Transverse prestressing and reinforced concrete as the key to restoration of masonry arch bridges

Enginee ing S uc u es 245 (2021) 112898 0141-0296/© 2021 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/). Con en s lis s a ailable a ScienceDi ec Enginee ing S uc u es jou nal homepage: www.else ie .com/loca e/engs uc 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 3 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 4 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 5 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 Enginee ing S uc u es 245 (2021) 112898 6 L. Klusáček e al. 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 Enginee ing S uc u es 245 (2021) 112898 7 L. Klusáček e al. 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 Enginee ing S uc u es 245 (2021) 112898 8 L. Klusáček e al. 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. Enginee ing S uc u es 245 (2021) 112898 9 L. Klusáček e al. 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 16 L. Klusáček e al. 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 17 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’’. Re e ences [1] O bán Z. Assessmen , eliabili y and main enance o mason y a ch ailway b idges in eu ope. S uc Des Cons 2004;152–61. [2] S oboda A, Klusáček L, Olšák M. S eng hening and ehabili a ion o U-shaped RC b idges using subs i u e cable duc s. Ad Ma e Sci Eng 2019;2019:21. h p: //dx.doi.o g/10.1155/2019/8920718, URL: h ps://www.hindawi.com/jou nals/ amse/2019/8920718/. [3] Recupe o A, Spinella N, Colajanni P, Scilipo i CD. Inc easing he capaci y o exis ing b idges by using unbonded p es essing echnology: A case s udy. Ad Ci Eng 2014;2014. h p://dx.doi.o g/10.1155/2014/840902. 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