Gamma process modelling for lifecycle performance assessment of corrosion affected concrete structures

Transcription

1 Gamma proess modelling for lifeyle performane assessment of orrosion affeted onrete strtres Jaya Nepal 1) and 1 *Ha-Peng Chen 2) 1), 2) Shool of Engineering, University of Greenwih, Chatham, Kent, ME4 4TB, UK 2) h.hen@gre.a.k ABSTRACT Life yle performane of orrosion affeted RC strtres is an important and hallenging isse for effetive infrastrtre management. The arate ondition assessment of orroded RC strtres mainly depends on the effetive evalation of deterioration orring in the strtres. Strtral performane deterioration ased by reinforement orrosion is a omplex phenomenon whih is generally nertain and non-dereasing. Therefore, a stohasti modelling sh as the gamma proess an be an effetive tool to onsider the temporal nertainty assoiated with performane deterioration. This paper presents a time-dependent reliability analysis of orrosion affeted RC strtres assoiated with the bond strength degradation. Initially, analytial soltions are provided to evalate the rak width at the over srfae and predit the orresponding loss of bond strength between the orroded steel and the srronding raked onrete. Then in order to model the progression of bond strength deterioration dring the life yle of the RC strtre, a gamma proess model is adopted. The time-dependent reliability analysis is then applied to evalate the probability of failre of the RC strtre. Finally, a nmerial example is sed to demonstrate the appliability of the proposed approah. The reslts from the illstrative example show that the proposed approah is apable of assessing performane of the bond strength of onrete strtres affeted by reinforement orrosion dring their lifeyle. 1. INTRODUCTION The performane of the reinfored onrete (RC) strtres exposed to aggressive environments sh as motorway bridges, ar parks and marine strtres is often seriosly affeted by orrosion in reinforement. The orrosion prodts formed dring orrosion proess are expansive in natre (Pantazopolo and Papolia 2001). This volme inrease reates expansive fore at the rebar srfae and sbseqently prodes radial splitting raks in the srronding onrete. Frthermore, the loss of ross-setional area of the rebar and the loss of bond strength between orroded steel and onrete diretly affet the flexral strength of the RC strtre (Bhargava et al. 2007a, Shetty et al. 2014). As a reslt, their performane is ompromised. Bond strength ating at the rebar srfae is the interation mehanism that enables * Corresponding athor

2 the fore transfer between rebar and the srronding onrete. Hene it maintains the omposite ation in RC strtres. When omposite ation is disrpted, load arrying apaity is also effeted (Rodrigez et al. 1994, Coronelli 2002, Hang and Chen 2013). This in trn hanges the overall behavior of the RC strtres. Hene for the satisfatory performane of the RC strtres adeqate bond between rebar and srronding onrete is essential. Many experimental investigations have been ndertaken dring the last two deades regarding bond behavior of orroded reinforement (Law et al. 2011). In general, these experimental investigations sggest that at low level of orrosion (<1%) bond strength inreases, and with frther inrease in orrosion bond strength dereases signifiantly. Loss p to 80-90% of the initial bond strength has also been observed for only abot 5-7% of the orrosion level in nonfined onrete (Rodrigez et al. 1994, Zhao et al. 2013, Banba et al. 2014). Similar reslts were observed from analytial and nmerial stdies arried ot by Coronelli (2002), Lndgren (2002), Wang and Li (2004) and Bhargava et al. (2007b). Few experimental investigations have also been arried ot in order to evalate the relationship between srfae rak width and bond behavior of orroded deformed rebar (Rodrigez et al. 1994, Almsallam et al. 1996, Fisher et al. 2010, Law et al. 2011, Li and Yan 2013, Banba et al. 2014). Some empirial relations have also been proposed to desribe the inflene of rak width on the bond strength of the orroded plain rebar based on the experimental reslts (Cairns et al. 2006). The smmary of the pblished reslts on the bond strength behavior of the orroded deformed rebar with respet to over srfae rak width obtained from varios referene literatres is presented in Fig. 1. Fig. 1 Relation between normalized residal bond strength and orrosion inded over srfae rak width The reslts in Fig. 1 are obtained by plotting normalized residal bond strength ratio of ltimate bond strength of the orroded element ( T bx ) to non-orroded element ( T bo ) verss over srfae rak width ( w x ), together with the reslts obtained from the empirial eqations proposed by Cairns et al. (2006). Signifiant satter an be

3 observed from these experimental investigations. Therefore a trend line has been plotted, whih indiates that with inrease in rak width at the over srfae residal bond strength is onsiderably dereased. Despite the satter and inonsistenies between the qantitative redtions in the residal bond strength, they learly indiate that residal bond strength of the orroded rebar is signifiantly dereased with an inrease in over srfae rak width. Researh on the predition of the life yle performane of orroded RC strtres assoiated with bond strength degradation is very limited. Stohasti modelling for bond strength deterioration has signifiant potential for assessing the ondition and life yle performane of the RC strtres. Therefore, this paper presents a timedependent reliability analysis of orrosion affeted RC strtres assoiated with the bond strength degradation together with the omprehensive approah of gammaproess for deterioration modelling. In reliability analysis, strtral failre is onsidered when its deterioration reahes the predefined allowable limit. The appliability of the proposed methodology is then presented with a nmerial example. 2. REINFORCEMET CORROSION Steel rebar embedded in the onrete is normally proteted by a passive layer reated by the high alkalinity of the onrete. This protetive layer an be broken down de arbonation or the hloride ingress from the environment. One the passive layer is broken down, orrosion initiates. The expansive layer of the orrosion prodt initiates raking at the steel onrete interfae and these raks propagate toward the over srfae of the onrete over (Pantazopolo and Papolia 2001). As a reslt, the bond strength between the steel reinforement and the srronding onrete starts dereasing (Law et al. 2011) This redtion in bond strength together with the dereasing rebar size an lead to signifiant redtion in residal load arrying apaity and stiffness of the RC strtres, after whih strtral ollapse is most like to or (Torres-Aosta et al. 2007, Nepal and Chen 2014). Hene, it is lear that rak propagation and redtion in residal strength an signifiantly affets the overall performane and shortens the servie life of the RC strtres sffering from reinforement orrosion. For the time-dependent reliability analysis of these strtres, qantifiation of these damages is essential. In this regard, the analytial investigations of these damages ased by reinforement orrosion are now presented. 2.1 Loss of ross-setional area of the rebar The reded diameter of the rebar from its initial state is generally evalated in terms of attak penetration (pitting attak or homogeneos orrosion), expressed as D D x (1) bx b p when 4 p 8and homogeneos orrosion at later stage when p 2 ( Vidal et al. 2004). Aording to the stdy arried ot by Zhang et al. (2010), in long-term natral

4 orrosion proess, at the beginning althogh orrosion appears as the loalized bt in later stage it appears as niform orrosion. Hene in this paper orrosion has been onsidered as niform. Therefore, radial displaement at the rebar srfae ( bx ) ased by expansive orrosion prodt is niform and axis symmetri, expressed here as V 1 ( 1) DX (2) D 4 bx vol b p b where V Vr Vs is the volme inrease per nit length of the rebar in whih V r is the volme of the rst prodt formed given by V r vol AX b p and Vs is the volme of loss of the orroded rebar, this an be obtained one V r is known. vol is the volme ratio of the orrosion prodt formed to its parent metal, this generally lies between1.8 to 6.4 (Pantazopolo and Papolia 2001, Lndgren 2002); A b is the original rosssetional area of the rebar and X p is the orrosion level, defined as the ratio of the mass loss of orroded rebar to its original mass. 2.2 Craking in onrete over Craking in the onrete over generally ors when the hoop stress on the onrete srfae reahes the tensile strength of the onrete. The onrete raking proess de to reinforement orrosion has been investigated analytially by adopting the anisotropy of raked onrete and thik walled ylinder model previosly tilized by Chen and Xiao (2012) together with the onept of eqivalent rak as tilized by Chen and Alani (2013). The shemati representation of thik walled ylinder model sed in this paper is shown in Fig. 2, in whih the onrete srronding the reinforing rebar is onsidered as thik walled ylinder with wall thikness eqal to lear over depth (C ). Fig. 2 Idealization of over onrete as thik-walled ylinder model for prediting onrete rak development and bond strength evoltion

5 The raking in the onrete over has been onsidered as ohesive in natre and residal tensile stress in the raked onrete has been obtained by adopting bilinear stress softening law of raked onrete as desribed in CEB-FIP (1990). In the ohesive rak model, the stress transferred throgh the ohesive raks is assmed to be a fntion of rak opening (softening rve), expressed as w t f a bw (3) where w is the tensile stress ating aross ohesive raks; f t is the maximm tensile strength of onrete at onset of raking; W is the normalized rak width defined as W fwr t () Gf in whih G f is the fratre energy of the onrete; wr () is the atal rak width at any point r between Rb and R as shown in Fig. 2. Coeffiients a and b are the bilinear oeffiients, depending on the pre-ritial stage ( 0 W Wr ) and post-ritial stage ( Wr W W ) of rak width, as a 1 b for pre ritial stage W 1; bi r (4a) biw bi a ; b W W W W r r for post ritial stage (4b) in whih bi is oeffiient of bilinear softening rve; W r is normalized ritial rak width and W is ltimate ohesive rak width. The ritial and ltimate ohesive rak widths an be determined from experiments for onrete. In the CEB-FIP(1990), the oeffiient bi is given as bi = 0.15; W r and W an be evalated from onrete strength, fratre energy and maximm aggregate size. From the anisotropi property and the bilinear softening law of the raked onrete, normalized rak width at the rebar srfae of thik walled ylinder ( R b ) an be expressed as 1 E Wbx bx arb bl ( o Rb) ft (5) where l o is the material onstant given by lo nl h 2 b in whih n is the nmber of 2 raks taken as 3 or 4 for thik walled ylinder model and lh EG f ft is the harateristi length; E E (1 ) is the effetive modls of elastiity of the onrete in whih E is the modls of elastiity of onrete and is the reep oeffiient; and bx is the radial displaement at the rebar srfae as desribed in Eq. (2). One the

6 raks initiate at the bond interfae, they propagates towards the over srfae ( R ). The orrosion level at the time to rak on the over srfae ( from X p ) an be obtained 2 f t 2R r r r X p 1 (1 ) ( lo Rb )( lo R ) ( R, Rb ) ( vol 1) E Db (6) where is the Poisson s ratio of the onrete and ( R, R ) is rak fator denoted by r ( R, Rb) and ( R, Rb) in pre-rital stage and post ritial stage of the raking, respetively, given by b r r R Rb 1 R o b ( R, Rb) ln r r r r 2 r lo ( lo R)( lo Rb) ( lo ) Rb lo R l R (7a) R Rb 1 R o b ( R, Rb) ln 2 lo ( lo R)( lo Rb) ( lo ) Rb lo R l R (7a) in whih r l o and l o are the material onstants for pre-ritial stage and post-ritial stage raking of the onrete over. Ignoring the Poisson s effet assoiated with the hoop strain of the ompletely raked onrete, the normalized rak width on the onrete over srfae W an be expressed as x W x a Wbx R ( lo R ). ( R, Rb ) b 1 R ( l R ). ( R, R ) o b (8) In ohesive rak model the proess of onrete raking ontines ntil they reah their ltimate ohesive vale at the over srfae. The orrosion level at whih the eqivalent rak at the over srfae reahes its ltimate ohesive vale an be obtained from X 2 f nl ( 1) E D t h p vol b W (9) At this stage de to the widening of the rak opening, the residal strength and the orrosion stress ating at the rebar srfae beome negligible. 2.3 Bond strength deterioration Corrosion in the rebar affets the bond properties ating at the steel-onrete interfae by hanging the shape and angle of the ribs of deformed rebar. It also

7 inflenes the mehanial interloking and onfinement between rebar and the srronding onrete by reding adhesion and fritional fore ased by the amlation of orrosion prodts and raking in the onrete over. Therefore orrosion in reinforement threatens all these fators reqired for good bonding ondition of the RC strtres. Considering these effets, deterioration of ltimate bond strength Tbx of the orroded deformed rebar an be evalated from ontribtions of three stresses ating at the bond interfae, i.e. adhesion stress T adx, onfinement stress T nfx and orrosion stress T orrx (Coronelli (2002). Tbx Tadx Tnfx Torrx (10) The adhesion stress ating between rebar and onrete is given by T adx nst Arx fohx oto tan( o ) (11) D S bx r where n st is the nmber of stirrps provided; A rx D bx h rx is the reded rib area in plane at right angle to rebar axis and hrx 0.07Dbx is the reded rib height of the rebar de to orrosion; fohx 2 10( x x ) is the adhesion strength oeffiient in whih x is the orrosion depth orresponding to the throgh raking of the onrete over, and is obtained from X ; tan( ) an be estimated from x (Coronelli and p o Gambarova 2000) in whih o is the orientation of the rib sally taken as 45 and is the angle of frition between steel and onrete; and Sr 0.6Db is the rib spaing (Wang and Li 2004). The onfinement stress is given by Tnfx KnfxPnfx (12) where K nfx is the oeffiient of onfinement stress evalated from Knfx nc st r tan( o ) in whih C r is the shape fator onstant taken as 0.8 for resent shape rebar. In this stdy ondition of nonfined onrete has been onsidered. Therefore, P nfx is the onfinement stress only provided by the raked onrete srronding the reinforement. By adopting the properties of the thik walled ylinder model with ohesive raks as desribed in Fig. 2, Nepal et al. (2013) has modified the expression of onfinement stress given by Giriani et al. (1991), expressed here as P nfx C Da ( w wbx ) ft R w( D kw ) bx a bx (13)

8 where wbx GW f bx ft is atal rak width at the rebar srfae orresponding to orrosion level X p and k is the onstant taken as 167(Giriani et al. 1991). The bond strength ontribted by the orrosion pressre is given by T P (14) orrx x orrx in whih x is the oeffiient of the frition between the orroded rebar and raked onrete defined as ( x x ) and P orrx is the orrosion pressre or the radial pressre ating at the bond interfae de to the amlation of the orrosion prodt at the rebar srfae. The orrosion pressre ating at bond interfae an be evalated from (Chen and Xiao 2012) P f a bw b bl W t orr bx orrx 1 2 bx bx bx o 1 ( lo Rb) Rb Rb (15) where orr is the orrosion fator given by orr Wbx ( R, Rb ) before throgh raking and orr Wx Wbx ( R, Rb ) after throgh raking of the onrete over and bx is the stiffness redtion fator assoiated with the raked onrete, given by bx 1 1 blow bx a bwbx Rb (16) 3. STOCHASTIC DETERIORATION MODELLING Deterioration ased by reinforement orrosion and its strtral response is a omplex phenomenon with high possibilities of nertainties. The nertainties assoiated with the deterioration and the orresponding strtral response an be dealt with the stohasti proess. Hene in this stdy, probability of failre of the orroded RC strtre is evalated by onsidering the bond strength deterioration as the stohasti proess. From Fig.1 it is lear that after raking of the onrete at the over srfae, the bond strength deterioration de to reinforement orrosion is ontinos and non-negative. Therefore from the definition of gamma proess (Van Noortwijk and Frangopol 2004, Chen and Alani 2012), the gamma proess is sitable for the stohasti modelling of bond strength deterioration in orrosion affeted RC strtres dring their life yle. In gamma proess deterioration model, the mlative bond strength deterioration ( J b ) is a random qantity, and has the gamma distribtion with the shape parameter ( w x ) 0 and sale parameter 0. The probability density fntion of bond strength deterioration ( J b ) at rak width wx 0 an be expressed as

9 ( wx ) ( wx ) 1 Jb? Jb e 젨for? Jb f J Ga J w (17) Jb ( wx )? ), ( w ) b b x x 0, 젨젨젨젨젨젨젨젨젨젨젨젨젨젨젨젨젨젨젨 elsewhere where ( wx ) 1 ( w ) e dis the gamma fntion for( ) 0. The sale parameter x 0 ( ) old be estimated from statistial estimation methods sh as a Maximm Likelihood Method by maximizing the logarithm of the likelihood fntion of the inrement of the parameter (Van Noortwijk 2009). Assming J b as the average bond strength deterioration rate assoiated with rak width ( w x ), the shape fntion ( ( w x )) an be obtained from ( wx ) J b ( wx ). Assming J L as the maximm allowable limit of the bond strength deterioration, from the definition of probability of failre and by integrating probability density fntion given in Eq. (17), the lifetime distribtion of failre assoiated with bond strength deterioration is given by ( wx ), J L P Pr[ J ( w ) J ] f J djb (18) ( w ) f b x L Jb ( wx ) b JbJL 1 where (, z) e d is the inomplete gamma fntion for z 0 and 0. z 4. NUMERICAL EXAMPLE In this setion the methodology mentioned in the preeding setion is applied to a nmerial example for a simply spported RC beam of span 5 m with minimm servie life of 50 years designed to resist aggressive environment as defined by Eroode 2. The ross-setional width and effetive depth of beam are b = 300 mm and d = 560 mm, respetively. For rebar of a diameter 20 mm ( D b = 20 mm) are provided as the tension rebar. Two bars of a diameter 16 mm ( D s = 16 mm) are provided as the ompression rebar with lear over thikness of 40 mm (C = 40 mm). The ompressive strength of onrete f k = 40 MPa and the yield strength of original reinforing steel f yk = 460 MPa with modls of elastiity ( E st ) = 200 GPa are adopted in this stdy. Material properties reqired for this analytial model are assmed as total rak nmber n = 4, Poisson s ratio = 0.18, reep oeffiient = 2.0, mean annal rrent density i orr = 1 μa/m 2, fratre energy G f = 200 N/m, density of steel s = 7850kg/m3, volme ratio of orrosion prodt vol = 2.0, and the orresponding molelar weight ratio mol = The ritial and ltimate ohesive rak width have been obtained from CEB-FIP (1990) for nominal maximm aggregate size D a = 20 mm. w x x

10 Other parameters sh as f t and E are evalated from Eroode 2. Fig. 3 Analytial predition of over srfae rak width verss orrosion level, ompared with experimental test reslts available from varios sores The reslts in Fig. 3 show the analytially predited eqivalent over srfae rak width ( w ) as a fntion of orrosion level ( X ) in perentage. The predited reslts x are then ompared with experimental investigations obtained from aelerated or natral orrosion tests in onrete (Rodrigez et al. 1994, Alonso et al. 1998, Vidal et al. 2004, Torres-Aosta et al. 2007, Coronelli et al. 2013, Banba et al and Khan et al. 2014). It an be seen from Fig. 3 that the predited rak width inreases as reinforement orrosion level inreases, agreeing well with the referred experimental reslts. p Fig. 4 Analytial predition of normalized residal bond strength verss over srfae rak width for nonfined onrete, ompared with experimental test reslts available from varios sores

11 The reslts of normalized residal bond strength ( T bx T bo ) verss eqivalent over srfae rak width for nonfined onrete predited by the present analytial stdy are plotted in Fig. 4. Then they are ompared with the pblished experiment data obtained from varios referenes (Rodrigez et al. 1994, Almsallam et al. 1996, Fisher et al. 2010, Law et al. 2011, and Banba et al. 2014). Here again, the trend of bond strength deterioration with inrease in srfae rak width predited by the present stdy is in good agreement with the experimental investigation of the referene literatres. The residal bond strength of nonfined onrete redes ontinosly with the inrease in rak width and finally beomes negligible when rak width is abot 1.5mm (ltimate ohesive vale). This is de to the absene of transverse reinforement (stirrps) in nonfined onrete. The deterioration of strtral performane in terms of over srfae raking of the onrete over is modelled as gamma proess. At first, srfae rak width ( w x ) is onsidered as an indiator of performane deterioration for the servieability of the RC strtre and adopted to replae Jb in Eq. (17). The lifetime distribtion of probability of failre ( P f ) of the orroded beam is obtained from Eq. (18) for different aeptable rak width limits, w L = 0.3, 0.4 and 0.5 mm, respetively. The reslts are then presented in Fig. 5 as a fntion of orrosion level. As expeted, the probability of failre assoiated with raking of the onrete over depends on the given aeptable rak width limit, with a higher probability of failre for a lower aeptable rak width limit. The probability of failre inreases steadily with time and reahes approximately 50% when orrosion level is approximately between 5% and 8%. Fig. 5 Probability of failre of orroded RC strtre verss orrosion level for varios aeptable rak width limits The reslts for probability of failre for nonfined onrete have been presented in Fig. 6. Here the deterioration of the strtral performane in terms of strtral apaity has been indiated by the bond strength deterioration. As shown in Fig. 4, when srfae rak width is abot 0.3mm, the residal bond strength of the nonfined

12 Fig. 6 Probability of failre of nonfined onrete verss srfae rak width for varios allowable bond strength deterioration limits onrete has lost approximately 70% of the original strength, at the onset of over srfae raking. Therefore to allate probability of failre, maximm allowable limit of bond strength deterioration is onsidered as: J L =70%, 75% and 80%, respetively. The probability of failre assoiated with the bond deterioration for different allowable limit inreases steadily with inrease in srfae rak width. Here again, as antiipated nonfined onrete shows the highest probability of failre in lowest allowable limit of deterioration and lowest probability of failre in the highest allowable limit. 5. CONCLUSIONS This paper presents a new approah for evalating the life yle performane of orrosion affeted RC strtres. At first, the bond strength deterioration ased by orroded reinforement and rak growth in onrete over is evalated by analytial investigations. Then the analytial reslts are validated by experimental data available. By sing the stohasti model, the probability of strtral failre assoiated with the srfae rak width and bond strength deterioration over the lifeyle of orrosion affeted RC strtres is evalated. The appliation of the proposed approah is illstrated with the nmerial example. On the basis of the reslts obtained from the nmerial example, following onlsions are drawn: a) The proposed approah is apable of evalating the rak growth and residal bond strength deterioration of the orroded RC strtres; b) Bond strength dereases with inrease in over srfae rak width; ) The probability of failre of orrosion affeted RC strtres dring their life yle depends on the predefined allowable limit of their deterioration. Ths, the proposed approah is apable of assessing the life yle performane of onrete strtres affeted by reinforement orrosion.

13 REFERENCES Almsallam, A.A., Al- Ghantani, A.S., Aziz, A.R. and Rasheedzzafar (1996), Effet of reinforement orrosion on bond strength. Constrtion and Bilding Materials, Vol. 10(2), Alonso, C., Andrade, C., Rodrigez, J., and Diez, J. M. (1998), Fators ontrolling raking of onrete affeted by reinforement orrosion. Materials and Strtres, Vol. 31, Banba, S., Abe,T., Nagaoka, K. and Mrakami, Y. (2014), Evalation method for bondsplitting behavior of reinfored onrete with orrosion based on onfinement stress of onrete against orrosion expansion. Jornal of Advaned Conrete Tehnology, Vol.12(1), Bhargava, K., Ghosh, A. K., Mori, Y. and Ramanjam, S. (2007a), Ultimate flexral and shear apaity of onrete beams with orroded reinforement. Strtral Engineering and Mehanis, Vol. 27(3), Bhargava, K., Ghosh, A. K., Mori, Y. and Ramanjam, S. (2007b), Corrosion-inded bond strength degradation in reinfored onrete- analytial and empirial models. Nlear Engineering and Design, Vol. 237(11), Cairns J., D, Y. and Law, D. (2006), Residal bond strength of orroded plain rond bars. Magazine of Conrete Researh, Vol. 58(4), CEB-FIP (1990), CEB-FIP Model Code 1990, Comité Ero-International d Béton (CEB), Thomas Telford, London, UK. Chen, H.P. and Alani, A. M. (2012). Reliability and optimised maintenane for sea defenes. Proeedings of the ICE - Maritime Engineering, Vol. 165(2), Chen, H.P. and Alani, A. M. (2013). Optimized maintenane strategy for onrete strtres affeted by raking de to reinforement orrosion. ACI Strtral Jornal, Vol. 110(2), Chen, H.P. and Xiao, N. (2012), Analytial soltions for orrosion-inded ohesive onrete raking. Jornal of Applied Mathematis, Artile ID Coronelli, D. (2002), Corrosion raking and bond strength modelling for orroded bars in reinfored onrete. ACI Strtral Jornal, Vol. 99(3), Coronelli, D. and Gambarova, G. (2000), A mehanial model for bond strength of orroded reinforement in onrete, Proeedings of the 14th Engineering Mehanis Conferene, Astin, Texas. Coronelli, D., Hanjari, K., and Lndgren, K. (2013), Severely Corroded RC with Cover Craking. Jornal of Strtral Engineering, ASCE, Vol. 139(2), orrosion in reinfored onrete. Cement and Conrete Researh, Vol. 34(1), Eroode 2 (2004), Design of Conrete Strtre, Eropean omitee for standardization, Brssels, Belgim. Fisher C. (2010). Experimental investigations on the effet of orrosion on bond of deformed bars, Proeedings of the 8th fib PhD Symposim, Kgs, Lyngby, Denmark. Giriani, E., Plizzari, G. and Shmm, C. (1991). Role of stirrps and residal tensile strength of raked onrete on bond. Jornal of Strtral Engineering, ASCE, Vol. 117(1), 1-18.

14 Hang T.L. and Chen H.P. (2013). Symptom-based reliability analysis and remaining servie life predition of deteriorating RC strtres. Key Engineering Materials, Vol. 569, Khan, I., Franois, R. and Castel, A. (2014), Predition of reinforement orrosion sing orrosion inded raks width in orroded reinfored onrete beams. Cement and Conrete Researh, Vol. 56, Law, D. W., Tang, D., Molyneax, T. K. C. and Gravina, R. (2011), Impat of rak width on bond: onfined and nonfined rebar. Materials and Strtres, Vol. 44(7), Li, F. and Yan, Y. (2013), Effets of orrosion on bond behavior between steel strand and onrete. Constrtion and Bilding Materials, Vol. 38, Lndgren, K. (2002), Modelling the effet of orrosion on bond in reinfored onrete. Magazine of Conrete Researh, Vol. 54(3), Nepal, J., Chen, H.P. and Alani, A.M. (2013), Analytial modelling of bond strength degradation de to reinforement orrosion. Key Engineering Materials, Vol. 569, Nepal, J. and Chen, H.P. (2014), Evalation of strtral behavior of orrosion damaged reinfored onrete bridges. Proeedings of 15 th Eropean Bridge Conferene & Exhibition - Strtral Falts and Repair 2014, London, UK. Pantazopolo, S. and Papolia, K. D. (2001), Modeling over-raking de to reinforement orrosion in RC strtres. Jornal of Engineering Mehanis, ASCE, Vol. 127(4), Rodrigez, J., Ortega, L. M., and Casal, J. (1994), Corrosion of reinforing bars and servie life of reinfored onrete strtres: orrosion and bond deterioration, Proeedings of International Conferene on Conrete Aross Borders, Odense, Denmark. Shetty, A., Venkataramana, K. and Narayan K.S. B. (2014), Flexral bond strength behavior in OPC onrete of NBS beam for varios orrosion levels. Strtral Engineering and Mehanis, Vol. 49(1), Torres-Aosta, A.A., Navarro-Gtierreza, S. and Teran-Gillen J. (2007), Residal flexre apaity of orroded reinfored onrete beams. Engineering Strtres, Vol. 29(6), Van Noortwijk, J.M. (2009), A srvey of the appliation of gamma proesses in maintenane. Reliability Engineering & System Safety, Vol. 94(1), Van Noortwijk, J.M. and Frangopol, D.M. (2004), Two probabilisti life-yle maintenane models for deteriorating ivil infrastrtres. Probabilisti Engineering Mehanis, Vol. 19(4), Vidal, T., Castel, A., and Franois, R. (2004), Analyzing rak width to predit Wang, X. H. and Li, X.L. (2004). Modelling effets of orrosion on over raking and bond in reinfored onrete. Magazine of Conrete Researh, Vol. 56(4), Zhang, R., Castel, A. and Franois, R. (2010), Conrete over raking with reinforement orrosion of RC beam dring hloride-inded orrosion proess. Cement and Conrete Researh, Vol. 40(3), Zhao, Y., Lin, H., W, K. and Jin, W. (2013), Bond behavior of normal/reyled onrete and orroded steel bars. Constrtion and Bilding Materials, Vol. 48,