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Qta 'xOvvmu}}aD w ?r=e |rt=a u=wvax@ KrUt uD@ |=yxR=U QO C=L}rUD |oOQwNVy=m =Q xOvQwN w sH=yt |=y\}Lt ZQat QO |=yxR=U xvwou}= |v=UQCtON'CU= xOW OwHwt `[w R= CUQO=v |@=} RQ= ?Hwt Qt= u}= x@ |yHwD|@ "OyO|t|=yxv} Ry xm 'CW=O Oy=wN x=Qty x@ =Q xR=U R= xOv=t}k=@ Qta Vy=m u}vJtyQO =m} Qt; QO xOWx=Q= Q=t; "OQm Oy=wN p}tLD xR=U lr=t x@ =Q |}xOWv |v}@V}B=ypB |oOQwN |=Q@ |QqO OQ=}r}t 9 7 =D 5 9 |xv} Ry OwHw x@ xQ=W= '2002 p=U|=yxWQa w =yx=QoQR@ QO |}=ORM} ltv R= xO=iDU= uwRi=RwQ V}=Ri= xwqa x@ [1]"OQ=OR= w OQ}o|t Q=Qk xO=iDU= OQwt Q=}U@ R}v =t QwWm QO xm 'Q}UOQU j]=vt QO =ypB=Q u; OQw;Q@ CQwQ[ w xO}OB u}= C}ty= 'CU= |oOQwN R=e; QO QF-wt |rY= pt=wauD@ |=yxR=U Ctw=kt |@=} RQ= R}v w O}OH KrUt uD@ |=yxR=U |L=Q] s=ovy x@

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C=@U=Lt QO |oOQwN Q=WDv= Ov};Qi R= pY=L |xH}Dv u=wvax@ QDt=Q=B u}= "OwW|tu=R}t x@ |@=}CUO CyH u=}t u}= QO "CU= |oOQwN u=R}t hQat w xOW xO}v=HvoMQv s=v x@ |QDt=Q=B O}=@ |oOQwN Q=WDv= ẁQW R= TB |v=tR `]=kt QO |oOQwNw[a \}=QW w |oOQwN ẁv x@ xHwD =@ QDt=Q=B u}= [10]"OwW h} QaD R}v |oOQwNCQ=wDU= w ww pOt R= Q=DWwv u}= QO "OwW h} QaD hrDNt |=ypOt T=U=Q@ Ov=wD|tQO w Q=DWwv u}= 4 VN@ QO xm [11]'CU= xOW xO=iDU= QDt=Q=B u}= u}}@D |=Q@ww pOt "CU= xOW xDN=OQB u; x@ \w@ Qt \@=wQ u=}@ x@ xOWx=Q= |xvwtv |UQQ@|oOQwN Q=WDv= |xrLQt pw] QO O}=Qrm uw} |oOQwN MQv x@ \w@ Qt CQ=wDU= wpt=m j@=]D TQ=i G}rN |xk]vt \}=QW =@ u; R= xO=iDU= |x}rw= \}=QW w CU=

"OQ=Ou}@ |a}@] |oOv@UJ Ctw=kt Vkv R= |QF= [9]'ww |xOWx=Q= |x]@=Q QO'CU}v |}=yv |oOv@UJ Ctw=kt QO (�AD) xOQwNlQD uD@ w xOWxOQwN QwD=tQ;x@ u=QoWywSB Q}=U |xOWO=yvW}B \@=wQ QO s}kDUtQ}e =} w ,=t}kDUt xm |DQwY QO(�AD) xOQwNlQD uD@ w xOWxOQwN QwD=tQ; u}@ |a}@] |oOv@UJ Ctw=kt Vkv

[7w3]"CU= xOW xQ=W= |}=yv |oOv@UJ Ctw=kt QO|oOv@UJ Ctw=kt QF= uDiQoQ_vQO |]N =@ w xOWx=Q= |=ypwtQi x@ xHwD =@'|}=yv|oOv@UJCtw=kt |x]@=Q QO xOQwNlQD uD@ w xOWxOQwN QwD=tQ; u}@|a}@]|}=yv |oOv@UJ Ctw=kt |x@U=Lt |=Q@ 2 |x]@=Q w KqY= ww |xOWx=Q= pwtQi

%CU= xOW O=yvW}B�Fr = �(x)� [pc;c(x) + pc;st(x) + pcorr(x)] + �AD (2)CQwYx@ |L]U Ctw=kt R= |WN@ u=wvax@ pOt u}= QO 2l =m]Y= ?} Q[

%CU= xOW xDiQo Q_v QO 3 |x]@=Q�(x) = 0 37� 0 26(x� xcr) (3)xt=O= QO xm 'CU= uD@ |QU=QU |oOQwNlQD =@ \@DQt |oOQwN jta xcr 'u; QO xm

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|a}@] |oOv@UJ "1"2xOW xO=iDU= 4 |x]@=Q 'xOWKqY= pOt QO |a}@] |oOv@UJ QF= uDiQoQ_vQO |=Q@

[12]%CU=�AD(x) =

n:Ar(x):fcoh(x): [cot �(x) + tan(� + �)(x)]�Dr(x):Sr

(4)

=yG; |xrY=i Sr 'xOWxOQwN |rw] QwD=tQ; |xDi=}Vy=m Q]k Dr(x) 'u; QO xm'u; QO xm � CU= xOW xDiQo Q_v QO 0 6Di CQwYx@ w}r w nv=w O=yvW}B j@] xm|rw] QwD=tQ; |xDi=}Vy=m Q]k Dr(x) [4]'�CU= |rw] QwD=tQ; |x}rw= Q]k Di|x]@=Q R= |rvwQm O=yvW}B j@] xm CU= |a}@] |oOv@UJ fcoh(x) w 'xOWxOQwN

[3]%OwW|t x@U=Lt 5fcoh(x) = 3 68� 22 08(x� xcr) (5)%OwW x@U=Lt 6 |x]@=Q j@] Ov=wD|t xm CU=yG; `]kt K]U Ar(x) 'u; QO xmAr(x) = �Dr(x):hr(x) (6)

x@ u=wD|t 'OwW xDiQo Q_v QO O}=@ pOt u}= QO xm |}=yQDt=Q=B u} QDQ=PoQ}F-=D R= "OR=OQB@pY=L CqwYLt OWQ '=yG; pmW '|oOQwN Ov};Qi QO QwD=tQ; `]kt K]U C=Q}}eD|oOv@UJ u=R}t QO |oty xm 'OQm xQ=W= lQD VQDUo Q=mwR=U R}v w |oOQwN R=

"OvQ=Po|t Q}F-=D QwD=tQ; w uD@ u}@uD@ |=[a= QO xm|t=ovy Ov=xO=O u=Wv 1973 p=U QO |D=k}kLD |] u=kkLt|oOv@UJ Ctw=kt QF= Vkv 'OW=@ xDW=Ov OwHw uD@ QO |oOWQwYLt QF= KrUtpOt QO |oOWQwYLt QF= uOQmOQ=w =@ xH}Dv u}= x@ xHwD =@ [2]"Ow@ Oy=wN |U=U=|WtN C}iQ_ w |oOv@UJ Ctw=kt QO QF= u}= u=R}t |UQQ@ x@ u=wD|t |r}rLD

"CN=OQB KrUt |vD@ w[a l} |xOv=t}k=@xDiQo CQwY |Q=}U@ C=ar=]t |}=yv |oOv@UJ Ctw=kt |x@U=Lt |=Q@|W=v |oOWQwYLt QF= x@ QwmPt C=ar=]t QO xOWx=Q= |=yx]@=Q QO [8�3]"CU=C@Uv x@ |rm Qw] x@ =t= 'CU= xOWv |t}kDUt |xQ=W= =yCwt=N OwHw R=|=ypOt '|oOv@UJ Ctw=kt OQw;Q@ |xv}tR QO xDiQoCQwY |=yQ=m ẁtHt|oOv@UJ Ctw=kt Q=Okt u}}aD QO |oOWQwYLt QF= |R=U|:tm x@ |OwOLt

"Ov=xDN=OQB\UwD uD@ |oOWQwYLt QF= =D OWwm|t w)w |xOWx=Q= pOt u=}t u}= QO[9]'Ovm |iQat |}=yv |oOv@UJ Ctw=kt QO Q=PoQ}F-=D |QDt=Q=B u=wvax@ =Q =yCwt=Nw xOWxOQwN QwD=tQ; u}@ |a}@] |oOv@UJ Ctw=kt uwJ |QDt=Q=B uOv=Hvo sOa =t='OQwN|t sWJ x@ xOWx=Q= |=ypwtQi |NQ@ QO xm |Dq=mW= R}v w xOQwNlQD uD@

"CU= xOQm KqY= OvtR=}v =Q pOt u}=OwHwt |v=QL@ |=yQDt=Q=B w [9]'ww |xOWx=Q= pOt |UQQ@ ut[ 'xar=]t u}= QOQ=DWwv u}= hOy u}=Q@=v@ "CU= xOW xDN=OQB QwmPt pOt p}tmD x@ u; |x]@=Q QOx@ KrUt uD@ |=yQ}D QO |oOv@UJ Ctw=kt u}}aD CyH xOWKqY= |rOt |x=Q=|xrLQt pw] QO xOWxOQwN |=yQ}D QO xOv=t}k=@ |WtN C}iQ_ |UQQ@ Qw_vt=@ x}rw= pOt w xOWKqY= pOt R= pY=L G}=Dv C}=yv QO "CU= |oOQwN Q=WDv=Qw_vt x@ "Ov=xDiQo Q=Qk |@=} RQ= OQwt |oOQwN |ak=w V}=tR; l} R= pY=L G}=DvxrLQt u}= QO xR=U R= xOW|QBU Qta w Q=WDv= |xrLQt QO |oOQwN u=R}t \=@DQ=|xvwtv \}=QW =@ ?U=vDt O}=@ xm CU= |oOQwN MQv |=ypOt R= xO=iDU= x@ R=}vK} QWD CyH QDt=Q=B u}= R= Q=DWwv |v=}=B VN@ QO [10]"OwW ?=NDv= |UQQ@ OQwt

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[9�3]"Ov=xO=O s=Hv= |}=yvuDiQoQ_vQO =@ |}=yv |oOv@UJ Ctw=kt |x@U=Lt |=Q@ OwN C=ar=]t QO [9]wwxOQm O=yvW}B =Q 1 |x]@=Q '=yCwt=N OwHw R= |W=v |xOt;OwHwx@ |oOWQwYLt QF=

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"OQ}o|t CQwY u; R= TB w |QU=QU |oOQwNlQD ẁkw|QU=QU |oOQwNlQD R= V}B "1"2"2

|oOQwNlQD R= TB =} V}B Cr=L |xOvvmXNWt �Rc� lQD |xy@H C}akwtQ@=Q@ Rc xm ODi=|t j=iD= |v=tR |QU=QU |oOQwN 'Qo}O CQ=@a x@ "CU= |QU=QU`=aW� Ri u}@ �Rc� lQD |xy@H `=aW Qo = u}=Q@=v@ "�Rc = Ro� OwW RoV}B Cr=L 'OW=@ �|vD@ VWwB |xy@H `=aW� Ro w �|D=L}rUD Oqwi |x}rw=x@ xHwD =@ u=wD|t =Q Cr=L u}= QO |oOQwN Q=Wi "CU= |QU=QU |oOQwNlQD R=

"|oOQwNlQD � |oOQwN pOt QO syt |=yQDt=Q=B "2 pmW

0 07Dr(x) Q@=Q@ w}r w nv=w O=yvW}B x@ xm CU= G; `=iDQ= hr(x) 'u; QO xmCQwYx@ |rvwQm O=yvW}B j@] R}v tan(� + ')(x) [4]"CU= xOW xDiQo Q_v QO

[3]%OwW|t x@U=Lt 7 |x]@=Qtan(� + ')(x) = 1 857� 0 9285x (7)

|oOQwN R= |W=v Q=Wi "2"2Vy=m |r}rLD pOt QO pcorr(x) |oOQwN R= |W=v Q=Wi syU OwQw |ovwoJ|x@U=Lt |=Q@ "CU= syt Q=}U@ |}=yv |oOv@UJ Ctw=kt x@ |@=}DUO w |oOv@UJ=@ =Q KrUt uD@ QO Q=WDv= |xrLQt QO |oOQwN Q=mwR=U O}=@ =OD@= QDt=Q=B u}='|oOQwN R= |W=v |=y?}U; '|oOQwN Q=JO KrUt uD@ `]=kt QO xmv}= x@ xHwDlQD � |oOQwN pOt l} CQwYx@ 'OwW xO}O u=t-=wD CQwYx@ |oOQwNlQD wxm 's}N[ Q=OH |xv=wDU= pOt R= u=QoWywSB R= |Q=}U@ "OQm x=Q= 3|oOQwNxO=iDU= OwN C=ar=]t QO 'CU= |oOQwNlQD w |oOQwN s-=wD QF= |xOvQ}oQ@ QO

[12w6'4]"Ov=xOQmQ=Wi Q}F-=D CLD pOt u}= QO xOWxDiQo Q_v QO |vD@ s}N[ Q=OH |xv=wDU=|=yQ=Wi R=|W=v|oOWQwYLt Q=Wi w|oOQwN CqwYLt \=U@v= R=|W=v|rN=O

[4]"|oOQwNlQD � |oOQwN pOt "1 pmW

101

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=yCWwv=B1. corrosion depth2. friction coe�cient3. corrosion-cracking model4. rust layer5. crack front6. concrete cover front7. radial pressure

�References� `@=vt1. Koch, G.H., Brongers, P.H., Thompson, N.G., Virmani,

Y.P. and Payer, J.H., Corrosion Costs and PreventionStrategies in the United States, Federal Highway Admin-istration, Report No. FHWA-RD- 01-156, Washington,DC (2002).

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6. Bhargava, K., Ghosh, A., Mor, Y. and Ramanujam, S.\Analytical model for time to cover cracking in RC struc-tures due to rebar corrosion", Nuclear Engineering andDesign, 236(11), pp. 1123-1139 (2006).

7. Hussein, L. \Analytical modeling of bond stress at steel-concrete interface due to corrosion", MASc Thesis, Ry-erson University, Toronto (2011).

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11. Vu, K. and Stewart, M.G. \Structural reliability of con-crete bridges including improved chloride-induced cor-rosion models", Structural Safety, 22(4), pp. 313-333(2000).

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