken in o accoun by some oad and b idge
owne s in he scope o b idge managemen sys ems, VoI
om Figu e 9 is e-pe o med by aking in o accoun only
di ec cos s incu ed by b idge owne . These esul s, aimed
pa icula ly a b idge owne s, in which all una ailabili y
cos s a e equal o ze o, a e p esen ed in he o m o a deci-
sion ee in Figu e 10.
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1700
1701
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1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
Table 6. Cos s o SHM measu emen s o Case S udy b idge.
Assessmen s a egy C
SHM
pe lane C
SHM
– o al
No addi ional da a –Le el 1 0 0
Reduced adjus men ac o s based on hea ies
measu ed a ic in he coun y–Le el 2
/ 10.000 EUR
Si e-speci ic a ic load model based on measu ed
WIM da a on he oad leading o he b idge –Le el 3
20.000 EUR 40.000 EUR
STRUCTURE AND INFRASTRUCTURE ENGINEERING 15
PROOFONLY
4.3.3. Voi analysis including only di ec cos s by
b idge owne
The esul s o e-pe o med VoI analysis gi en in Figu e 10
p esen a simila end as he ones in Figu e 9, as he assess-
men s a egy S
2
is s ill he mos op imal one, ollowed by
he s a egy S
1
.
VS1, ela i e ¼B1S1
ðÞ
B0S0
ðÞ
B0S0
ðÞ
jj
¼0:3335ð0:9200Þ
0:9200
jj
¼0:6375
¼63:75 %
VS2, ela i e ¼B2S2
ðÞ
B0S0
ðÞ
B0S0
ðÞ
jj
¼0:0840ð0:9200Þ
0:9200
jj
¼0:9086
¼90:86 %
4.3.4. Case s udy b idge VoI esul s –discussion
Resul s p esen ed in his case s udy clea ly emphasize he
bene i s o inco po a ing b idge assessmen esul s based on
a ic load moni o ing da a in he decision-making p ocess
o b idge main enance and managemen . The implemen a-
ion o coun y speci ic a ic load measu emen s (s a egy
S1) should be included in he assessmen o exis ing b idges
as hey educe di ec cos s o he b idge owne (Figu e 10
and esul wi h 63.75% ela i e bene i ). Addi ionally,
al hough he Case S udy b idge is no iconic and is ela i ely
small, he in es men in si e speci ic WIM measu emen s
(wi h he s a egy S2) would bene i he b idge owne e en
mo e (90.86%).
When di ec cos o he owne and indi ec use cos s
due o b idge una ailabili y a e conside ed, bo h a ic load
collec ion me hods (coun y speci ic a ic load measu e-
men s as a pa o s a egy S1, and si e-speci ic WIM meas-
u emen s a he oad leading o he ce ain b idge as a pa
o s a egy S2) esul in e en highe bene i s o socie y in
gene al (65.15% and 96.46% espec i ely). The di e ence o
he bene i s o wo s a egies would become e en la ge o
b idges wi h lowe speci ic a ic loads. Addi ionally, in
o de o p esen he dominan e ec o indi ec use cos s
in o al cos educ ion (in EUR), he absolu e alues o add-
i ional SHM in o ma ion a e gi en in Table 9, as o al sa -
ings o bo h b idge use s and i s owne (calcula ed using
Equa ions (10) and (11)).
5. Conclusions
The assessmen p ocedu e o he Case S udy b idge
desc ibed in his pape is based a ound he implemen a ion
o addi ional a ic in o ma ion, ob ained wi h ehicle
weighing p ocess and WIM echnology. The pu pose was o
p o e ha a ic da a, egula ly collec ed by mos oad
di ec o a es wo ldwide mainly o a ic analyses and selec-
ion o o e loaded ehicles, can addi ionally be used as a
basis o si e-speci ic assessmen o exis ing oad b idges,
which will consequen ly lead o a mo e e icien
b idge managemen .
The bene i o bo h he b idge owne and b idge use is
p esen ed, and bo h he ela i e and absolu e alue o add-
i ional in o ma ion o each assessmen s a egy a e sum-
ma ized in Tables 8 and 9. I is impo an o no e ha he
calcula ed ela i e alues o addi ional SHM in o ma ion a e
e y dependen on he inpu pa ame e s (p obabili ies o
ailu e and co esponding eliabili y indices om Table 4).
In cases when b idges ha e highe eliabili y le els, he di -
e ence be ween ela i e alues when only di ec cos s a e
aken in o accoun and when use cos s a e added is much
la ge , as p esen ed on wo newe b idges in
(Skokandi
c, 2020).
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1800
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1833
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1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
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1859
1860
1861
1862
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1865
1866
1867
1868
1869
1870
1871
1872
Table 7. Inpu da a o VoI analysis o he Case S udy B idge.
Choice S
i
Choice a
i
To al cos s C
TOT
C
REP
C
SHM
C
N/A
C
FAIL
S
0
– e e ence s a egy wi h no
addi ional a ic da a
a
0
–do no hing 0.000C
BV
0.000 0.000 0.000 0.000
16.456C
BV
0.000 0.000 12.456 4.000
a
1
–b idge epai 14.456C
BV
2.000 0.000 12.456 0.000
18.456C
BV
2.000 0.000 12.456 4.000
S
1
–s a egy wi h educed load model
based on a ic measu emen s
a
0
–do no hing 0.0171 C
BV
0.000 0.0171 0.000 0.000
16.473 C
BV
0.000 0.0171 12.456 4.000
a
1
–b idge epai 14.473C
BV
2.000 0.0171 12.456 0.000
18.473 C
BV
2.000 0.0171 12.456 4.000
S
2
–s a egy wi h si e-speci ic a ic load
model based on WIM measu emen s
a
0
–do no hing 0.068 C
BV
0.000 0.068 0.000 0.000
16.524 C
BV
0.000 0.068 12.456 4.000
a
1
–b idge epai 1.589 C
BV
0.587 0.068 0.934 0.000
17.111 C
BV
0.587 0.068 12.456 4.000
Table 8. Summa ized esul s –VoI analysis o addi ional da a – ela i e alue [%].
Assessmen s a egy
The ela i e alue o addi ional SHM in o ma ion [%]
Including bo h b idge
owne and use ’s cos s
Including only di ec
cos s by b idge owne
S a egy S1: Reduced adjus men ac o s based on
hea ies measu ed a ic in he coun y –
Le el 2
65.15 63.75
S a egy S2: Si e-speci ic a ic load model based
on measu ed WIM da a on he oad leading o
he b idge –Le el 3
96.46 90.86
16 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
The added alue o he p esen ed esea ch can be sum-
ma ized as ollows:
1. he global cos unc ion is de eloped wi h de ailed mod-
elling o each cos pa ame e as a pe cen age o he
o al b idge alue
2. he ade-o be ween he b idge owne pe spec i e
(smalle o al bene i s) and socie y pe spec i e (highe
o al bene i s) o bo h s a egies S1 and S2
3. he c i ical in luence ha indi ec cos s ha e on he ou -
comes o he VoI analysis is iden i ied – he dominance
o use s’cos s in global cos unc ion –di e ence
be ween he o al cos s educ ion wi h and wi hou
use s’cos s in Table 9
VoI based case s udies, as he one p esen ed in his
pape , can con ince b idge ope a o s, and consequen ly
decision make s a he go e nmen le el, abou bene i s o
employing a ic load moni o ing da a in s uc u al assess-
men o exis ing b idges and, consequen ly, in making
knowledge-based main enance decisions o an op imum
b idge ne wo k managemen . In his way, he p ac ical alue
o p oac i e b idge managemen is clea ly demons a ed –
emb acing inno a i e ools and me hods, as opposed o
eac i e managemen –employing isual inspec ion-based
condi ion assessmen .
Fu he s udy, in con inua ion o he p esen ed esea ch,
is aimed a c ea ing he da abase wi h mul iple a ious
b idges and he co esponding measu ed a ic da a. By
doing so, he likelihoods o SHM indica ion used could be
es ima ed wi h su icien eliabili y o be applied in he p e-
pos e io analysis. Consequen ly, unce ain ies in he ana-
lysis (b idge ca ying capaci y, a ic load e ec a iabili y,
and es ima ed cos s) would be educed as mo e and mo e
b idges a e analysed. In o de o conduc p e-pos e io ana-
lysis using he p esen ed algo i hm, he decision ee (Figu e
7) can easily be modi ied by adding he p obabilis ic chance
node labelled WIM ou come (SHM Indica ion) p io o
ac ion choice node on b anches S
1
and S
2
. By doing so,
p io p obabili y o ailu e, ob ained wi hou any addi ional
a ic in o ma ion, and he de ined SHM likelihoods, will
be su icien o eliable es ima ion o p obabili ies o ailu e
and he co esponding cos s and bene i s on subsequen
b anches (wi h addi ional a ic in o ma ion). The es ima-
ion p ocedu e can be conduc ed using he Bayesian upda -
ing heo y, and will hus p o ide decision-make s wi h a
alue o addi ional WIM in o ma ion o selec ed b idges o
b idge ne wo k be o e he in o ma ion is ac ually ob ained.
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1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
Figu e 9. VoI analysis o addi ional a ic da a in assessmen o he Case S udy b idge, including bo h di ec and indi ec cos s.
STRUCTURE AND INFRASTRUCTURE ENGINEERING 17
PROOFONLY
Addi ionally, he p esen ed algo i hm can be used o
p io i y anking o b idges in he ne wo k based on u gency
o epai . By implemen ing he ime- a ian analysis, i is
possible o es ima e he ime pe iod o he ealisa ion o
main enance ac i i ies. In o de o do so, he es ima ed cos s
need o be modi ied as hey a e based on p esen -day alues
and cu en ly a ailable knowledge. The discoun ing model
p oposed by Rackwi z (2006) o indus ial coun ies can be
used o modi ica ion o u u e-in es men cos s.
I is impo an o no e ha he accu acy and obus ness
o he p esen ed algo i hm o es ima ion o all cos s and
bene i s ela ed o he b idge managemen p ocedu e is
closely ela ed o he selec ion o me hod and s a is ical
pa ame e s o eliabili y analysis (Tables 2 and 3), and o
he es ima ion o o al cos s. The e o e, c ea ion o a da a-
base wi h ealis ic pa ame e s o selec ed b idges would
educe de ia ion o es ima ed cha ac e is ics and cos s om
eali y, making he p oposed me hod e en mo e sui able o
implemen a ion in b idge managemen sys ems.
No a ions lis
AADT A e age Annual Daily T a ic
B-WIM B idge Weigh-in-Mo ion
CDF Cumula i e dis ibu ion unc ion
DAF Dynamic Ampli ica ion Fac o
FORM Fi s O de Reliabili y Me hod
GSW G oss Vehicle Weigh
JCSS Join Commi ee o S uc u al Sa e y
LDF Load Dis ibu ion Fac o
LM1 Load Model 1
LSE Limi S a e Equa ion
MC Mon e Ca lo me hod
NCHRP Na ional Coope a i e Highway Resea ch P og am
POT Peaks o e Th eshold
RC Rein o ced Conc e e
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
Table 9. Summa ized esul s –VoI analysis o addi ional da a –absolu e alue [EUR].
Assessmen s a egy
The absolu e alue o addi ional SHM in o ma ion [EUR]
Summa ized sa ings o bo h
b idge owne and i s use s
Di ec sa ings o
b idge owne
S a egy S1: Reduced adjus men ac o s based on
hea ies measu ed a ic in he coun y –
Le el 2
1.438.821,00 342.187,00
S a egy S2: Si e-speci ic a ic load model based
on measu ed WIM da a on he oad leading o
he b idge –Le el 3
2.130.081,00 476.087,00
Figu e 10. VoI analysis o addi ional a ic da a in assessmen o he Case S udy b idge, aking in o accoun only di ec cos s incu ed by b idge owne .
18 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
SHM S uc u al Heal h Moni o ing
SiWIMV
RSlo enian Weigh-in-Mo ion
TS Tandem Sys em (concen a ed a ic load)
UDL Uni o mly Dis ibu ed Load (dis ibu ed a ic load)
VoI Value o In o ma ion
WIM Weigh-in-Mo ion
Lis o Symbols
a
0
;a
1
Ac ions ega ding he b idge (no epai ; epai )
aQ,i;aq,i;aq, Adjus men ac o s o a ic load model LM1
bReliabili y index
hE,GRandom a iable o model unce ain ies o pe man-
en load e ec
hE,QRandom a iable o model unce ain ies o a ic
load e ec
hRRandom a iable o model unce ain ies o esis ance
lMean alue
S anda d de ia ion
BiTo al bene i s o s a egy S
i
C
0
B idge cons uc ion cos s
C
BV
To al alue o he b idge
C
FAIL
Cos o b idge ailu e
C
SHM
Cos o b idge moni o ing
C
N/A
Cos o b idge non-a ailabili y
C
REP
Cos o b idge epai
C
TOT, assessmen
To al cos s o b idge assessmen
BFac o o mul iplica ion o b idge alue due o
i s impo ance
CCons uc ion ac o
REP Fac o o complexi y o b idge epai s
G
AADT
G ading ac o –AADT
G
DD
G ading ac o –De ou dis ance
G
LS
G ading ac o –La ges span
G
RC
G ading ac o – oad ca ego y
G
TL
G ading ac o –To al b idge leng h
p
P obabili y o ailu e
S
0
;S
1
;S
2
Assessmen s a egies ega ding addi ional SHM da a
X
1
;X
2
Sys em ou comes (sys em sa e; sys em no sa e)
Acknowledgemen s
This a icle is based upon wo k conduc ed in he scope o COST
Ac ion TU 1402 –Quan i ying he Value o S uc u al Heal h
Moni o ing, suppo ed by COST (Eu opean Coope a ion in Science
and Technology), and on he C oa ian na ional p ojec Pe o mance
Indica o s o he Assessmen o Exis ing B idges, suppo ed by he
Uni e si y o Zag eb.
Disclosu e s a emen
No po en ial con lic o in e es was epo ed by he au ho s.
Q1
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2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
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2147
2148
2149
2150
2151
2152
2153
2154
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2156
2157
2158
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2160
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2164
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2166
2167
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2169
2170
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2173
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2175
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2177
2178
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2180
2181
2182
2183
2184
2185
2186
2187
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2189
2190
2191
2192
2193
2194
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2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
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20 D. SKOKANDIĆAND A. M. IVANKOVIĆ
PROOFONLY
