A STUDY OF REPAIR ALTERNATIVES BASED ON LCC ESTIMATION FOR RC INFRASTRUCTURE

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1 -Techncal Paper- A STUDY OF REPAIR ALTERNATIVES BASED ON LCC ESTIMATION FOR RC INFRASTRUCTURE Md. Shafqul ISLAM *1, Dr. Toshharu KISHI * ABSTRACT Enormous amoun of money s nvesng for he rehablaon of nfrasrucure lke brdges by he governmen. Effcenly manage he nfrasrucure sysem hus become crcal ssue o he engneers and decson makers. The amoun of deeroraon and manenance sraeges wll affec exremely he lfe cycle cos of brdges. In hs sudy, he varaon of cover deph, permeably and degree of sauraon are consdered n probablsc naure wh log-normal dsrbuon n servce lfe predcon. 5 dfferen ypes of repar mehods and dfferen repar alernaves are aken as repar sraeges. Fnally he analyss resuls are compared o help he decson makers o selec he approprae sraegy. Keywords: cover concree, permeably, LCC, repar sraegy 1. INTRODUCTION Transporaon sysem s of major mporance ou of nfrasrucures ha provdes mobly of economy. Brdges play he key lnk n ransporaon sysem. Bu s very dffcul o conrol he performance of brdge n severe aggressve envronmenal aack. Chlorde nduced seel corroson s one of he major deeroraon problem for seel renforced concree brdge n US caused by saly envronmen. The cos of hghway brdge repar n US s esmaed $7 bllon. However cos effecve manenance plan and proper decson makng can effcenly reduce he lfe cycle cos of nfrasrucure lke brdges. To asss he decson makers for nang beer manenance sraegy he engneers and economss have o hnk for he beer managemen sysem. JSCE concree commee TC335 found ha ar permeably does no gve ndcaons smlar o srengh characersc ndcaes [1]. I suggess ha durably of concree s no bes ndcaed by srengh only. Mos of he popular models gave preferences on cover sze, dffuson coeffcen and surface chlorde. Bu s very mporan o ake consderaon abou cover qualy such as permeably characerscs o desgn servce lfe of srucure. Lfe cycle cos of he nfrasrucure s ncluded here wh he coss ncorporae by agng of srucure and repar when needs as drec cos and delay cos, by raffc, a he me of repar s consdered as ndrec cos. Moreover 5 ypes of repar mehods and ypes of repar alernaves are compared o help he owner o choose he bes. The predcon framework saed here wll be useful o he engneers o desgn consderng durably parameer and wll help he owner o choose he requred repar sraegy ha cos leas.. DETERIORATION MODEL.1 Corroson Inaon The flow of chlorde on hrough pores n concree s modeled here under boh dffuson and convecon same as solue ranspor shown as follows. C C C D V x x (1) where C s chlorde on concenraon (kg/m 3 ), D s he apparen dffuson coeffcen (cm /sec), V s average lnear rae of flow (cm/s) and follows Darcy s law when concree pores are sauraed. k h V () n x where k s he hydraulc permeably (cm/s), n s h porosy (.) and s hydraulc graden (.). The x soluon of Eq. 1 for sem nfne column of porous meda s gven n references [][3] as follows. C o C x, x V.5 erfc D Vx exp D erfc x V D (3) where C(x,) s chlorde on concenraon a deph x (cm) afer me sec. (kg/m 3 ). C o s he surface chlorde concenraon (kg/m 3 ), D s he apparen dffuson coeffcen (cm /sec). *1 Docoral Suden, Deparmen of Cvl Engneerng, The Unversy of Tokyo, Japan * Professor, Insue of Indusral Scence, The Unversy of Tokyo, Japan

2 D D o T S e (3a) D o s he dffuson coeffcen n pore waer, φ s he porosy, S s he degree of sauraon, T s he emperaure n concree. Tme dependency of surface chlorde (C o ) and apparen dffuson coeffcen (D) are consdered accordng o references [4][5]...Crack Formaon Corroson produc s formed and nernal pressure s gradually ncreased afer corroson naes. As nernal pressure reaches o he ensle srengh of concree cracks are generaed. Based on he concep of fracure mechancs and hck-wall cylnder L e al. (3) [6] formulaed he crack wdh generaon model. w c 4d s bf b E ef v c a a 1 1 v c b (4) where w c s he crack wdh (mm), v c s he posson s rao of concree, α s he sffness reducon facor whch can be deermned from L e al (6) [7], f s he ensle srengh of concree (MPa) aken as 1% of f c ', E ef s effecve modulus of concree, E c s he elasc 1 cr D d b o modulus of concree, a s equal o, b s equal D d b o o x, D b s he seel dameer (mm), d o s hckness of pore band of seel-concree nerface (mm) whch s dependen on hckness of corroson produc rng d s () and can be deermned based on Lu and Weyers (1998) [8]. d s E c W rus 1 rus D b d o rus s (4a) Thckness of corroson produc s relaed o mass generaon of rus produc W rus () (mg/mm) and s saed n leraure of Lu and Weyers (1998). α rus s he coeffcen for rus produc, ρ rus s he corroson produc densy (36 kg/m 3 ) and ρ s s he seel densy (785 kg/m 3 ). 3. RELIABILITY BASED FAILURE Brdge performance s defned n erms of relably ndex (β) and he profle of relably s he varaon of relably ndex wh me β(). Smlar brdges desgned and consruced o he same requremens, for varous reasons, end up wh dfferen relably levels [9]. Ths varaon s nfluenced by dfferen loadng and degradng ressance condons ha can be usefully presened by random varables of durably parameers. The performance lm sae for corroson naon of renforcng seel and crack wdh are shown below. z C lm C x, (5) z w d w c (6) Eqs. 5 and 6 can be generalzed as load capacy model shown n Eq. 7. Performance Srengh Load A B (7) where C lm and w d are he hreshold chlorde concenraon and maxmum allowable crack wdh. Relably ndex can be deermned usng load-capacy model. 1 z ln A ln B (8) V z z ln A ln B V z s he coeffcen of varaon of performance funcon z. All random varables are aken as log-normal dsrbuon. Thus µ lna, µ lnb, σ lna andσ lnb are he mean of srengh, load and sandard devaon of srengh, load respecvely. I s assumed ha corroson wll nae when β()<.8 usng Eqs. 3 and 5 and smlarly crack wll exceed s allowable wdh when β()<.8 usng Eqs. 4 and 5. The me o naon of corroson s referred as and cr s named as me o reach allowable crack. Thus, he sudy repors he falure me as he summaon of boh he mes ndcaed above. f cr (9) where f s he me o falure. The performance of deerorang srucure s characerzed by probably of falure or damage over he nerval [, T] as shown n Eq. 1. P f (1) where P f () s he probably of falure of srucure whch s fxed a 1.% corresponds o β() value and φ s he sandard normal cumulave dsrbuon funcon. 4. RANDOM VARIABLES Table 1 presens he cases used n hs sudy. Cover deph, hydraulc permeably and degree of sauraon are consdered as he man durably

3 parameers vared accordng o Table 1. Varaon of permeably s mananed accordng o prevous leraure [1]. The mporance of curng me can be undersood by varyng he hydraulc permeably of cover concree. Table 1 Case Defnon Case Mean COV Cover deph, x (cm) 4, 5, 6.1 Hydraulc Permeably, k 1e -9, 1e -11, 1e -1.1 (m/s) Sauraon Degree, S (%) 8, 9, 1.1 Table Random Varables Varables Mean COV References C o (kg/m 3 ) 9.1 C lm 1..1 Enrgh and Frangopol, 1999 (kg/m 3 ) w d (mm)..1 f ' c (MPa) 35. Nowak e al φ cr JSCE (5-3) v c Lu & Weyers, 1998 d o (μm) Lu & Weyers, 1998 D b (mm) 1. α rus.57 Lu & Weyers, 1998 All he followng calculaons are based on he npu random varables shown n Table. 5. LIFE CYCLE COST ESTIMATION LCC plays key role n mananng he nfrasrucure and provdes necessary nformaon o he manager or owner. In hs sudy LCC s compued n he followng way. LCC T ( AgngCos DelayCos ReparCos) The hree erms n he rgh hand sde were assumed as explaned by he followng secons. 5.1 Agng Cos Ths s he cos carred by he owner due o regular manenance operaon. Agng cos s assumed o be proporonal o he falure probably, as boh of hem ncrease wh he ncrease of age of he nfrasrucure. f... u Agng Cos Inal Cos.5 P f... u 1 Agng Cos Inal Cos.5 P (11) (1) I s assumed ha 5% of nal consrucon cos wll be expended for manenance. P(f) s he probably of falure a yrs., number of repar s subscrp, s he h repar, u s he decson for repar, u= means no repar and u=1 represens do repar. 5. Delay Cos Ths s he par of expendure carred by he road user for exra fuel consumpon and delay due o congeson a he me of repar for paral or full closure of raffc way. I s assumed o be proporonal of age as raffc volume s ncreased wh he age and capacy of he road f remans consan. Delay Cos... u (13) Delay Cos % raffc delay raffc volume repar me average delay un Cos... u 1 (14) where % raffc delay s he number of vehcle delayed a he repar me and s kep assumed here 1%, raffc volume s he funcon of me, repar me s he me aken by he repar n days, average delay s he % me delay due o repar by car or ruck, un cos s he me value of delay. Delay cos s calculaed from leraure saed n reference [11]. 5.3 Repar Cos Ths cos s provded by he owner due o repar when he performance goes down below he requred. In hs sudy he repar s aken o be happened a relably or sae of srucure goes below 8% of nal. Repar cos s modeled n wo dfferen alernaves accordng o level of mprovemen of performance by repar Alernave 1 The schemac naure s shown below n Fg. 1. x Repar Cos Repar Cos Fxed Cos x 1 Tme x 1 Funcon of Sae Fg. 1: Concep of Reparng cos for alernave 1 Repar Cos... u un Cos area P f... u 1 x 1 (15) RSL Repar (16)

4 where un cos s he cos of repar for un area, P f s he falure probably jus before repar, 1 x s he change of sae done by repar a me, RSL s he resdual servce lfe n years, Repar s he lfe me of repar maeral. I s assumed ha he performance wll be mproved up o x ha wll mee nal level of performance Alernave Repar cos s calculaed wh some dfference based on he followng equaons. Repar Cos Repar Cos Repar Cos Fxed Cos... u un Cos area P x x x f f f... u 1 Tme Tme x k 1 x k RSL End of Lfe (17) RSL Repar Fg. : Concep of Reparng cos for alernave (18) Above Fg. s he schemac represenaon of he alernave. I s assumed here ha he mprovemen done by repar wll no always be up o nal level. Change of sae x s mulpled by k named as mprovemen facor, whch s equal o RSL, where RSL s he resdual f servce lfe and f s he me o frs falure. In hs alernave he manager s src o repar he srucure once n whole servce lfe. 5.4 Repar Mehods To nvesgae he effec of dfferen repar mehods on LCC, 5 ypes of repar mehods from references [1] and [13] are ncluded n he calculaon as n Table EFFECT OF REPAIR METHODS ON LCC The cos of reparng ncluded n LCC compuaon s accordng o Table 3. For boh alernaves lower bound of degradng sae s 8% of nal bu upper bound s same as nal for alernave 1 bu depends on resdual servce lfe for alernave sraeges. Fgs. 3 and 4 show sae dynamcs and cumulave cos over enre servce lfe for alernave 1. The repar akes place more han 1 me n hs case and cos s compared among no repar and repar wh dfferen mehods. Table 3 Cos of Reparng Caegory RM1 RM Types Cahodc Proecon (Mouned Conducve Polymer w/ concree overlay) Cahodc Proecon (Tanum mesh w/ shocree) Fxed Cos ($) Varable Cos ($/m ) Lfe me (yrs.) RM3 Pachng RM4 RM5 Relably or Sae (x) Overlay (Low slump dense concree) Overlay (Ho mx asphalc concree wh a membrane) Case 1 A Servce Lfe (yrs.) No Repar Repared Fg. 3: Effec of reparng on Sae dynamcs

5 Relably or Sae (x) LCC ($) k=1e-1 (Wk) Lfe Tme (yrs.) No Repar RM1 RM RM3 RM4 RM5 Fg. 4: Effec of repar mehods on LCC Case 1 A Servce Lfe (yrs.) varable cos lower han mehod 4. Toal Cos ($) k=1e-1 (Wk) RM1 RM RM3 RM4 RM5 Repar Mehods Alernae 1 Alernae Fg. 7: Effec of repar sraeges on oal cos for maxmum permeably Toal Cos ($) x=4 (Wx) RM1 RM RM3 RM4 RM5 Repa r Me hods No Repar Repared Alernae 1 Alernae Fg. 5: Effec of reparng on Sae dynamcs k=1e-1 (Wk) Fg. 8: Effec of repar sraeges on oal cos for mnmum cover k=1e-13, x=6 (Bk,Bx) LCC ($) Lfe Tme (yrs.) Toal Cos ($) RM1 RM RM3 RM4 RM5 Repar Mehods Alernae 1 Alernae No Repar RM1 RM RM3 RM4 RM5 Fg. 6: Effec of repar mehods on LCC Fg. 9: Effec of repar sraeges on oal cos for mnmum permeably, maxmum cover Fgs. 5 and 6 show sae dynamcs and cumulave cos for alernave. The sae s mproved greaer han ha of nal by 1 me reparng n whole servce lfe. Fgs. 3 o 6 descrbe he case of bes cover (6 cm.), Fully sauraed (1%) and wors permeably (1e-9). All 5 ypes of repar mehods and repar alernaves are consdered n calculang oal cos ha s shown n Fgs. 7, 8 and 9. These fgures explan hree exreme cases based on durably parameers. In all cases repar mehod 3 shows hghes cos due o hghes varable cos of reparng. Repar mehod 4 has lowes cos due o low varable cos and longer servce lfe compared o mehod 5 havng 7. EFFECT OF REPAIR ALTERNATIVES ON LCC Fgs. 7 and 8 show ha he cos s lower for alernave han ha of alernave1. bu oppose scenaro s found n Fg. 9. Due o change of durably parameers he me o falure and resdual servce lfe are changed. Ths s facor ha affecs he cos of alernaves. Fg. 1 s ploed for oal cos wh 7 durably cases as n Table 1. For each case and alernave, oal cos s aken as he average of 5 ypes of repar mehods o exclude he effec of repar mehods. I can be seen ha for parcular 6 durably cases he oal cos s less for

6 alernave 1 han ha of alernave. Alernave has lower cos for res of he cases. Toal cos ($) The rao beween resdual servce lfe and falure me s ploed In Fg. 11 agans each case. The 6 cases marked by green crcle havng larger cover deph and lower permeably where falure come laer han md of lfe span. Ths means f he falure comes afer mddle of servce lfe of he srucure, s beer o adop alernave 1 as repar sraegy else alernave should be chosen. 8. CONCLUSIONS Case No. Alernae 1 Alernae Fg. 1: Effec of repar alernaves on oal cos RSL/f Case No. Fg. 11: Improvemen facor ( RSL / f ) for dfferen cases The compuaon framework leads o he followng conclusons. (1) RM3 coss hghes o he owner due o maxmum varable cos of reparng. () RM4 coss lowes due o low varable cos and greaer lfe me of reparng as well. (3) One me reparng wh he mprovemen of performance greaer han ha of nal level s preferable when he falure comes before mddle of age of servce lfe. (4) Reparng wh he mprovemen up o nal level of performance s suable when he falure comes afer mddle of age of servce lfe. ACKNOWLEDGEMENT I would lke o express my profound graude o Dr. Toshharu KISHI, professor, IIS, The Unversy of Tokyo, who s currenly my supervsor n docoral course. REFERENCES [1] Ksh, T., A Necessy of Fnal Inspecon on Acqured Qualy of Surface Concree o Ensure he Effecveness of Durably Performance Desgn, SSMS 9 [] Freeze, R. A. and Cherry, J. A., Groundwaer, Prence-Hall, Inc. New Jersey, 1979 [3] Bear, J., Dynamcs of Flud n Porous Meda, Dover Publcaons, Inc. New York [4] Takeda, N., Sogo, S., Sakoda, S., Idemsu, T., An Emprcal Sudy on Predcon of Chlorde Ions no Concree and Corroson of Renforcng Bars n Varous Marne Envronmens, Concree Lbrary of JSCE, No. 34, pp , December 1999 [5] Manga, P. S., and Molloy, B. T., Predcon of Long Term Chlorde Concenraon n Concree, Maerals and Srucures, vol. 7, pp , 1994 [6] L, C. Q., Lfe Cycle Modelng of Corroson Affeced Concree Srucures-Propagaon, Journal of Srucural Engneerng, ASCE, 19[6], , 3 [7] L, C. Q., Melchers, R. E. and Zheng, J. J., Analycal Model for Corroson-Induced Crack Wdh n Renforced Concree Srucures, ACI Srucural Journal, vol. 11, No. 4, pp , 6 [8] Lu, Y., Weyers, R. E., Modellng he Tme-o-Corroson Crackng n Chlorde Conamnaed Renforced Concree Srucures, ACI Maerals Journal, 95[6], , 1998 [9] Das, P. C., Prorzaon of Brdge Manenance Needs, Case Sudes n Opmal Desgn and Manenance Plannng of Cvl Infrasrucure Sysems, D. M. Frangopol, ed., ASCE, Reson, Vrgna, 6-44, 1999 [1] Hearn, N., Dewler, R. J., Sframel, C., Waer Permeably and Mcrosrucure of Three Old Concrees, Cemen and Concree Research, vol. 4, No. 4, pp , 1994 [11] NCHRP 1-43, Brdge Lfe Cycle Cos Analyss, Gudance Manual, Par II [1] Sraegc Hghway Research Program (1993-3), Naonal Research Councl, Cahodc Proecon of Concree Brdges, SHRP-S-37, USA [13] Sraegc Hghway Research Program (1993), Naonal Research Councl, Concree Brdge Proecon, Repar, and Rehablaon Relave o Renforcemen Corroson, A Mehods Applcaon Manual, SHRP-S-36, Washngon