1. Background. Key Words: Pavement Stretches Prioritization, Pavement Distress Parameters, Priority Index FMCDM, Fuzzy Logic

Transcription

1 Prortzaton of Pavmnt Strtchs usng Fuzzy MCDM pproach - Cas Study Sandra..K, Vnayaka Rao.V.R, Raju. K.S, Sarkar..K Cvl Engnrng Group, Brla Insttut of Tchnology and Scnc (BITS) Plan, Rajasthan, Inda Emal : aksandra@bts-plan.ac.n Synopss: Effctv pavmnt managmnt rqurs th prortzaton of th road strtchs for logcal dsbursmnt of th funds avalabl toards mantnanc of th pavmnt. Svral mthods hav bn dvlopd and mplmntd toards ths goal. Hovr, th uncrtanty nvolvd th som of th paramtrs has not bn addrssd adquatly n most of th orks. On such paramtr has bn dntfd as th svrty of dstrss hch s dffcult to assss accuratly. Hnc a Fuzzy Mult Crtra Dcson Makng (FMCDM) approach has bn proposd n ths papr. For dmonstraton of th approach, pavmnt dstrsss th rspct to thr xtnt and svrty hav bn collctd ovr a numbr of strtchs. In addton, an xprt opnon survy has bn carrd out to quantfy th nflunc of ths paramtrs on th functonal condton of th pavmnt. Prorty Indx (PI) has bn orkd out, basd on hch th rankng of th strtchs has bn arrvd at. Ky Words: Pavmnt Strtchs Prortzaton, Pavmnt Dstrss Paramtrs, Prorty Indx FMCDM, Fuzzy ogc. Background Propr upkp of th xstng pavmnts s ssntal n addton to th dvlopmnt of n hghay and road lnks for th conomcal groth of any country. Inadquat and napproprat mantnanc polcs adoptd by svral countrs s rsultng n havy fnancal loss n th form of vr ncrasng Road Usr Costs (RUC) and causs dscomfort to th road usrs. Ths problm multpls tslf svral folds th th ncrasng road lngth. In a dvlopng country lk Inda, th funds bng lmtd for th mantnanc of th xstng pavmnt, t s mportant to utlz th mony n th most approprat mannr. holsom pavmnt managmnt approach at both ntork and projct lvls ll dfntly rsult n optmal soluton for road mantnanc. Pavmnt Managmnt Systm (PMS) s an dal tool n ths knd of stuaton and offrs a mthodcal ay of upkpng th road ntork n ts bst possbl srvcablty lvl. In any PMS, prortzaton plays a major rol spcally hn th funds avalabl for road mantnanc ar lmtd [Ramadhan t al. ()]. Svral rsarchrs hav orkd n ths drcton to dvlop prorty ranks for th avalabl ntork of roads. Hass t al. (), FHW () and NCHRP () hav dscussd n dtal, dffrnt rankng and optmzaton mthods. Rddy & Vraragavan (00) hav proposd a Prorty Indx (PI) as a functon of Pavmnt Dstrss Indx (PDI) and prortzaton factor for rankng th road ntork. Chn t al. () and Sharaf () hav dmonstratd th us of Compost Indx (CI) mthod for prortzaton and ndcatd that ths tchnqu has yldd optmal solutons for th cas studs consdrd. Hovr, n ths studs, th xtnt and svrty of falurs ar consdrd smultanously n quantfabl trms nspt of th fact that th magntud of svrty of dstrss has unavodabl uncrtanty. Golab & Prra (00) hav usd optmzaton procss to ork out th solutons for prortzaton of pavmnt sctons basd on road condton, traffc and nvronmntal charactrstcs. NCHRP (), Brotn (), Golab & Prra (00) hav dscussd th applcablty of varous optmzaton tools such as nar Programmng, Intgr Programmng, Markov Dcson nalyss, Dynamc Programmng tc. for ntork prortzaton. Brotn () has ndcatd that th us of optmzaton tool alon ll not b abl to solv th problm n a holsom mannr snc ths tools tnd to achv th ntork goals hl falng from th pont of v of nsurng optmal tratmnt at a gvn pont of tm. In such uncrtan stuatons, Fuzzy Mult-Crtra Dcson Makng (FMCDM) approach provds an dal opton and as such t has bn trd and tstd by numbr of rsarchrs for rakng altrnatvs for dffrnt stuatons [Bandara & Gunaratn (00), Chn-Tung Chn (00), Sanja & Radvoj (00), M-Fang Chn t al.(00), Prakash (00), Wang & Fnton]. Bandara & Gunaratn (00) hav usd fuzzy approach for prortzaton and hav ncludd both svrty and xtnt of pavmnt falur n th ovrall procss. Hovr, fuzzy approach has to b utlzd only hn uncrtanty s prdomnant. In othr ords, Corrspondng uthor

2 hn partcular paramtr s quantfabl th far dgr of accuracy, ths approach nd not b usd. It s n ths drcton that th prsnt ork has bn carrd out th fuzzy logc bng appld to only thos paramtrs hch ar prdomnantly uncrtan n natur. Most usually, th polcs rgardng th mantnanc of roads ar takn th rspct to th functonal condton of road as t drctly affcts th RUC. Hnc, Dffrnt functonal dstrss paramtrs ar collctd th rspct to both svrty and xtnt of falur. Snc t s possbl to masur th xtnt of falur th hgh accuracy, ths paramtr has bn proposd as a drct paramtr n th prortzaton procss. s such, thr s an nbult ambguty hl assssng th svrty of th dstrss. Hnc th Fuzzy approach has bn suggstd to assss th svrty. Th broad objctvs of ths ork ar mntond blo. To conduct xprt opnon survy for assssng th lvl of nflunc of slctd pavmnt dtroraton paramtrs on th functonal condton of th pavmnt. To collct th dffrnt dstrsss nfluncng th functonal condton of pavmnt on slctd road strtchs. Prortzng th road pavmnt sctons usng Fuzzy Mult Crtra Dcson Makng FMCDM approach. Data Collcton Prmary data has bn collctd through fld nvstgatons as ll as xprt opnon survys. Th opnon of slctd xprts from all ovr Inda has bn sought to ascrtan th nflunc of dffrnt dstrss paramtrs on th functonal condton of th pavmnt. Th dstrsss consdrd ar crackng, pothols, ruttng, patchng, ravlng and dg falur th rspct to thr svrty lvls namly lo, mdum and hgh. qustonnar as prpard and snt to slctd xprts all ovr Inda for ths purpos. In addton, thy r also gvn photographc cus and clus th a v to rduc th possblty of varablty and bas amongst thmslvs. Furthr. thy r askd to ndcat thr prfrncs rgardng th nflunc of svrty of varous dstrss paramtrs n trms of lngustc varabls such as Nglgbl (N), o (), Modrat (M), Hgh (H) and Vry Hgh (VH) as t ould b dffcult to xprss th ghts n quantfabl trms. Th rsponss gvn by a group of xprts hav bn summarzd and prsntd n Tabl. Tabl : Summry of Exprts Opnons Exprts Crtra E E E E E E E E E E0 E E E E E C N N N N N N N N N N CM M M M N M M M CH H H M H M M VH M H H M H M P M M N M M M M M M M PM H H M H H H H H H H M M M H PH VH VH H VH H VH VH VH VH VH VH VH H H VH R M N N M N N N N N RM H M M N H M M M N RH VH H H M M VH VH H M H M H M H M P N N N M N N M M N N PM M M M H M M H M M M PH H H H M M VH M VH H VH M M M H H RU M N N N N N N RUM H M M M M M M M M M RUH VH VH M M VH H M M H H H H M H H E M N N N N N N N EM H H M M M H M M N EH VH VH H H VH M H VH H M M H H H N EGEND C=o lvl crackng CM=Mdum lvl crackng CH =Hgh lvl crackng P=o lvl pothols PM=Mdum lvl pothols PH =Hgh lvl pothols

3 R=o lvl ravlng RM=Mdum lvl ravlng RH=Hgh lvl ravlng P=o lvl patchng PM=Mdum lvl patchng PH=Hgh lvl patchng RU=o lvl ruttng RUM=Mdum lvl ruttng RUH=Hgh lvl ruttng E=o lvl dg falur EM=Mdum lvl dg falur EH=Hgh lvl dg falur N= Nglgbl = o M=Mdum H = Hgh VH= Vry Hgh Not: Dfntons rgardng th svrty of dffrnt dstrsss hav bn dtald n PPENDIX For collctng pavmnt condton data, four dffrnt strtchs domnatd by dffrnt typs of functonal falurs hav bn chosn n th stat of Rajasthan, Inda for a total lngth of km. Car has bn takn to s that ths strtchs ar rprsntng dffrnt functonal classs of hghays vz. Natonal Hghays (NH), Stat Hghays (SH) and Major Dstrct Roads (MDR). tam of numrators hav bn ngagd n collctng th svrty and xtnt of all th falurs mntond n th Exprt Opnon Survy proforma. Each km lngth of road as dvdd nto 0 strtchs of 0m long. For mantanng unformty n th data, all th numrators r trand n th fld and also r suppld th photographc cus and clus. Dstrss paramtrs such as crackng, pothols, ravlng, patchng, dg falur r masurd n %of total ara of pavmnt strtch and ruttng as masurd n mllmtrs. To dmonstrat th proposd mthodology of prortzaton a typcal strtch of km lngth has bn consdrd for furthr consdraton.. Pavmnt Prortzaton through Fuzzy ogc. Fuzzy Numbrs Th fuzzy st thory as proposd by Zadh,.. n, to rprsnt th uncrtanty nvolvd n any stuaton n lngustc trms. fuzzy numbr s a fuzzy st, and ts mmbrshp functon s µ ( x) : R [0, ] [Dubos & Prad (); You-Gng Hsu t al. (00); M-Fang Chn t al.(00)], hr x rprsnts th crtra. lnar mmbrshp functon s th dly usd and th corrspondng fuzzy numbrs ar calld Trangular Fuzzy Numbrs (TFNs). TFNs ar th spcal class of fuzzy numbrs hos mmbrshp s dfnd by thr ral numbrs (l, m, n).. µ ( x) = (l, m, n)), hch s pctorally shon n Fg.. Th TFNs can b xprssd as follos. ( x l) ; ( m l) ( n x) ( x) = ; ( n m) 0; µ µ ( x) l x m; m x n; Othrs; ().0. Opratons on Fuzzy numbrs Whn ( l, m, n) B = ( p, t al.(00), Prakash (00) ]. = and q, r) 0 l m n Fg : Mmbrshp Functon for th Trangular Fuzzy Numbrs to TFNs, th gnral opratons ar as follos [ M-Fang Chn x

4 ddton of to fuzzy numbr ( l, m, n) ( p, q, r) = ( l+ p, m+ q, n+ r) Subtracton of to fuzzy numbrs ( l, m, n) Θ ( p, q, r) = ( l r, m q, n p) Multplcaton of any ral numbr k and a fuzzy numbr k ( l, m, n) = ( kl, km, kn). Prortzaton Procss In th prsnt study, pavmnt scton altrnatvs hav bn prortzd basd on th mthods proposd by varous rsarchrs [Bandara & Gunaratn (00), Chn-Tung Chn (00), Huang ()]. Prortzaton procss s xpland n th follong stags. Stag : Data collctd n th fld s bng normalzd n th scal of 0 to 00 th rspct to th maxmum valu n th srs through a smpl normalzaton as shon blo. Normalzd Data Pont = (Data Pont) x 00 / (Mod of th Data Srs) () summary of normalzaton data s prsntd n Tabl. Furthr, ths valus ar bng arrangd nto 0 groups th a unform ntrval of 0 and ratngs hav bn gvn, hch s prsntd n Tabl. Tabl : Normalzd Pavmnt Condton data on Slctd Strtch Strtch Crtra No. C CM CH P PM PH R RM RH P PM PH RU RUM RUH E EM EH Tabl : Ratngs for th Normalzd Valus Normalzd Valu Ratng 0 Ths ratng valus ar bng arrangd n a matrx form, namd as Ratng Matrx ( ) N M th ach ro rprsntng altrnatv (,., N ) and ach column rprsntng crtra. Th Ratng Matrx has bn prsntd n Tabl. Stag : Th lngustc varabls utlzd for xprssng th svrty of dffrnt dstrsss hav bn xprssd as TFNs. TFNs assgnd for varous lngustc varabls ar shon n Tabl. R

5 Tabl : Ratng Matrx C CM CH P PM PH R RM RH P PM PH RU RUM RUH E EM EH [ ] R M N = Tabl : Trangular Fuzzy Numbrs (TFNs) for ngustc Varabls ngustc Varabl TFN Nglgbl (0, 0, 0.) o (0, 0., 0.) Mdum (0., 0., 0.) Hgh (0., 0., ) Vry Hgh (0.,, ) Stag : Exprts opnon avalabl for th varous dstrss svrts n th form of lngustc varabl as prsntd n Tabl ar bng convrtd nto fuzzy numbrs. To normalz dffrncs xstng n xprt opnon, smpl avrag of fuzzy numbrs for all th lngustc varabls has bn calculatd and th corrspondng ghts ar bng orkd out and prsntd n th Tabl. Fuzzy ghts for all crtra can b xprssd n th form of follong ro matrx. ]...,, [ M W = () Whr, M...,, ar th fuzzy ghts for all crtra xprssd n Trangular Fuzzy Numbrs. ),, ( j j j j = j=,,.m Tabl : Fuzzy ghts for varous dstrss paramtrs Crtra Fuzzy Wght C (0, 0.0, 0.) CM (0.0, 0., 0.) CH (0.0, 0.0, 0.) P (0.0, 0., 0.) PM (0., 0.0, 0.) PH (0., 0.,.000) R (0.00, 0.0, 0.0)

6 RM (0., 0., 0) RH (0.0, 0.0, 0.0) P (0.00, 0., 0.) PM (0., 0.0, 0.0) PH (0.0, 0.0, 0.0) RU (, 0.0, 0.) RUM (0., 0., 0.) RUH (0.0, 0., 0) E (, 0.00, 0.) EM (0.0, 0., 0.0) EH (0., 0., 0.0) Stag : Fuzzy valuaton valu p ) s thn calculatd by multplyng th ratng matrx th th ght ( matrx and summd up for all th strtchs, hch ar prsntd n Tabl. Ths procss s mathmatcally xprssd as follos. P M = R j, j= Tabl : Fuzzy Evaluaton Valus for all th strtchs =,,.N and j=,,.m () Stag : To stablsh th rlatv prfrnc of all th strtchs, dffrnc btn all combnatons of th fuzzy valus has bn computd. Ths s mathmatcally xprssd as F ) = ( p p ) = to N j= to N and j () ( j Strtch No. Fuzzy Evaluaton valu p (.,.0, 0.) p (.,.,.0) p (.,.,.) p (.0,.,.) p (.,.,.) p (.,.,.) p (.,., ) p (.,.,.) p (., 0.,.) p 0 (.,.,.0) p (.,.,.) p (.,.,.0) p (0.,.,.) p (.,.,.) p (.,.,.) p (.,.,.) p (.,.,.) p (0.,.,.0) p (.,.,.0) p (.,.,.) 0

7 It s to b notd that p and j p ar th Trangular Fuzzy Numbrs hnc ( p ) s also Trangular p j Fuzzy Numbr. sampl of ths valus ar summarzd and prsntd blo for rady rfrnc p p p (-.,.,.) p p (.,.,.) p (-., 0.,.) p : : p 0 (-.,.,.) Stag : Th fuzzy prfrnc rlaton matrx [E] has bn dvlopd, to kno th dgr of prfrnc strtch ovr strtch. j E = N N Whr, s th ral numbr ndcats th dgr of prfrnc btn th rspctv th and j th pavmnt strtchs. It has bn calculatd usng postv ( + ) p. dffrnc btn to fuzzy valus ( ) p j + S = + S + S ( S S = Total ara of ( p ) + + Whr, ) N N NN () S and ngatvs aras ( ) () p j S of Postv and ngatv aras hav bn computd usng th mmbrshp functon [ µ ( x)] of th p p j. n xampl of computaton of F = ( p ) = (., 0.,.) ( ) p µ ( x) s shon n Fg.. For xampl, f th F.0 Postv ra 0. Ngatv ra x Fg. : Computaton of Total ara form th Fg =. Postv ara =. Ngatv ara= 0. = (.)/. = 0.

8 Hr = 0. and + j =.0. If > 0. th strtch s to b gvn prorty ovr strtch j and vc vrsa. Computd valus of for all th combnatons ar summarzd and prsntd n Tabl. Tabl : Fuzzy Prfrnc Rlaton Matrx [ ] E N N = Stag : Prorty Indx (PI) for all th pavmnt strtchs ar computd from th fuzzy prfrnc rlaton matrx usng th follong mathmatcal form. n = ( PI ) ( 0.) = to N () j= Basd on th PI, all th strtchs hav bn rankd and prsntd n Tabl. Th prortzaton procss, as xpland n th abov stags s qut complx and cumbrsom du to a larg numbr of strtchs and crtron. Hnc, a cod has bn dvlopd n MTB [(.mathorks.com)] and bng usd n th prsnt study. From Tabl t can b notd that scton no. th prorty ndx of. s to b gvn th frst prorty and scton no. th prorty ndx of -. s to b gvn last prorty. Tabl : Rankng of th Pavmnt Strtchs Strtch No. Prorty Indx Rank

9 Conclusons Th follong conclusons hav bn dran from th prsnt ork. Th proposd Fuzzy Mult Crtra Dcson Makng approach s dmonstratd th th data collctd from th fld and xprt opnon and ths approach can b xtndd for prortzaton of any gvn road ntork. Th dvlopd softar ntrfac s xpctd to hlp n stablshng th prorts th as and thr s no lmtaton as far as th numbr of roads n th gvn ntork s concrnd. Th road lnk hch has th hghst Prorty Indx (PI) ll b gvn top prorty and vc vrsa. Th ork can b xtndd by ncludng mor numbr of varabls and th sam phlosophy can b xtndd for th addtonal varabls consdrd. mor dtald Dstrss dntfcaton manual ncludng clus and photographc cus, xclusvly dvlopd for Indan condtons, ll mprov th qualty of th data as t hlps n rducng th varablty / bas sn amongst dffrnt xprts. ppndx : Dscrpton of Pavmnt Dstrss Svrty vls S.No Typ of Dstrss Crackng Pothols Ravllng Patchng Ruttng Edg Falur Svrty Dscrpton o Wdth of th crackng s lss than mm Mdum Wdth of th crackng s gratr than mm and lss than mm Hgh Wdth of th crackng s gratr than mm o Dpth of th pothol s lss than mm Mdum Dpth of th pothol s mor than mm and lss than 0 mm Hgh Dpth of th pothol s mor than 0 mm o Th aggrgat or bndr has startd to ar aay but has not progrssd sgnfcantly. Th pavmnt appars only slghtly agd and s lghtly rough. Mdum Th aggrgat or bndr has orn aay and th surfac txtur s modratly rough and pttd. oos partcls may b prsnt and fn aggrgat s partally mssng. Hgh Th aggrgat and/or bndr hav orn aay sgnfcantly, and th surfac txtur s dply pttd and vry rough. Fn aggrgat s ssntally mssng from th surfac, and pttng xtnds to a dpth approachng on half (or mor) of th coars aggrgat sz. o Patch has lo svrty dstrss of any typ ncludng ruttng < mm; pumpng s not vdnt Mdum Patch has modrat svrty dstrss of any typ or ruttng from mm to mm; pumpng s not vdnt. Hgh Patch has hgh svrty dstrss of any typ ncludng ruttng > mm, or th patch has addtonal dffrnt patch matral thn t; pumpng may b vdnt. o Barly notcabl, dpth lss than mm Mdum Radly notcabl, dpth mor than mm lss than mm Hgh Dfnt ffct upon vhcl control, dpth gratr than mm o pparanc of dg stp th a f ntal cracks on th btumnous surfac along th dg porton of th carragay

10 Mdum Hgh pparanc of dg stp th a numbr of ntrconnctd hgh ntnsty cracks on th btumnous surfac along th dg porton of th carragay Prmannt loss of part of carragay and pothol formaton along th dg porton Rfrncs ) Bandara, N & Gunaratn, M; Currnt and Futur Pavmnt Mantnanc Prortzaton Basd on Rapd Vsual Condton Evaluaton, Journal of Transportaton Engnrng, Vol., No., March/prl (00). ) Brotn, M; ocal agncy pavmnt Managmnt applcaton gud, Th Northst Tchnology Transfr Cntr, Washngton Stat Dpartmnt of Transportaton, Olympa, W, (). ) Chn, X., Wssmann, J., Dossy, T. and Hudson, W. R.; URMS: a graphcal urban roaday managmnt systm at ntork lvl, Transportaton Rsarch Rcord, Transportaton Rsarch Board, Washngton, DC, pp. 0-, (). ) Chn-Tung Chn; fuzzy approach to slct th locaton of th dstrbuton cntr, Fuzzy Sts and Systms, pp. -, (00). ) Dubos, D & Prad, H; Opratons on Fuzzy Numbrs, Intrnatonal Journal of systm scnc, (), -, (). ) FHW; Pavmnt and Road Surfac Managmnt for ocal gncs Cours Notbook, prpard by Txas Transportaton Insttut Txas &M Unvrsty for th Pavmnt Dvson of th Fdral Hghay dmnstraton, Washngton, D.C (). ) Golab, K & Prra, P; Innovatv Pavmnt Managmnt and Plannng Systm for Road Ntork of Portugal, journal of Infrastructur Systms, SCE, Jun 00, pp. -0 (00). ) Haas, R; Hudson, W. R.; and Zansk, J.; Modrn Pavmnt Managmnt, Krgr Publshng Co., Malablar, Florda, (). ) Huang, C. C; study on th fuzzy rankng and ts applcaton on th dcson support systms, Ph.D. dssrtaton, Tamkang Unv., Taan, R.O.C.,. 0) M-Fang Chn; Go-Hshung Tzng; Chrng G. Dng; Fuzzy MCDM pproach Slct Srvc Provdr Th IEEE Intrnatonal Confrnc on Fuzzy Systms, (00). ) NCHRP Synthss ; Pavmnt Managmnt Mthodologs to Slct Projcts and Rcommnd Prsrvaton Tratmnts, Natonal Coopratv Hghay Rsarch Program, Transportaton Rsarch Board, Washngton, D.C (). ) Prakash, T.N; and Sutablty nalyss for grcultural Crops: Fuzzy Multcrttra Dcson Makng pproach, Mastr of Scnc thss submttd to Intrnatonal Insttut for Go-Informaton Scnc and Earth obsrvaton, Enschd, Th Nthrlands, Dcmbr, (00). ) Ramadhan, R.H; l-bdul Wahhab & Duffuaa, S.O ; Th us of an analytcal hrarchy procss n pavmnt mantnanc prorty rankng Journal of Qualty n Mantnanc Engnrng, Vol., No., pp - (). ) Rddy, B.B & Vraragavan (00); Prorty Rankng modl for managng flxbl pavmnts at ntork lvl Tchncal Papr Publshd n nd annual ssson of Indan Roads Congrss ( IRC), th- th January, Koch, Inda, (00). ) Sanja, P & Radvoj, P; n fuzzy mult-crtra mthodology for rankng altrnatvs, Intrnatonal Transactons n Opratonal Rsarch, Rs., pp. -, (00). ) Sharaf, E.; Rankng vrsus smpl optmzaton n sttng pavmnt mantnanc prorts: a cas study from Egypt, Transportaton Rsarch Rcord, Transportaton Rsarch Board, Washngton DC, pp. -, (). ) Wang. W &Fnton. N; Rsk and Confdnc nalyss for Fuzzy Multcrtra Dcson Makng, Rsk nalyss and Dcson Rsarch Group, Dpartmnt of Computr Scnc, Qun Mary Unvrsty of ondon, Ml End Road, ondon. ).mathorks.com ) You-Gng Hsu; Go-Hshng Tzng & Josph Z.shyu; Fuzzy Multpl Crtra Slcton of Govrnmnt-sponsord frontr tchnology R&D projcts, R&D Managmnt, Blackll Publshng td.,, (00). 0) Zadh,..; Fuzzy Sts Informaton and Control, Vol.,pp.-, ().