Enginee ing S uc u es 245 (2021) 112898
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T ans e se p es essing and ein o ced conc e e as he key o es o a ion o
mason y a ch b idges
Ladisla Klusáček, Radim Nečas, Michal Požá , Robin Pěkník, Adam S oboda∗
Ins i u e o Conc e e and Mason y S uc u es, B no Uni e si y o Technology, Ve eří 331/95, 602 00 B no, Czech Republic
ARTICLE INFO
Keywo ds:
A ch b idge
T ans e se p es essing
Wall
Res o a ion
Pos - ensioning
Mason y
ABSTRACT
The e is s ill a la ge numbe o mason y a ch b idges on he oad and ailway ne wo k. Mo e han 80 % o
a ch b idges a e o e 100 yea s old so hei se ice li e has been exceeded signi ican ly. The gene al ocus o
he pape is o show he me hod o s eng hening and es o a ion o hese b idges, especially i hey ha e
been damaged by longi udinal c acks.
The es o a ion is pe o med using new spand el walls om ein o ced conc e e s abilized by ans e se
p es essed cables. This pape illus a es he s eng hening p ocess wi h ou examples o es o ed oad o
ailway b idges. In addi ion, i includes examples o basic cable a angemen s and a design o he new conc e e
walls, which a e used as ancho age a eas o ans e se p es essing. The e iciency o his me hod will be
de e mined using da a measu ed du ing he p es essing and a load es .
The measu emen s ha e shown an ex emely a ou able e ec o he addi ion o ho izon al p es essing
wi hin he new ein o ced conc e e walls. A e an e alua ion o he de o ma ion o he op c oss-sec ion
educed up o 40 % o he alues be o e s eng hening.
1. In oduc ion
In he oad and ail ne wo k, he e a e s ill ens o housands
o b idge a ches made o s one o b ick mason y h oughou Eu ope
(Fig. 1) olde han 120 yea s. Many b idges do no mee he cu en
s anda ds and ha e eached he end o hei heo e ical du abili y [1].
Howe e , he eplacemen o all hese s uc u es is economically un e-
alis ic, since he disposi ion, low p o ile and mason y quali y o he
a ch b idges o en comply wi h he espec i e s anda ds. Howe e ,
hey a e oo na ow and hei la e al alignmen ends o be b oken
by longi udinal c acks, mos o en caused by he ea h p essu es o
he oad embankmen , as well as by ans e se ensile s esses, oc-
cu ing a ound he cen e and a he edges o he a ches, caused
by o e laying and inc eased li e load (mul iple inc ease o ehicle
axle loads and a ic in ensi y). T ans e se p es essing ep esen s one
op ion o ein o cemen o such damaged a ches. This op ion is e ec i e
o cylind ical oad b idges and ail a ches, which a e, con a y o
he a ches in building cons uc ion, damaged by longi udinal c ack
sys ems. The c acks b eak he a ch no only a he connec ing poin s
o he spand el walls and he a ch, bu also in he middle o s uc u e
wid h, oughly in he axis o he ans e ed oad.
Res o a ion o a ch b idges using he pos - ensioning me hod p e-
sen ed in his pape is pa ially de i ed om pos - ension echniques
∗Co esponding au ho .
E-mail add esses: [email p o ec ed] (L. Klusáček), [email p o ec ed] (R. Nečas), [email p o ec ed] (M. Požá ), [email p o ec ed]
(R. Pěkník), [email p o ec ed] (A. S oboda).
o s eng hening o ein o ced conc e e b idges, as shown o example
in [2]. This echnique o addi ional p es essing is based on he d illed
subs i u e duc s which enable ac ing o adial o ces di ec ly o he mass
o he s uc u e wi hou any ancho ed weldmen s o auxilia y mechan-
ical de ices. The subs i u e cable duc echnique is a he unique while
he s anda d ex e nal p es essing echnique using ex e nal endons
is e y well known a ound he wo ld. Fo example, in a icles [3]
and [4] Recupe o e al. p esen ed an applica ion o ex e nal p es essing
echnique o s eng hening o a single span conc e e ailway b idge in
I aly. Pe angeli e al. [5] published a pape ocused on s eng hening o
con inuous ein o ced conc e e b idge ac oss he Gibe i e in E hiopia
also using ex e nal p es essing endons. In a icles [6] and [7] Daly
e al. p esen ed wo applica ions o s eng hening composi e b idges in
Indonesia using ex e nal p es essing. In his hesis, Nilimaa e al. [8]
ocused on s eng hening o conc e e ailway b idges (in Sweden) in
ans e se di ec ion using p es essed ba s ins alled in addi ionally
d illed holes in he exis ing conc e e o p e en shea ailu e. I is also
possible o see he use o an ex e nal pos - ensioning sys em using
p es essed cables in o de o educe s uc u al ulne abili y and o
p ese e he a is ic and aes he ical alues o his o ical s uc u es. In
a icle [9] is discussed he igid block analysis o modelling such
h ps://doi.o g/10.1016/j.engs uc .2021.112898
Recei ed 1 Feb ua y 2021; Recei ed in e ised o m 13 July 2021; Accep ed 21 July 2021
Enginee ing S uc u es 245 (2021) 112898
2
L. Klusáček e al.
a sys em. O he in o ma ion abou s eng hening using p es essing
me hod can be ound in [10,11] o [12].
The seismic p o ec ion o mason y s uc u es by implemen a ion o
e ical p es essing a key loca ions is p esen ed in esea ches [13–15]
and [16] . The main idea o his p es essing echnique is o imp o e
he seismic pe o mance by he applica ion o a uni o m dis ibu ion o
comp essi e s esses which is e y a ou able o hese s uc u es.
O he echniques use mode n composi e ma e ials (FRP, CFRP,
GFRP) o s eng hening o s uc u es, o example [17–21] o [22]. The
echnique o GFRP was also esea ched expe imen ally o he pu poses
o s eng hening o RC a ch b idge as shown in a icle [23]. The
esea ch o applica ion o he FRP me hod o s eng hening o mason y
aul s is p esen ed in [24] and an example o usage o he CFRP
me hod o s eng hening o mason y aul s is p esen ed in [25]. Design
app oaches o calcula ing o he addi ional s eng hening o mason y
a ches using he S u -and-Tie model and he applicable s anda ds
and hei compa ison o he expe imen s can be ound in [26]. In
pape [27] a non-linea con inuum model o he analysis o mason y
a ches s eng hened wi h FRP composi es is p esen ed. The p oposed
nume ical models o one uns eng hened and one FRP-s eng hened
mason y a ch we e calib a ed based on expe imen al es s. Also he
FEM model was han used o heo e ical esea ch o s eng hening o
P es wood b idge o which expe imen al da a om a des uc i e es
was a ailable.
Ano he inno a i e app oaches o s eng hening mason y a ches
used in expe imen al s udies a e FRCM ( ib e ein o ced cemen i ious
ma ix) o SFRM (s eel ib e ein o ced mo a s) me hod. The ad an-
age o hese me hods is ha hey can be easily applied in in ados
he aul s while he b idge s uc u e is in ope a ion. The e ec i eness
o FRCM s eng hening is examined in [28] and compa ison be ween
bo h is shown in [29].
A ch b idges ha e a a he signi ican load-bea ing capaci y o
e ical loads. Resea ch o he load-bea ing capaci y o hese b idges
o esis ho izon al impac is p esen ed in [30].
I ein o ced conc e e spand el walls a e used, pos - ensioning ep-
esen s a signi ican ly sa e me hod o obus cap u e o spand el walls
in compa ison o o he me hods. Lowe p obabili y o ealiza ion e o s
and simul aneous ac i e co ec ion o he cu en condi ion o he
s uc u e a e o he ad an ages o pos - ensioning. Ho izon al ans e se
p es essing comple ely es o es he exis ing s uc u e o he a ch b idge
(a e a p e ious injec ion o c acks). The c acks a e being sealed and
a gene al imp o emen o he condi ion o he load-bea ing s uc u e
caused by he in oduc ion o s ess ese e occu s. In compa ison o
o he me hods, he obus ness o his me hod lies in he ac ha he
ensile s ess in he mason y o he o iginal s uc u e in he ans e se
di ec ion can be comple ely elimina ed.
Passi e me hods such as FRCM, FRP and SFRM a e su ely app o-
p ia e unde ce ain s uc u al condi ions, bu i longi udinal c acks
a e al eady opening and deg aded spand el walls al eady lean ou , he
in oduc ion o p essu e o ce h ough newly buil conc e e spand el
walls wi h ancho a eas o pos - ensioning is i ually he only op ion
o hei conse a ion and comple e es o a ion.
2. Causes o b idge a ches damage
Damage ypical o hese b idges is shown in Fig. 2. The a ches a e
damaged by c acks in planes pa allel o he oad axis o (wi h he span
plane), i.e. by longi udinal c acks. The wid h o hese c acks can be
up o se e al ens o mm and hese longi udinal c acks hen di ide
he a ch in o se e al sepa a e a ch s ips. The bea ing s eng h o such
a ches in he longi udinal di ec ion de e mined on common calcula ion
models ends o be high; he a ches in he longi udinal di ec ion ha e a
su icien load-ca ying capaci y o mee a ic equi emen s. Bo h he
e ec o ele a ed ea h p essu e on he spand el walls and he spa ial
e ec o he s uc u e can be iden i ied as a cause o he longi udinal
c acks in he cou se o he su ey o damaged s uc u es.
Fig. 1. Example o s one mason y a ch b idge.
His o ical mason y a ch b idges we e designed in acco dance wi h
ame models and he e o e, he en i e ans e se ension was ne-
glec ed, espec i ely, hese e ec s we e conside ed negligible. Ne e -
heless, hese s uc u es ha e been se ing o 100 o mo e yea s, and
he ans e se ensions a e caused by he long- e m e ec o cons an
s ess in which he cen e o he a ch is s essed by he embankmen
(o he cons an s ess) mo e han he edges. In ac , he s uc u e wo ks
as a shell sys em and he de lec ion line in he ans e se di ec ion is
bulging downwa d. This means ha ans e se momen s and ans e se
no mal o ce, which cause ensile no mal s esses in he ans e se
di ec ion o he a ches, occu wi hin he s uc u e. The e o e, a ound
he cen e o he s uc u e, he c acks we e p edominan ly caused
by he spa ial e ec o he s uc u e. C acks obse es in a ch edges
(app ox. 0.5 m o 1.5 m om he ou e edge) can also be suppo ed by
he long- e m s ess in addi ion o he spa ial e ec , he e ec s o ea h
p essu e on he spand el walls and by he e ec s o he empe a u e
s esses. In he a ch edges, he shell igidi y p e en s ee expansion
o spand el walls and ha is how ensions a e c ea ed e en in hese
a eas. The e ec o he a ic is compounded wi h he a o emen ioned
e ec s o cons an s esses ( he weigh i sel , o he cons an s esses,
ea h p essu es), a igue and clima e s esses (especially hose caused
by he empe a u e). Compu a ional op ions o oday allow us o swi ch
om he ame model o he spa ial (shell) model, which, con a y o
he o iginal assump ions, mani es s ans e se ensions and ans e se
momen s wi h ensions on he bo om s ands which can be analysed in
his way. The addi ionally inse ed p es essing ein o cemen is usually
led a ine o he de lec ion line o he ans e se di ec ion, which is e y
sui able.
Inc eased ea h p essu e occu s especially in oad a ches, whose
le els ha e been inc eased by con inuous o e laying by up o 1,2 m
(Fig. 3). The inc ease o he ea h p essu e is u he suppo ed by he
inc eased axle p essu es o cu en ehicles, which go di ec ly o he
edges o he b idge, and by he a ic in ensi y, which is se e al imes
highe han in he ime o he b idge cons uc ion (see [31]). Inc eased
ea h p essu e o he embankmen abo e he a ch g adually pushes
away he spand el walls, which damage ou e edges o he a ches wi h
wid hs anging om 0.8 o 1.5 m. In case o ailway a ches, o e laying
o embankmen s o li e load s esses nea he a ch edges do no occu ,
bu hey a e o en damaged by longi udinal c acks passing h ough
he cen e o he a ches, no by he causes men ioned abo e. Ins ead,
ans e se h us s and ans e se bending momen s esul ing om he
spa ial e ec o he a ch causes hese c acks, which can be illus a ed
by a spa ial nume ical shell o olume models (Fig. 17). Obse a ions
om se ice load es ing indica e ha he de elopmen o c acking and
non-linea i ies unde se ice loads can be a signi ican indica o o he
capaci y o he s uc u e [32].
Enginee ing S uc u es 245 (2021) 112898
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L. Klusáček e al.
Fig. 2. Typical damage in a ch b idges caused by longi udinal c acks.
Fig. 3. Example o inc eased oad le el by asphal o e lay.
Longi udinal c acks c ea e na u al c e ices o pene a ion and pe -
manen d ainage o ainwa e . Massi e e osion o he embankmen
abo e he a ch and behind he suppo s can o en be eco ded. The
expansion o longi udinal c acks accele a es wi h ime, mainly be-
cause o he e ec s o ice in looded c acks in win e . Lea ing he
s uc u e wi hou epai leads o a collapse o edges o he a ches
and o necessa y eme gency measu es, al hough hei unc ion in he
longi udinal di ec ion is unimpai ed. I is clea ha longi udinal c acks
o en elimina e e en some a ch b idges wi h su icien load-bea ing
capaci y ou o se ice and ha a eliable es o a ion o hese c acks,
i.e. s eng hening he a ches in he ans e se di ec ion, is desi able.
The pape is ocused on a ch b idges wi h una ec ed longi udinal
di ec ion.
3. Design o epai
T ans e se p es essing o he a ches can be applied as a pa o
a s uc u al sys em consis ing o new spand el walls and p es essing
cables (Figs. 4–6) [33]. Connec ion o hese wo ea u es is bene icial,
because in he new ein o ced conc e e spand el walls, he cables can be
ancho ed in a p o en way and an almos uni o m dis ibu ion o o ces
in he ancho s o he a ch mason y can be achie ed. S abili y o he
new walls is ensu ed by he o ces in he ancho s, by he wall s i ness
o he abu men s and by he spa ial s i ness o he al eady ein o ced
a ch.
In his use case, he new ein o ced conc e e spand el walls ul il 3
possible oles:
Fig. 4. A ch b idge wi h a new spand el wall.
Fig. 5. T ans e se pos - ensioning a angemen .
1. They p o ide es o a ion and s abili y o he o iginal c umbling
spand el walls.
2. They allow ancho ing o ans e se p es essing, which can hus
be designed in compliance wi h p ocedu es acco ding o echni-
cal s anda ds.
3. I necessa y, hey also allow expansion o he ope a ional space,
which is o en e y desi able in case o his o ical oadway
a ches. In new ein o ced conc e e walls, can ile e s uc u es
o walkways o e en o expansion o sake o ans e ed
oadway can easily be cons uc ed.
The p inciple o he design is based on he app oach o conside ing
he ancho s as elas ic suppo s and on he design o he p es essing
o ces, which mus include app op ia e sa e y ma gins and s ill exceed
he ac i e e ec s o eac ions in suppo s in he nume ical model.
In he a o emen ioned applica ions, he o ces in ancho s a e de-
signed using a slab model (o a shell one), which is suppo ed wi h
elas ic suppo s in he expec ed ancho ing loca ions o he addi ional
p es essing ein o cemen . The model is unde cons an s ess, ea h
p essu e o he embankmen and he added s ess caused by a ic is
being aken in o conside a ion. The s eng hs o he suppo eac ions
on he a o emen ioned design model hen s a e he necessa y sizes
o p es essing o ces in he gi en loca ions. The ac ual p es essing
o ce is hen de i ed om hese eac ions while allowing o sa e y
coe icien s and p es essing changes.
The o ces in he ancho s o m an equilib ious sys em in he ho i-
zon al di ec ion. T ans e se p es essing sys em uses a ailable common
cons uc ion de ails and p ocedu es o he subs i u e cable duc me hod.
In addi ion o he s abili y o he spand el walls, i is necessa y o
check he maximum amoun o p es essing in he a ch wall and he
abu men s, which ac in pa allel o he bed join o he mason y.
New walls can be designed as ela i ely hin ein o ced conc e e walls,
bu he p edominan s ess is o a slab ype. Thei weigh du ing
cons uc ion is ans e ed by small la ounda ions (indi idual o
con inuous oo ings). A e p es essing using he mason y a ch, he
s ess is g adually edis ibu ed, and hei weigh is ans e ed by he
ounda ions o he o iginal b idge suppo s. Shape o he spand el walls
can be easily adap ed o he obs acle (c oss d aining canal, e c.). A g ea
ad an age o his cons uc ion sys em lies in he easy expansion o he
Enginee ing S uc u es 245 (2021) 112898
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L. Klusáček e al.
Fig. 6. A ch wi h newly ein o ced spand el walls and p es essing cables —
pe spec i e model.
Fig. 7. Example o he econs uc ion — mason y a ch oad b idge in Sem ín ( he
Czech Republic).
oadway on he b idge, e en ually in a cons uc ion o pa emen s by
means o massi e can ile e s ha can easily be placed on bo h sides
o he spand el walls. Figs. 7,8,24,27 and 43 show examples o
comple ed econs uc ions o a ched b idges on oads.
Mechanical compa ibili y o he addi ional sys em is based on a co -
ec solu ion o ancho a eas in new conc e e spand el walls (s anda d
p oposal). In addi ion, i is based on such an amoun o ans e se
p es essing, which usually ep esen s a 0.2–0.3 mul iple o he s eng h
o he mason y in ension pe pendicula ly o he bed join , which is
a e y sa e limi a ion ( e i ied by ealiza ions). Compa ibili y o he
o iginal s uc u e wi h he addi ionally applied sys em is also based on
he ans e o adial o ces om de ia o s h ough he a ch s eng h.
In e ms o ma e ials, he compa ibili y is based on an injec ion o
all c acks in he mason y so ha pa asi e mo emen s, which could
damage he a ch s uc u e, we e elimina ed. Th ough he applica ion
o p es essing, ensile s esses, which a e he only ones which damage
he a ch mason y, a e elimina ed. T ans e sally led p es essing cables
a e p o ec ed agains co osion, because cables o he monos and ype
a e used as well as he closed sys em including he ‘‘encapsula ed’’
ancho s. Edge local p essu es, which damage he monos and shea h,
a e elimina ed by he use o de ia o s wi h he sui able adius o
cu a u e.
3.1. Design o spand el walls and p es essing o ces
Magni ude o he o e s aining o ces is connec ed o he s abili y
o he spand el walls. The new spand el walls a e s abilized by he
Fig. 8. Example o he econs uc ion — s one mason y a ch oad b idge in Ransko
( he Czech Republic).
Fig. 9. Loca ions o p es essing o ces.
o ces in he ancho s ha push hem o he o iginal walls, e en ually o
he a ch i sel . These o ces can be examined as o ces in he in ended
suppo s, which a e he ancho s on he ac ual s uc u e. Suppo s mus
be modelled as nonlinea (only p essu e) in o de o p ope ly simula e
leaning o he wall agains he a ch and no o hinde i s de o ma ion
in he di ec ion away om he a ch. The o ces in he ancho s mus be
designed o be la ge han he suppo eac ions examined. In s anda d
cases, he new spand el walls can be examined as slabs subjec ed o
he ea h p essu e o he oad body and embankmen , suppo ed in he
Enginee ing S uc u es 245 (2021) 112898
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L. Klusáček e al.
Fig. 10. Loads on spand el wall.
e y ancho si es and on he ounda ion le el (Figs. 9 and 10). The
ea h p essu e mus be inc eased by he e ec o he li e load. The
ea h p essu e pa e n is hen apezoidal and inc eases linea ly wi h
dep h. Fo sa e y pu poses, he s i ness o he o iginal spand el walls
is neglec ed. Because o he a iable shape o he spand el walls and he
inc easing load wi h he dep h o he embankmen , i is ecommended
o model he spand el walls using he Fini e Elemen Me hod (FEM)
and o choose a slab elemen which conside s he shea e ec as he
basic elemen . On his model, he suppo eac ions and in e nal o ces
(momen s) o he ein o cemen design a e de e mined. The model can
also be used o e i y de o ma ions o new spand el walls (Fig. 17). I
can be ecommended ha he de o ma ion o he spand el wall end
does no ho izon ally exceed he alue
𝑤ℎ=𝑙𝑠
350 (1)
whe e 𝑙𝑠is he span o a subs i u e ho izon al can ile e wi h a igid
suppo in he a ch axis.
The in ensi y o he ans e se p es essing in he c oss-sec ion o
he a ch can be assessed in he same way as mason y s uc u es. In yp-
ical cases, 20% o he calcula ed comp essi e s eng h o he mason y
should no exceed pe pendicula o he loading a ea. The in ensi y o
he ans e se p es essing in he a ch can be easily de e mined in
he same manne as in a c oss-sec ion: he a ea o he esis ing c oss-
sec ion is he a ea o he longi udinal c oss-sec ion o he a ch and he
abu men s, he ac ing o ce is he esul an o ce om all he ancho s,
and he poin o ac ion is he cen e o g a i y o all ancho s. Mo e
speci ically, he in ensi y o he p es essing o ce can once again be
de e mined on he shell a ch model using FEM p og ams ha model
he a ch including he new spand el walls.
3.2. Cons uc ion solu ion
When ein o cing he s uc u es wi h addi ional p es essing, i is
necessa y o apply he app op ia e cons uc ion de ails so ha all con-
di ions o eliable ope a ion o bo h he o iginal ein o ced s uc u e
and he addi ionally a ached o e s aining sys em a e main ained. This
can be achie ed wi h a p ope design and pe o mance o cons uc ion
de ails. Wi hou p ope de ails, nei he can he e ec o addi ional ein-
o cing in acco dance wi h heo e ical assump ions be ensu ed, no can
he long- e m eliabili y o he applied p es essing be gua an eed [34].
3.2.1. Subs i u e cable duc s
P es essing cables (mos ly single-s and cables; some imes mul i-
s and cables) a e a anged in a polygonal ajec o y. Subs i u e cable
duc s o m a pa o he ajec o y, and he cen al pa o he ajec o y
is guided in ca ed slo s on he ob e se side o he a ch (Fig. 11).
This solu ion signi ican ly imp o es he p oduc i i y o he p epa a o y
Fig. 11. Slo s on he ob e se side o he a ch.
Fig. 12. Ancho age a ea in new monoli hic ein o ced spand el walls.
wo ks by educing d illing leng hs. Duc s can be d illed using an impac
o a diamond d illing. D illing wi h a diamond d ill is used o mul i-
ope cables wi hou excep ion. Radial o ces a he de ia o loca ion
do no endange he mason y o he a ch because he adial o ces
a e small when duc slopes a e used wi h 𝛼= 5◦ o 8◦. The cables
a e a anged app oxima ely uni o mly o e adial planes o he a ch
in dis ances anging om 600 o 1200 mm. Theo e ically, he en i e
leng h o he cable can be s o ed in a cable duc al e na ely c ea ed
by diamond d illing a he le el o he cen e o g a i y o he a ch
c oss-sec ion, bu his is no economically ad an ageous o s a ically
necessa y.
3.2.2. De ia o s
The design o he p es essing sys em mus also include he design o
he de ia o s, indica ing all he pa ame e s necessa y o he design and
cons uc ion o he de ia o [35]. Diamond d illing is equi ed o make
he langing su aces o he g oo es and de ia o s, especially because
o he gen le app oach o he a ch mason y. In es iga ion o ul ima e
s eng h o cu ed s and endons is also p esen ed in [36].
3.2.3. Ancho s
New monoli hic ein o ced conc e e spand el walls also pe o m he
unc ion as ancho age a eas. Rein o cemen o ancho ing a eas can hen
be designed and ealized acco ding o he ules commonly applied in

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Fig. 13. Newly made ein o ced conc e e spand el wall.
case o p es essed conc e e. B idge a ches a e s uc u es exposed o
en i onmen s wi h inc eased agg essi eness, so i is essen ial o use
encapsula ed ancho sys ems. Ancho s o he indi idual s ands a e
dis ibu ed in he pass o he spand el wall. Fo his pu pose, ancho ing
weldmen s a e used, which p o ide ancho posi ions du ing pou ing o
conc e e o g ou ing and dis ibu e o ces om he ancho s in o he
conc e e o he spand el wall (Fig. 12).
3.2.4. Monoli hic walls
The s uc u al design o he ein o cemen o he a ches by ans-
e se p es essing elies on he newly made ein o ced conc e e span-
d el walls, which, in addi ion o ein o cing hemsel es, also es o e
he o iginal s one spand el walls (Fig. 13). Thus, he hickness o he
new wall luc ua es, and he e o e, illing o possible ca e ns and ixing
o loose blocks o he o iginal mason y will occu . The o iginal b ick
spand el walls o m a lea e-in-place o mwo k. New spand el walls
may be ela i ely hin (400 o 600 mm); hei s abili y is ensu ed by he
esul an o ces o he p es essing cables in he ancho s. A hickness o
a leas 500 mm is ecommended because o he one-sided app oach
o moun ing o he ein o cemen .
3.2.5. Possibili ies o b idge widening
By u ilizing he o e hang o he can ile e s, he exis ing a ch can
be ad an ageously widened in acco dance wi h he equi emen s o he
econs uc ion. The can ile e s can be designed as massi e, p e e ably
wi h haunches, which is aes he ically pleasing wi h ega d o he
massi eness o he o iginal a ch s uc u e (Figs. 4,5and 14). As a
esul , he a ches can be expanded by up o 2.5 m on each side o he
b idge.
3.2.6. P es essing ein o cemen
Fo ans e se p es essing, cables dis ibu ed e e y 1.2 o 1.5 m
along he pe ime e o he a ch can be used; s a ic analysis o he s uc-
u e p o ides he numbe o s ands necessa y. I is usually possible o
use h ee- ope o ou - ope cables made up o monos ands (Figs. 4–
6). The use o p o ec ed ein o cemen (monos ands) is a equi emen
because o he ambien agg essi eness and humidi y. Absence o co-
he ence be ween he o iginal mason y and he p es essing cables does
no cause any di icul ies since he elas ic de o ma ions o he a ch and
he abu men s in he ans e se di ec ion caused by he li e load a e
comple ely negligible.
The used p es essing le els a e low and he analysed p es essing
losses ( e i ied wi h an expe imen al measu ing) a e unde 15%.
Fig. 14. The exis ing a ch can be ad an ageously expanded.
3.2.7. C ack injec ion
C acks mus be illed be o e he o e s aining o ce is in oduced
(Figs. 15 and 16). The o ma ion o c acks has occu ed o e a long
pe iod o ime and wi h a con ibu ion o he mason y c eeping. The e-
o e, hey canno be closed by p es essing, as his would lead o
undesi able displacemen s o he sepa a ed pa s o he a ch and he
suppo s, as well as o an eme gence o new c acks. By illing he
c acks, all unwan ed mo emen s and shi s du ing p es essing a e
minimized, and wi h a sligh ho izon al p essu e ension, es o a ion
o he monoli hic cha ac e and in eg i y o he damaged mason y will
be ensu ed.
Injec ion o c acks wi h wid h abo e 0.5 mm is usually pe o med
wi h a cemen ed ac i a ed injec ion mix u e. Smalle c acks i ually
canno be injec ed. Al e na i ely, injec ion o non- oamy polyu e hane
esin ( ensile s eng h in a bend o e 100 MPa) can be used.
3.3. Ma e ial cha ac e is ics
The ein o cemen o he a ches using he a o emen ioned s uc u al
sys em is necessa ily dependen on he cha ac e is ics o he used ma-
e ial. The main condi ion is he su icien quali y o he a ch mason y
as i de e mines he u he se ice li e o he ein o ced b idge and
o he ans e o he ans e se p essu es om he p es essing. The
cha ac e is ics o he used ma e ial mus be de e mined wi h a de ailed
cons uc ion diagnos ics. Examples o non-des uc i e mason y es ing
a e p esen ed in [37].
Diagnos ics a e he necessa y inpu o econs uc ion design.
Wi hin he diagnos ics, a gene al knowledge o c acks (mapping o he
en i e s uc u e) and hei de elopmen mus be achie ed. This in o -
ma ion is necessa y o a compila ion o a de ec mechanism, whose
knowledge is he key o he ac ual es o a ion design. In o ma ion
o he ma e ial cha ac e is ics o he indi idual building ma e ials,
mo a and he ac ual mason y in acco dance wi h he usual p ocedu es
based on p ocedu es acco ding o echnical s anda ds (‘‘eu ocodes’’)
a e ano he necessa y ou pu o he diagnos ic esea ch. The diagnos ic
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Fig. 15. G ou ing o c acks.
Fig. 16. G ou ed a ea in he back side o he a ch b idge.
esea ch usually also includes some d illing o p obes o he pu pose
o de e mina ion o o he wise inaccessible dimensions (dimensions o
suppo s, heigh o a ch c oss sec ion, hickness o he o iginal spand el
walls). Examples o ma e ial cha ac e is ics o s eng hened b idges
ob ained by diagnos ic su eys a e gi en in Table 1.
Unlike conc e e, mason y is an aniso opic ma e ial, i.e. a ma e ial
whose p ope ies a y in di e en di ec ions. Some imes i is e e ed
o as o ho opic, i.e. a ma e ial whose p ope ies a e di e en in wo
pe pendicula di ec ions. Fo mason y, i is usually i al o es i s
mechanical p ope ies in wo main, mu ually pe pendicula di ec ions,
espec i ely pe pendicula ly o he bed join s o he mason y (usually
in he e ical di ec ion) and pa allel o hem (usually in he ho izon al
di ec ion). Basic de o ma ion p ope ies o mason y include he modu-
lus o elas ici y and he c eep coe icien . The s uc u e diagnosis be o e
he design o epai mus iden i y he ollowing da a:
•The quali y o he a ch mason y in e ms o i s long- e m use:
The a ch b idges a e made o s one o b ick mason y. S one
mason y uses g ani e, gneiss, limes one, sla e and sands one;
b ick mason y mos o en used bu n ull b icks wi h inc eased
esis ance o wa e abso p ion and os b eakdown. I is p ecisely
he esis ance o damage caused by os b eakdown ha is he
decisi e condi ion o a u he use o he a ch s uc u e and o
s eng hening o he a ches a all. Mason y consis ing o b icks
om igneous and me amo phic ocks; sedimen ocks a e sui able
condi ionally. The mason y can also be o med om sands one o
g eywacke, which a e comple ely una ec ed by os e en in he
condi ions o se e al yea s o leakage in o he mason y a ch om
he oadway. In con as , some less cohesi e sands ones can be
damaged by b eakdown by os ac ion o a dep h o 80 mm o
mo e. Simila ly, b ick mason y is gene ally highly abso ben and
hus poo ly esis an . F os b eakdown occu s as a esul o oad
leakage. The o iginal insula ion o he b idge a ches was made o
laye s o compac ed clay. A e mo e han 100 yea s, hese laye s
a e al eady washed ou and do no ul il he insula ion unc ion
any mo e. A new wa e p oo ing laye is es ablished as a pa o
he econs uc ion by ans e se p es essing; he e o e, he issue
o u he leakage is no impo an a he momen o and sho ly
a e he econs uc ion. The e o e, we can summa ize ha a ches
om s one mason y (g ani e, gneiss, limes one, sands one) a e
sui able o s eng hening and widening o a ches; he condi ion
o mo a is o en no a c ucial ac o . B ick mason y a ches
a e condi ionally app op ia e because hey almos always equi e
oadway exca a ion and implemen a ion o wa e p oo ing.
•The s eng h o he mason y suppo ing s uc u e o he a ch: he
classi ica ion o he b icks and he mo a has o be pe o med ac-
co ding o he s anda ds and using in si u s eng h measu emen s.
The s eng h o he b icks can be de e mined by a non-des uc i e
ebound me hod o by aking samples o p essu e es ing in
a p ess. Mos ly, jus he non-des uc i e me hod is su icien
because he a ia ion in he s eng h o he building ma e ial
leads o minimum di e ences in he esul ing design s eng h o
he mason y. In o de o de e mine he s eng h o he mason y,
we ha e o de e mine he s eng h o he mo a , o example by
using a modi ied d ill-based es ing. F om he acqui ed s eng hs
o he b icks and he mo a , he design s eng h o he mason y
is de e mined.
The s eng h o he mason y ension is usually de ined e ically
o he bed join . In he pa allel di ec ion o he bed join , he
ension is e y small, ha d o measu e o no de ined a all. In
pe iodically s essed mason y s uc u es o s uc u es s essed o
a long pe iod o ime, he ensile s eng h in he di ec ion pa allel
o he bed join is almos ze o.
•The hickness o he oadway and all laye s abo e he a ch, in-
cluding he p ecise de e mina ion o he a ch hickness: Laye size
de e mina ion should be done by d illing ial pi s in o he oad
using diamond cu ing echnology o by bo e holes. Mo eo e , i
is necessa y o d ill a bo e hole h ough he a ch o de e mine he
a ch hickness. De e mina ion o he ac ual dimension o he a ch
is necessa y because he hickness o he a ch inside he s uc u e
may no be iden ical o he a ch depic ed on he o iginal spand el
wall.
•De ec s and ailu es o he b idge a ch be o e ein o cemen and
econs uc ion: These include de e mining he ex en and sou ce
o leaking in o he a ch. These a e he de aul da a o he inal
design o wa e -p oo ing o he e e se side o he a ch.
3.4. Nume ical model
In o de o e i y he a ch beha iou and epai design, he ideal
app oach is o pe o m a h ee-dimensional (3D) disc e e analysis using
he ini e elemen s me hod wi h nonlinea ma e ial beha iou . Such
analysis will allow calcula ion o limi s a es and de e mina ion o
ailu e mechanisms, bu i is e y demanding in e ms o inpu pa-
ame e s — cons uc ion geome y, mason y p ope ies, back ill soil
p ope ies and con ac elemen pa ame e s [38–40]. C ea ion o a
h ee-dimensional spa ial model consis ing o plana and beam ele-
men s is su icien o use in p ac ice (Fig. 17 — a ch b idge in Rybná
nad Zdobnicí). This sample nume ical model was c ea ed om 302
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Table 1
Ma e ial cha ac e is ics o s eng hened a ch b idges a e diagnos ic su eys.
Ma e ial cha ac e is ics Loca ion o he a ch b idge
Sem ín Ransko B no-Špi álka Rybná nad
Zdobnicí
Comp essi e s eng h o building ma e ial 𝑓𝑢25 MPa
(bu n clay b.)
120 MPa
(g ani e b.)
25 MPa
(bu n clay b.)
60 MPa
(sands one b.)
Comp essi e s eng h o mo a 𝑓𝑚1.2 MPa
(lime m.)
0.4 MPa
(lime m.)
1.4 MPa
(lime m.)
1.2 MPa
(lime m.)
Comp essi e s eng h o mason y 𝑓𝑘3.6 MPa 6.2 MPa 3.8 MPa 5.2 MPa
Secan modulus o elas ici y (sho - e m) 𝐸3.6 GPa 6.2 GPa 3.8 GPa 5.2 GPa
Fig. 17. Shell model de o ma ion caused by s a ic load (a ch b idge in Rybná nad
Zdobnicí).
beam elemen s, 6716 shell elemen s and a o al o 7202 nodes. The
basic elemen size was chosen o be 0.3 m. Examples o ma e ial p ope -
ies used in shell model o a ch b idge in Rybná nad Zdobnicí a e shown
in Table 2, whe e 𝐸is modulus o elas ici y, 𝐺is modulus o shea , 𝜈is
he Poisson’s a io, 𝛾is densi y and 𝛼is he mal expansion coe icien .
Ma e ials can be en e ed as iso opic, elas ic and linea in o his model.
In case o homogenized mason y, i is necessa y o check he ensile
s ess so ha no ensile bea ing s eng h is exceeded in any di ec ion
( he usual alue is 0.05–0.1 MPa). The e is a pa allel con ac be ween
he exis ing s one spand el wall and he new ein o ced conc e e, in
which he ansmission o o ces is expec ed because o he applied
p es essing and he ic ion be ween he su aces. I is ad isable o
c ea e a simpli ied slab model o design he hickness o he spand el
walls and p es essing cables (see Sec ion 3.1). The p es essing cables
a e modelled using beam elemen s. P es essing is in oduced in o he
s uc u e h ough ancho s in new ein o ced conc e e walls and buil -
in de ia o s. In he case o de ia o s, i is necessa y o check o a oid
local con ac b eaking o he mason y. In his model, i is also necessa y
o cap u e he beha iou o he su ounding back ill, which a ec s he
load dis ibu ion on he mason y a ch and he bounda y condi ions o
he model, i.e. suppo s. Gene ally, he soil exhibi s a so e esponse
o he load han he a ch. The e o e, i he maximum load on he
mason y a ch is no exhaus ed, he su ounding soil has minimum
e ec on he model. I he ensile load-bea ing capaci y is exceeded, a
Fig. 19. C acks be ween spand el wall (blocks) and mason y caused by buckling.
mechanism is c ea ed, and he a ch in e ac s wi h he su ounding soil.
In hese cases, i is no enough o model only he co esponding s i ness
o he ounda ion, bu you also ha e o model a comple e elas ic–
plas ic back ill. Fo hese needs, i is necessa y o p o ide a de ailed
hyd ogeological su ey o de e mine all he necessa y pa ame e s o
he nume ical model. The model is suppo ed by nonlinea suppo s
wi h adequa e s i nesses, which a e ine ec i e in ension.
The inabili y o he mason y a ch o esis ensile s esses was
simula ed by inse ing linea join s and hus he non-linea beha iou
o he his o ical mason y o he b idge a ches was subs i u ed.
Tensile s esses a e comple ely elimina ed by he ans e se p e-
s essing and a he same ime, comp essu e in en ionally induced
by p es essing is designed a low le els wi h ega d o he mason y
s eng h. The e o e, use o elas ically linea model complies comple ely
wi h he esul ing beha iou o he s uc u e. This basic p esump ion o
s uc u es ein o ced in his way was e i ied by he measu ing.
Fig. 18. Road b idge in Sem ín, econs uc ion by pos - ensioning.
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Table 2
Examples o ma e ial p ope ies used in nume ical shell model o a ch b idge in Rybná nad Zdobnicí (Fig. 17).
Type o ma e ial Ma e ial p ope ies
E [GPa] G [GPa] 𝜈[–] 𝛾[kN/m3]𝛼[1∕◦C]
Mason y (sands one, lime mo a ) 15 5.7 0.3 24.0 9.0E06
Rein o ced conc e e (C30/37) 33 13.7 0.2 25.0 1.0E05
P es essing endon (Y1860-S7-15.7) 195 75.0 0.3 78.5 1.0E05
Fig. 20. Measu ing o ho izon al s ain du ing pos - ensioning.
4. De o ma ion o a ch mason y du ing p es essing
An impo an ques ion is how does he mason y o he o iginal
a ch and he mason y o suppo s eac o he ho izon al p es essing,
i.e. pa allel o he bed join o he b icks. I is necessa y o know he
mason y s ain o a co ec es ima ion o p es essing losses. Because
o he low p es essing le els (up o 20% o mason y s eng h, 0.1 o
0.3 MPa in p ac ice), he s ain can be expec ed o no be la ge and
a he simila o he s ain in case o a s ess applied in a pe pendicula
di ec ion upon he loading su ace. The in e ac ion o he adjacen
embankmen s and back ills behind he a ch o suppo is also unknown
as well as he in e ac ion o he base o ounda ion.
The au ho s o he a icle a e p obably he i s o conduc a sho -
e m measu emen o a de o ma ion esponse o ho izon al p es essing
o b idge a ches. The ob ained esul s a e p esen ed o wo cases o
s eng hening o he a ch b idge.
4.1. B idge a ch in he ci y o Sem ín
The b idge consis s o a cylind ical a ch wi h a cen e line in he
shape o a ci cula segmen o b ick mason y wi h a hickness o
450 mm. Sands one blocks o m he suppo o a ch mason y on each
side o he b idge span. The o iginal spand el walls and suppo s we e
made o s one mason y. The o iginal mo a is lime, pa ly washed ou ,
o he 0.2 o 0.4 MPa s eng h class. The a ch span is 4.5 m, he a ch
wid h is 10 m, and he leng h o he newly made spand el walls is 18.4
m. Schema ic sec ions o he s uc u e a e shown in Fig. 18.
The basic eason o he econs uc ion was he leaning ou o bo h
spand el walls o he b idge and ledges, ollowed by he o ma ion
o longi udinal c acks be ween he a ch and spand el walls wi h a
wid h o 20–30 mm on he downs eam side o he b idge (Fig. 19)
and a ound 10 mm wide on he ups eam side. In acco dance wi h
he na u e o he de ec s men ioned abo e, he ein o cemen o he
a ch was designed in such way so ha new ein o ced conc e e walls
Fig. 21. Rela i e s ain o a ch mason y du ing ho izon al p es essing.
Fig. 22. Road b idge in Ransko, econs uc ion by pos - ensioning.
Enginee ing S uc u es 245 (2021) 112898
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Fig. 40. Rela i e s ains a he op o he a ch du ing c ossing on ack no. 2 (be o e
and a e s eng hening).
Fig. 41. Rela i e s ains a he op o he a ch du ing c ossing on ack no. 1 (be o e
and a e s eng hening).
minimum o −174.10 μm/m o −68.36 μm/m on he e e se side and
om he measu ed minimum o −34.68 μm/m o −10.59 μm/m on
he ob e se side. The inc ease o he a ch s i ness in he ans e se
di ec ion be o e and a e he es o a ion can be s a ed p opo ionally
as 2.55:1 o he e e se side o he a ch and as 3.27:1 o he ob e se
side o he a ch. Gene ally, i can be s a ed ha he s i ness o he a ch
in place o ack no. 2 abo e he moun ed MA1 inc eased app oxima ely
h ee imes.
Simila ly o he ack no. 1 abo e he moun ed MA2, when he
ain was c ossing on he ack no. 2, he s ain almos did no change
on he ob e se side o he a ch ( ensile o ces we e c ea ed), and on
he e e se side o he a ch, he s ain dec eased om he measu ed
minimum −86.31 μm/m o −30.19 μm/m, i.e. in he a io o 2.86:1.
C ossings on ack no. 1 — MA2 (Fig. 41)
On he basis o he measu ed alues, i is clea ha when c ossing
ack no. 1 abo e he moun ed mechanical ampli ie MA2, he a ch
in he place o he moun ed MA1 was pushed on he e e se side
and pulled on he ob e se side be o e and a e he es o a ion. A e
s eng hening, he ela i e s ain was educed om he measu ed mini-
mum o −28.59 μm/m o −12.33 μm/m on he e e se side o he a ch.
The ela i e s ain on he ob e se side o he a ch dec eased om he
measu ed maximum o 10.94 μm/m o 3.15 μm/m. The inc ease o he
a ch s i ness in he ans e se di ec ion be o e and a e he es o a ion
can be p opo ionally s a ed as 2.32:1 o he e e se side o he a ch
and as 3.47:1 o he ob e se side o he a ch. In gene al, i can be
s a ed ha he s i ness o he a ch in he place o moun ed MA1 was
inc eased app oxima ely h ee imes.
In he case o ack no. 1 abo e he moun ed MA2, he s ain was
educed while c ossing on ack 1 om he measu ed maximum o
51.61 μm/m o 10.51 μm/m o he a ch ob e se side, i.e. in he a io o
4.91:1. On he e e se side o he a ch, he ela i e s ain was educed
om he measu ed minimum o −430.57 μm/m o −89.53 μm/m, i.e. in
he a io o 4.81:1.
The pe o med measu emen con i med he high e iciency o he
es o a ion by in oducing he p es essing in o he b idge a ch. By
in oducing he p es essing in he ans e se di ec ion, he s i ness
has been p o en o inc ease, and he sepa a ed pa s o he b idge a ch
once again ac as a single uni — con inuously and mu ually dependen .
Fig. 42. A ch b idge in Rybná nad Zdobnicí — be o e econs uc ion.
Fig. 43. Rein o ced a ch b idge in Rybná nad Zdobnicí wi h new spand el walls.
The es o a ion has signi ican ly educed he s ain a he op o he
a ch du ing c ossing o ains o abou 1/2 o 1/5, which esul s in an
p olonged se ice li e o he s uc u e.
6. The e ec o empe a u e upon measu ing
Du ing he measu emen , he e a e de ia ions om he heo e ical
assump ions in he eco d. These de ia ions ange om uni s o h o
uni s o %. The o a ion o he mechanical ampli ie s, changes o he
ambien empe a u e, he ib a ions caused by he echnical seismici y,
and he human ac o , o name a ew, a e among he mos c i ical
ac o s in luencing he accu acy o he measu ed da a.
The compensa ion o he in luence o empe a u e changes du ing
he measu emen can be shown in he beha iou o he b idge a ch in
he ci y o Rybná nad Zdobnicí, Czech Republic [42]. The main eason
o he econs uc ion o he b idge a ch was he leaning ou o bo h
he spand el walls by up o 180 mm, ollowed by a disin eg a ion o
he mason y and alling ou o he s one blocks. The s abili y o bo h
spand el walls was dis up ed, and he s abili y o he en i e s uc u e
was endange ed. The b idge a ch was also dis up ed by longi udinal
c acks o a hickness om 2 o 5 mm, which di ided he a ch in o
sel -ac ing sec ions.

Enginee ing S uc u es 245 (2021) 112898
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L. Klusáček e al.
Fig. 44. The mechanical ampli ie s we e ins alled a wo places on he a ch.
Fig. 45. Mechanical ampli ie ins alled a he op o he a ch.
Fig. 46. A ully loaded uck was used as a bu den o s a ic and dynamic
measu emen s.
6.1. Desc ip ion o measu ed b idge, pe o med measu emen s and es s
The suppo ing s uc u e o he b idge consis s o an o iginal s one
a ch wi h a clea span o 5.7 m and a clea cambe o 2.85 m (Fig. 42).
The heigh o he a ch base abo e he ein o ced bank o he s eam
is 3.2 m, and he heigh o he a ch op abo e he s eam is 7.43 m.
The a ch hickness is app oxima ely 0.65 m. The new spand el walls
a e 0.6 m hick and a e made o C- / 28 conc e e and ein o cing s eel
10505 (R). The econs uc ion also included an inc ease in he ee
wid h o 12.0 m using sui ably shaped spand el walls and ledge linings
Fig. 47. Rela i e s ain on he ou e ib es o he a ch wi hou il e ing ou he
empe a u e.
Fig. 48. De elopmen o su ounding empe a u e in he cou se o he measu emen .
on which sidewalks a e placed (Fig. 43). Replacemen cable duc s wi h
a diame e o 52 mm we e placed in o he o iginal s one a ch o
accommoda e he p es essing cables. These we e c ea ed by p ecision
d illing wi h diamond co e d ills and diamond cu ing machines. The
de ia o s we e designed om s ip s eel wi h a adius o R = 2.0 m. All
he c acks in he a ch and suppo s had been illed wi h g ou be o e
he monos ands we e s e ched. Also, a sealing injec ion o 0.5 ×0.5 m
g id was ca ied ou , which, o da e, con inues o p e en wa e lowing
in o he suppo ing s uc u e.
The measu emen o he a ch was designed so ha was possible
o ind ou he syne gy o he a ch in he ans e se di ec ion and
a he same ime o e ine he calcula ion model o s a ic analysis
and e alua ion o esul s. Measu emen s using he p e iously desc ibed
mechanical ampli ie s we e pe o med a wo loca ions o he a ch. The
i s loca ion was in he middle o he a ch wid h; he second loca ion
was in he 1/4 o he s one a ch wid h (Figs. 44 and 45). The a ch
de lec ion was also measu ed in he middle o he a ch wid h o e i y
he a ch beha iou . In se e al loca ions a ound he s uc u e and nea
he a ch and senso s, empe a u e was measu ed so ha he 41 e ec s
o he empe a u e could be compensa ed o .
Bo h s a ic and dynamic load measu emen s we e pe o med on he
s uc u e. A ully loaded Liaz 150 uck was used as a bu den (Fig. 46).
To al ehicle weigh was 18.14 ons ( ea axle 11.6 ons; on axle
6.54 ons). In he s a ic load es , he ehicle was placed in he igh
lane wice, in he middle o he oad wice, and in he le lane once.
The ea axle has always been posi ioned abo e he cen e o he a ch
span. Dynamic measu emen s du ing c ossings we e pe o med wice
a 30 km/h in he igh lane and wice in he middle o he oad.
Enginee ing S uc u es 245 (2021) 112898
18
L. Klusáček e al.
Fig. 49. Rela i e s ain a e il e ing ou o he e ec s o olume changes o he a ch
caused by empe a u e.
Fig. 50. Rela i e s ain du ing axle es no. 3 — ehicle in he middle o he oad
abo e MA1.
6.2. Measu emen e alua ion
Co ec ing he eco d o he e ec s o empe a u e change can be
di ided in o wo basic g oups. Du ing he measu emen , because o
empe a u e luc ua ions, he measu ing de ice is in luenced, bu also
he mason y s uc u e i sel is subjec o olume changes because o
he mal ine ia. In Fig. 47, i is possible o see he ela i e s ain on
he ou e ib es o he b idge a ch wi hou il e ing ou he olume
changes o he mason y b idge a ch. The ed and blue colou s show
he esul s om mechanical ampli ie no. 1 in he cen e o he span
and he g een and o ange colou s show he esul s om mechanical
ampli ie no. 2 in he 1/4 o he s one a ch wid h. I is also possible o
easily iden i y indi idual s a ic on axle es s and dynamic es load
c ossings om he igu e. Posi i e s ains o he c oss-sec ion be ween
he indi idual on axle es s (a e emo al o he load) we e measu ed
wi hou il e ing ou o he olume changes o he mason y a ch. These
ensile s ains a e caused by a ying empe a u e. In ou case, du ing
he measu emen , he ambien en i onmen was cooled down (Fig. 48),
which led o olume changes o he mason y a ch. Mo eo e , because
he mechanical ampli ie s a e moun ed on he ou e su ace, posi i e
s ains a e immedia ely eco ded. The ac ual s ain o he a ch a he
om he su ace will be di e en because o he empe a u e ine ia o
he massi e c oss-sec ion. The e o e, he measu ed alues ha e been
adjus ed o compensa e o his empe a u e e ec . Cooling o he
ambien en i onmen causes he p essu e ese e o be pumped ou
in he op o he a ch and has an almos a ine cou se o empe a u e
de elopmen .
A e il e ing ou he e ec s o olume changes o he a ch caused
by empe a u e (Fig. 49), he alues o he s ains in he uppe and
Fig. 51. De lec ion du ing he dynamic c ossings.
lowe ib es a e as expec ed — posi i e s ains (elonga ion) on he
su ace and nega i e s ains (sho ening) on he e e se side o he
a ch. The measu ed alues on bo h su aces a e almos iden ical in
absolu e alues (Fig. 50) — inaccu acies a e caused by he a iable
a ch hickness and he con ibu ion o he su ounding embankmen ,
which shi s he c oss-sec ional cen e o g a i y u he om he ou e
su ace o he a ch.
Fig. 50 shows he measu ed alues om he on axle es no. 3
when he ehicle s ops in he middle o he a ch (Fig. 46). Du ing he
on axle es , locally ele a ed c oss-sec ional s ain alues caused by
he egula a ic can be seen; he a ic could no be elimina ed du ing
he measu emen , only limi ed and slowed down o he le ou e lane
o he oad.
Du ing he dynamic c ossings a a speed o 30 km/h, i was possible
o measu e s ain and de lec ion om he indi idual axles o he ehicle
used as a bu den. Fig. 51 illus a es he de lec ions in he middle o he
b idge a ch in all ou c ossings. Fi s , he e is app oxima ely hal he
de lec ion om he ligh e on axle and hen he de lec ion inc eases
because o he hea ie ea axle. A e c ossing o he ehicle, he
measu ed alues e u n o ze o, so he e is no pe manen de o ma ion
o he a ch.
7. Conclusion
The desc ibed me hod o s eng hening and widening o a mason y
b idge a ch using hin ein o ced conc e e spand el walls s abilized
by ans e se p es essing cables has se e al ad an ages. I is simul-
aneously simple, du able and e ec i e. I can be ca ied ou wi h
a ic limi ed o a single lane h ough he cen e o he b idge in case
o oad a ches, o wi h a ic limi ed o only one ack in case o
ailway a ches. The es o a ion wi h only a pa ial limi a ion o a ic is
welcomed by bo h b idge manage s and in es o s. On a e age, he cos s
o econs uc ion ep esen 40% o he p ice o he new b idge. I he
quali y o he mason y is sa is ac o y (s one mason y is almos always
sa is ac o y, b ick mason y is condi ional on quali y), i can always be
ecommended. The au ho s o he pape p o e he eliabili y and long-
e m li e ime o his me hod wi h p ac ical ealiza ions, and he oldes
applica ion has been in ope a ion wi hou any de ec s o mo e han
15 yea s.
The desc ibed s uc u al sys em is also ad an ageous because he e
is no need o demolish any pa o he exis ing s uc u e in he cou se
o he applica ion o he new sys em. The o iginal spand el walls
become a pe manen shu e ing o new ein o ced conc e e spand el
walls, which will co e he o iginal ones (including hei de ec s) hus
au oma ically causing a es o a i e e ec o he addi ional s uc u e.
Enginee ing S uc u es 245 (2021) 112898
19
L. Klusáček e al.
The s ain o he a ch du ing he p es essing p ocess, which has
been e i ied expe imen ally, mani es s e y small o negligible p e-
s essing losses and he p edic abili y o he s a ic calcula ions used.
By using a la ge numbe o mechanical ampli ie s ac oss he a ch,
i is possible o s udy in mo e de ail he syne gy o he pa s o he a ch
a c sepa a ed by c acks. The monoli hic cha ac e o he a ch has been
achie ed by he addi ional la e al p es essing. The desc ibed me hod-
ology can be used o complex moni o ing o he beha iou o he whole
s uc u e, e alua ing i s damage and e ining he compu a ional model
acco ding o he cu en s a e o he damaged s uc u e.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing inan-
cial in e es s o pe sonal ela ionships ha could ha e appea ed o
in luence he wo k epo ed in his pape .
Acknowledgemen
This pape has been inancially suppo ed by he Technology
Agency o he Czech Republic unde he p ojec n.
CK01000042 ‘‘Speci ica ion o esidual load-capaci y o p es essed
b idges’’.
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