ESTIMATING VEHICLE ROADSIDE ENCROACHMENT FREQUENCY USING ACCIDENT PREDICTION MODELS

Transcription

1 ESTMATNG VEHCLE ROADSDE ENCROACHMENT FREQUENCY USNG ACCDENT PREDCTON MODELS ShawPin Miaou Cntr for Transportation Analysis, Enrgy Division Oak Ridg National Laboratory P.O.Box 28,MS 6366, Building 55A Oak Ridg, TN 37831, USA Phon: (423) ; Fax: (423) ; July 1996 Submittd for rviw for PRESENTATON in TRB 1997 Annual Mting and PUBLCATON in TransDortab*onRsarch Rcord Prpard by th Oak Ridg National Laboratory Oak Ridg, Tnnss managdby LOCKHEED MARTN ENERGY RESEARCH COW. for th U.S. DEPARTMENT OF ENERGY undr contract DEAC596R \

2 DSCLAMER This rport was prpard as an account of work sponsord by an agncy of th Unitd Stats Govrnmnt. Nithr th Unitd Stats Govrnmnt nor any agncy throf, nor any of thir mploys, maks any warranty, xprss or implid, or assums any lgal liability or rsponsibility for th accuracy, compltnss, or usfulnss of any information, apparatus, product, or procss disclosd, or rprsnts that its us would not infring privatly ownd rights. Rfrnc hrin to any spccific commrcial product, procss, or srvic by trad nam, tradmark, manufacturr, or othrwis dos not ncssarily constitut or imply its ndorsmnt, m m mndation, or favoring by th Unitd Stats Govrnmnt or any agncy throf, Th viws and opinions of authors xprssd hrin do not ncssarily stat or rflct thos of th Unitd Stats Govrnmnt or any agncy throf.

3 DSCLAMER Portions of this documnt may b illgibl in lctronic imag products. hags ar producd from th bst avaiiabl original documnt.

4 ESTMATNG VEHCLE ROADSDE ENCROACHMENT FREQUENCES USNG ACCDENT PREDCTON MODELS ShawPin Miaou Cntr for Transportation Analysis, Enrgy Division Oak Ridg National Laboratory P.O.Box 28, MS 6366,Oak Ridg, TN 37831, USA Phon: (423) ,Fax: (423) ; ABSTRACT Th xisting data to support th dvlopmnt of roadsid ncroachmntbasd accidnt modls ar xtrmly limitd and largly outdatd. Undr th sponsorshipof th Fdral Highway Administration and Transportation Rsarch Board, svral roadsid safty projcts hav attmptd to addrss this issu by providing rathr comprhnsiv data collcticjn p l m and conducting pilot data collction fforts. t is clar from th rsults of ths studis that th rquird fild data collction fforts will b xpnsiv. Furthrmor, th validity of any fild collctd ncroachmnt data may b qustionabl bcaus of th tchnical difficulty to distinguish intntional from unintntional ncroachmnts. This papr proposs an altrnativ mthod for stimating th basic roadsid ncroachmnt data without actually fild collcting thm. Th mthod is dvlopd by xploring th probabilistic rlationships btwn a roadsid ncroachmnt vnt and a runoffthroad vnt. With som mild assumptions, th mthod is capabl of providing a wid rang of basic ncroachmnt data from convntional accidnt prdiction modls. To illustrat th concpt and us of such a mthod, som basic ncroachmnt data ar stimatd for rural twolan undividd roads. n addition, th stimatd ncroachmnt data ar compard with th xisting collctd data. Th illustration shows that th mthod dscribd in this papr can b a viabl approach to stimating basic ncroachmnt data without actually collcting thm which can b vry costly. Ky Words: Vhicl Roadsid Encroachmnt, Roadsid Dsign, Accidnt Prdiction Modl

5 Miiou, S.P., July ESTMATNG VEHCLE ROADSDE ENCROACHMENT FREQUENCES USNG ACCDENT PREDCTON MODELS ShawPin Miaou Cntr for Transportation Analysis, Enrgy Division Oak Ridg National Laboratory P.O.Box 28, MS 6366, Oak Ridg, TN 37831, USA Phon: (615) ,Fax: (615) NTRODUCTON Past rsarch on th safty of roadsid nvironmnt has producd mor forgiving roadsid hardwar and improvd roadsid dsign practics [Transportation Rsarch Board, Howvr, th latst national statistics still indicat that about onthird of th fatal traffic crashs ar associatd with vhicls running off th road W S A, For xampl, 1,473 out of 34,928 fatal traffic crashs occurrd in 1992 wr rlatd to collision with roadsid fixd objcts and, in addition, a larg prcntag of th 3,281 fatal rollovr crashs occurrd on sidslops and ditchs. Ths statistics on runoffthroad accidnts (RORA) continu to indicat th nd for mor rsarch to dvlop costffctiv road, drivr, and vhiclrlatd countrmasurs to rduc th frquncy and consquncs of such accidnts [Vinr, 1993; Ray t al., To dvlop costffctiv roadrlatd countrmasurs, on nds to hav a good undrstanding of th rlationship btwn roadsid safty and roadsid dsign. To dat, much of what is known about th roadsid saftydsign rlationships rmains to b ithr qualitativ in natur or dpndnt on subjctiv nginring gusss [Daily, t al., 1994; Ray t al., Rcnt studis hav suggstd that nw and costffctiv analysis approachs and data collction fforts ar ssntial if a mor objctiv basis of such rlationships is to b dvlopd wak and Sicking, 1992; Vinr, 1995; Mak and Bligh, Modls usd in prvious studis to dvlop th rlationships btwn th RORA frquncy, traffic flows, and roadsid hazards, such as mbankmnts, utility pols, trs, luminaris, guardrail, mdian barrirs, hav bn catgorizd as ithr an accidntbasd approach or an ncroachmnt basd approach [Daily, t al., Th first approach uss statistical rgrssion modls to dvlop th rlationships, in which th RORA fiquncy of hitting a particular or a combination of roadsid hazards is th dpndnt variabl, and traffic flows, roadway mainlin dsigns, roadsid dsigns, and othr variabls ar th xplanatory variabl (or covariats). For xampl, in on of th modls dvlopd in Zgr t al. [19871, singl vhicl (SV)RORA fiquncis, including fixdobjct and

6 4 Miabu, S.P., July rollovr accidnts, wr rgrssd ovr avrag annual daily traffic (AADT), lan width, shouldr width, clar roadsid rcovry distanc (CRRD), and trrain typ, whr CRRD is a summary masur of th width of th flat, unobstructd, and smooth ara adjacnt to th outsid dg of th shouldr within which thr is a rasonabl opportunity for th saf rcovry of an outofcontrol vhicl. n anothr study by Zgr t al [1991, RORA frquncis hitting various typs of roadsid fixd objcts such as utility pols, trs, guardrails, wr rgrssd ovr AADT,lan width, and dnsity and latral offst of th objct. Th modls so dvlopd ar typically rfrrd to as accidnt prdiction modls. t should b notd, howvr, that Zgr t al.'s studis hav havily rlid on th us of lognormal rgrssion modls. Mor appropriat accidnt prdiction modls basd on th Poisson and ngativ binomial rgrssion modls hav bn advocatd and widly usd in rcnt yars [.g., Maycock and Hall, 1984; Miaou and Lum, 1993; Miaou, 1994; Mahr and Summrsgill, 1996; Miaou, forthcoming]. Data on roadsid variabls (xcpt shouldr width and shouldr typ) wr, howvr, mostly unavailabl in ths rcnt studis. Th scond approach uss a sris of conditional probabilitis to dscrib th squnc of vnts rsulting in a roadsid accidnt. An xampl squnc of vnts would b: (1) an rrant vhicl lavs th travld way and ncroachs on th shouldr; (2) th location of ncroachmnt is such that th path of travl is dirctd towards a potntially hazardous objct; (3) th hazardous objct is sufficintly clos to th travl lans that control is not rgaind bfor ncountr or collision btwn vhicl and objct; and (4) th collision is sufficintly svr nough to rsult in an accidnt of som lvl of svrity. This typ of modls hav traditionally bn calld roadsid ncroachmnt modls [Glnnon, 1974; Transportation Rsarch Board, 1987; Daily t al., Th ida of th ncroachmntbasd approach was to formulat and stimat ach of ths conditional probability basd on traffic flow thory, gomtry, vhicl dynamics, drivr's bhavior, and probability thory. Th Appndix F of th Transportation Rsarch Board's Spcial Rport 214 (SR214) [1987] provids a good dscription of th ncroachmnt modl and its application on twolan undividd roads. A rcnt rviw of such an approach and its rlationship with th accidntbasd approach is givn in Miaou [forthcoming]. n th last 3 yars, thr has bn a constant ffort attmpting to dvlop and rfin roadsid ncroachmnt modls, including th National Cooprativ Highway Rsarch Program (NCHRP) Rport 77 [1969], NCHFW Rport 148 [1974], and th modl includd in Amrican Association of Stat Highway and Transportation Officials' (AASHTO) Roadsid Dsign Guid [ 19881, known as

7 modls includ Mak and Sicking [19921 and N C W Projct 229 that is currntly bing conductd by Txas Transportation nstitut (TT), Txas A&M Univrsity. Dspit of ths fforts, th ncroachmntbasd approach has bn criticizd as bing full of wishful assumptions and lack of mpirical basis (or supporting data) Daily t al For xampl, on ach road sction, th most basic data rquird by an ncroachmnt modl is th vhicl roadsid ncroachmnt frquncy and th probability disrribution of latral xtnt of ncroachmnts whn ncroachmnt occurs. Th ncroachmnt fiquncy is xpctd to vary from on road sction to anothr, dpnding on roadway class, AADT, lan width, horizontal curvatur, vrtical grad, tc. Whil th probability distribution of latral xtnt of ncroachmnts is xpctd to vary by sidslop and othr roadsid dsign factors. At prsnt, th xisting data for dvloping ncroachmntbasd modls wr largly outdatd [Mak and Sicking, 1992; Daily t al., 1994; Mak and Bligh, n addition, ths data wr collctd on a small numbr of road sctions and for a limitd tim priod in a yar,.g., during wintr or summr months. Th Fdral Highway Administration (FHWA) and Transportation Rsarch Board (TRB) hav bn addrssing th rquirmnts and collction of such data through thir sponsorship of svral roadsid safty projcts. As a rsult, rathr comprhnsiv data collction plans and pilot data collction fforts hav bn rportd in Mak and Sicking [1992], a rcnt intrim rport prpard for th NCHRP Projct wak and Bligh, 19961, and Daily t al. [ A rviw of ths plans and pilot data collction rsults suggsts that th fild data collction ffort of such data will b difficult and xpnsiv. Furthrmor, th validity of any fild collctd ncroachmnt data may b qustionabl bcaus of th tchnical difficulty to distinguish intntional fkom unintntional ncroachmnts. Th purpos of this papr is to propos an altrnativ mthod for stimating th basic roadsid ncroachmnt data without actually fild collcting th data. Th mthod is dvlopd by xploring th probabilistic rlationships btwn a roadsid ncroachmnt vnt and a RORA vnt. With som mild assumptions, th mthod is capabl of providing a wid rang of basic ncroachmnt data fiom convntional accidnt prdiction modls. To illustrat th concpt and us of such a mthod, th basic ncroachmnt data ar stimatd for rural twolan undividd roads. n addition, th stimatd ncroachmnt data ar compard with th xisting collctd data. This papr is organizd as follows. To facilitat th illustration of th proposd mthod, a rural twolan road accidnt prdiction modl, which was dvlopd in Miaou [1996], is first

8 1%. Mhou, S.P., July prsntd in Sction 2. Sinc th thory bhind th accidntbasd prdiction modls hav bn dscribd quit xtnsivly in many rcnt publications [.g., Maycock and Hall, 1984; Miaou and Lum, 1993; Miaou, 1994; Mahr and Summrsgill, 1996; Miaou 19961, th radrs ar rfrrd to ths publications for a rviw of th Poisson and NE3 rgrssionbasd accidnt prdiction modling thoris. Sction 3 dscribs th proposd mthod and its assumptions. Sction 4 illustrats th concpt and us of th proposd mthod by utilizing th accidnt prdiction modl prsntd in Sction 2. Som discussions on th potntial xtnsions of such a mthod is providd in th last sction. n th following discussion, a "roadsid ncroachmnt" is said to occur whn an rrant vhicl crosss th outsid dgs of th travlway and ncroachs on th shouldr, including both insid and outsid shouldrs. Thus, for a twolan undividd road which has no insid shouldr th total numbr of roadsid ncroachmnts includs dparturs of vhicls from narsid and farsid dgs of th travlway in both dirctions. t is also important to not that roadsid ncroachmnts rfr only to "unintntional ncroachmnts." n othr words, th "intntional ncroachmnts" as a rsult of vhicls intntionally drivn outsid of th travl lan on,.g., adjacnt lan (in th sam or opposit dirction), shouldrs, and travrsabl mdians, ar not countd as ncroachmnts. 2. A RUNOFFTHEROAD ACCDENT PREDCTON MODEL Runoffthroad accidnts and roadway data for rural twolan undividd roads from a roadway crosssction dsign data bas [Hummr, 19861, administrd by FHWA and TRl3, wr usd by Miaou [forthcoming] to dvlop an accidnt prdiction modl. On of th important fatur of this particular data bas is that it contains a rathr dtaild dscription of ky dsign lmnts of various roadsid obstacls. Th roadway data usd in this study includ traffic and gomtric dsign data of 596 road sctions in thr Stats: Alabama, Michigan, and Washington. Th total lngth of ths sctions is 1,788 mi (2,861 km).about 5 yars of SV RORA data &om 198 to 1984 wr availabl for analysis. During th 5yar priod, thr wr 4,632 SV rportd to b involvd in R O W on ths road sctions, rgardlss of vhicl and accidnt svrity typ. With th total vhicl mils stimatd to b 7,639 million vhicl mils (14, 514 million vhicl kilomtrs), th ovrall SV RORA rat was.61 SV R O W pr million vhicl mils (.38 SV RORA pr million vhicl

9 5 kilomtrs). Th sam data st has bn usd in Zgr t al. [1987] to valuat th ffct of sidslop on th rat of SV RORA. Dtaild dscription and statistics of ths road sctions can b found in Hummr [1986] and Zgr t al. [1987]. n addition to vhicl mils travld, th covariats considrd for individual road sctions ar prsntd in Tabl 1. Thy includ (1) dummy variabls for Michigan and Washington to captur th ovrall diffrnc in SV RORA rat among Stats, du to diffrncs in omittd variabls such as wathr, socioconomic and gographic variabls, accidnt rporting thrshold, and undrrporting rat; (2) AADT pr lan, usd as a surrogat masur for traffic dnsity; (3) lan width, (4) mdian clar roadsid rcovry distanc, masurd from th right dg of th shouldr, (5) pavd shouldr width, (6) arth, grass, gravl, or stabilizd shouldr width, (7) mdian sidslop; (8) trrain typ,usd as a surrogat masurs for horizontal curvatur and vrtical grad; (9) postd spd limit, (1) numbr of intrsctions pr mil, (1 1) numbr of drivways pr niii, and (12) numbr of bridgs pr mil. Many of ths covariats wr also considrd by Zgr t al. [ Horizontal curvatur and vrtical grad data wr not usd in this xrcis bcaus 147 sctions (about 25%) wr found to hav no curvatur data and 341 sctions (about 57%) did not hav grad information. Th NB rgrssion modl, as dscribd in Miaou [1994] and Miaou [forthcoming], was mployd and th stimatd paramtrs as wll as thir associatd standard dviations and t statistics ar prsntd in Tabl 1, All covariats in th modl hav th xpctd ffcts. Discussions on th choic of covariats and th modl's goodnssoffit can b found in Miaou [forthcoming]. About 62% of th "xplainabl varianc'' wr xplaind by th covariats includd in this modl. t was suggstd that a highr xplanatory powr may b achivd if horizontal curvatur and vrtical grad wr availabl. Not that thr is an ongoing rsarch ffort attmpting to nhanc this modl. Postd spd limit was not found to b significant bcaus of th lack of variation; 53 out of th 596 sctions had a postd spd limit of 55 mph. Although th numbr of intrsctions pr mil had th xpctd ffct, it was not found to b statistically significant (at a 2% a lvl) and was rmovd from th final modl. Major findings fkom th modl can b summarizd as follows: f all considrd variabls hav th sam valus, Michigan has th highst SV RORA rat and Alabama has th lowst rat. Michigan's rat is about 2 prcnt highr than

10 . Midou,S.P., July Washington bcaus of th diffrnc in wathr and socioconomic conditions; whil Alabama is about 34 prcnt lowr than Washington mainly bcaus of th incomplt Alabama accidnt data and diffrncs in wathr and othr factors. AADT pr lan shows a ngativ ffct. Although many xplanations hav bn offrd in on plausibl xplanation is that, all ls bing qual, highr vhicl dnsity th litratur, rsults in highr multiplvhicl ( M V ) accidnt rat and lowr SV accidnt rat. All ls bing qual, incrasing lan width is xpctd to rduc SV RORA rat. Figur 1 givs an illustration of th SV RORA rats for various lan widths and sidslops. n addition, this figur shows th sam rats drivd by Zgr t al. [1987]. t can b sn that th rats from this study ar much highr than thos fiom Zgr t al.'s study. Th main rason is that thr is a fundamntal problm in th mthod usd by Zgr t al. to comput th man rat. This problm is on of ovrlmkilg an important adjustmnt factor prtaining to th us of lognormal distributional assumption, which has bn pointd out in Miaou and Lum [1993]. Th ffct of pavd shouldr width was not found to b significantly diffrnt from th ffct of stabilizd shouldr width. All ls bing qual, incrasing shouldr width by 1 ft is. xpctd to rduc SV RORA rat by about 9%. Stpr sidslop is associatd with highr SV RORA rat. Figur 2 shows th rlativ rats for various sidslop ratios whn compard to th rat of a sidslop of 7:1. This figur also shows that th sam rlativ rats drivd fiom Zgr t al's modl. t can b sn that this study shows lowr rlativ rats than thos from Zgr t al's study. Th tstatistic of th stimatd paramtr in Tabl 1 shows that th sidslop was not as wll dtrmind as othr variabls. On possibl rason is that for ach road sction th 5th prcntil) sidslop masurmnt was usd as th most rprsntativ sidslop, but th actual sidslop may vary considrably within a givn sction [Zgr t al. [1987]. As xpctd, all ls bing th sam, highr numbrs of drivways and bridgs pr mil rsult in highr SV RORA rats as xpctd. n th nxt sction, this modl will b usd to illustrat how an accidnt prdiction modl can b usd to stimat roadsid ncroachmnt frquncy and to driv th probability distribution of latral xtnt of ncroachmnt whn ncroachmnt occurs.

11 . 7 Mibou, S.P., July THE PROPOSED METHOD Th rlationship btwn SV RORA probability and SV roadsid ncroachmnt probability for a vhicl travling through a 1mi or 1kmroad sction can b mathmatically xprssd as follow: Dsign)x P (SV ROM1 Mdnlin, Rdsiak Dsign) P (RdridE m 4 Mainlin, P(SVRRA UidEncro, Mainlin, RdSidDsign) whr Mainlin Rdsid Dsign Mainlin traffic and gomtric dsign variabls; = Rdsid dsign variabls; P(SV RORA /Mainlin,Rdsid Dsign) conditioiid probability of bing involvd in a SV RORA whn a vhicl travls through a 1mi or 1kmroad sction that has a givn gomtric dsign and traffic charactristics as dscribd in Mainlin and Rdsid Dsign; (Not that it is assumd hr that th probability of having mor than on SV RORA by a vhicl is zro); P(Rdsid Encro Mainlin, Rdsid Dsign) conditional probability of having an SV roadsid ncroachmnt whn a vhicl travls through a 1mi or km road sction that has a givn gomtric dsign and traffic charactristics as dscribd in Mainlin and Rdsid Dsign; (Not that it is assumd hr that th probability of having mor than on SV roadsid ncroachmnt by a vhicl is zro); P(SV ROM Rdsid Encro, Mainlin, Rdsid Dsign) conditional probability of bing involvd in an SV RORA whn a vhicl travls on a 1mi or 1kmroad sction that has a givn gomtric dsign and traffic charactristics as dscribd in Mainlin and Rdsid Dsign and has ncroachd on th roadsid. By assuming that Rdsid Dsign has a vry small and ngligibl ffct on roadsid ncroachmnt. probability, Eq. (1) can b rwrittn as:

12 . Miabu, S.P., July P (SV RORA Mainlin, Rdsid Dsign) P (Rdsid Encro Mainlin)x P (SV RORA Rdrid Encro, Miainlin, Rdrid Dsign) Now, lt's pictur a condition whr thr xists an xtrmly bad roadsid dsign such that whn a vhicl ncroachs on th roadsid at any point on th road sction it is 1 prcnt sur that th vhicl will rsult in a RORA. For xampl, on can pictur a road sction which has no shouldrs and a ditch with a 1:1 sidslop ratio built right nxt to th travld lan. Not that vry dns point objcts, such as trs and utility pols, alon th roadsid would also b good xampls. Of cours, a road sction with such a bad roadsid dsign may not xist in th sampl. Thus, in practic, xtrapolations byond th rang providd by th sampl may b rquird. Th rasonablnss of th xtrapolations dpnd th xtnt of th xtrapolation and functional rlationship in qustion (.g., whthr it is linar or nonlinar). Not that som nginring and statistical judgmnts ar rquird if a rathr farout xtrapolation is rquird and th functional rlationship appars to b nonlinar. Undr such a bad roadsid dsign condition, P(SVRRA Rdsid Encro, Mainlin, "xtrmly bad" Rdsid Dsign) = 1, and thrfor Eq. (2) can b rxprssd as: P ( SV RORA Mainlin, "xtrmlybad" Rdrid Dsign) P (M& Encrol Mmniin) (3) To stimat th xpctd a n n d numbr of RORA on a road sction with P mils, on can simply multiply a.(3) with (VXP),whr Vis th total numbr of vhicls travling through th sction pr yar (=365 xaadt). That is, P ( SV RORA 1 Mainlin, "xtrmlybad Rdrid Dsign) x V x P P (&& EM Mainlin) x V x P (4) n Eq. (4), th right hand sid is th annual roadsid ncroachmnt fkquncy of intrst, and th lft hand sid is th xpctd numbr of SV RORA pr yar, which can b stimatd using a convntional accidnt prdiction modl such as th modl prsntd in th last sction. 4. LLUSTRATONS To stimat th roadsid ncroachmnt fiquncy using th modl prsntd in Tabl 1, an xtrmly bad roadsid dsign condition can b cratd by stting shouldr width =, mdian clar roadsid rcovry distanc =, and mdian sidslop = 1. (Not that sidslop ratio of 1:1 is th maximum mdian sidslop obsrvd in th sampl sctions.) Excpt lan width and M T, othr

13 ~ Mi&u, S.P., July variabls wr st qual to thir avrag valus. Also, bcaus Alabama has incomplt accidnt data, only Michigan and Washington modls ar usd. Figur 3 shows th stimatd roadsid ncroachmnt fiquncis pr mil pr yar by various lan widths and AADT's using Eq. (4) undr th dscribd bad roadsid conditions. Th ncroachmnt fkquncis collctd by Knndy and Hutchinson [1966] and Coopr [198], and th stimats givn in SR214 basd on an ncroachmnt modl ar also prsntd in th figur for comparison. On important obsrvation can b mad from Figur 3 is that th stimatd ncroachmnt frquncis ar vry compatibl with th ncroachmnt data collctd by othrs. Not that th ncroachmnt frquncis rportd in SR214 ar highr thanthy should b for th following rason: An ad hoc ordinary last squars procdur was usd for paramtr stimation &r log transformations hav bn takn. Essntially, sam as in Zgr t al.'s study, th procdur ovrlookd an important adjustmnt factor as pointd in Miaou and Lum [1993]. n addition, a validation tst rsults providd in th SR214 indicatd that th prdictd accidnt rat fiom th modl dvlopd in SR214 xcdd actual rats by up to 16 prcnt. Svral commnts can b mad about this particular approach of stimating roadsid ncroachmnt fiquncy: On advantag of such an approach is that th ncroachmnt fiquncy can b stimatd for all kind of mainlin dsign and traffic conditions. For xampl, if horizontal curvatur and vrtical grad wr includd in th accidnt prdiction modl prsntd in Sction 2, th ncroachmnt fiquncis could b stimatd for various horizontal curvaturs and vrtical grads as wll. To actually collct such dtaild ncroachmnt data will b vry xpnsiv and mayb impractical. t has bn suggstd that "Th ncroachmnt fiquncy stimatd in this mannr can only b as accurat as th accidnt data usd as input" [Daily t al., Th suggstion is mainly rlatd to th concrn about th undrrporting of minor accidnts. This author would lik to point out that this concrn is not particularly srious for th approach proposd in this papr. Th rason is that undr th "xtrmly bad" roadsid dsign condition statd abov, th rsulting RORA is xpctd to b vry svr and undrrporting of such accidnts is vry unlikly. Thrfor, providd a flxibl man functional form is usd in dvloping accidnt prdiction modls, th ncroachmnt fiquncy stimatd fiom such an approach is rlativly unaffctd by th undrrporting of accidnts.

14 Anothr advantag of such an approach is that th stimatd ncroachmnt frquncy is rlativly uncontaminatd by intntional ncroachmnts. Again, th rason is that intntional ncroachmnts ar not likly to occur undr such a bad roadsid dsign condition. t is important to point out that indd a small xtrapolation is usd in th stimation (bcaus of th assumd xtrm roadsid conditions whr shouldr width =, mdian clar roadsid rcovry distanc =, and mdian sidslop =l). t is this author's judgmnt that th stimatd ncroachmnt frquncy rprsnts only potntially harmful and unintntional ncroachmnts (which ar what th ncroachmnt modl nd). n addition, th stimat is xpctd to b lowr than what would actually happn on th roads, spcially for thos roads with wid shouldrs whr drivrs tnd to b mor rlaxd and harmlss and unintntional roadsid ncroachmnts do occur quit oftn. Anothr possibl us of such an approach is to stimat th probability of th latral xtnt of ncroachmnt whn a roadsid ncroachmnt occurs. That is, givn a roadsid ncroachmnt has occurrd, th approach can b usd to stimat th probability that th ncroachd vhicl, in th absnc of roadsid obstacls, will lav th travld lan by at last a distanc of, say, L. Concptually, this stimat can b achivd by a simpl xtnsion of th approach dscribd abov. Spcifically, it can b achivd by stting shouldr width = L, mdian clar roadsid rcovry distanc =, and mdian sidslop = 1. Th othr variabls can b st in xactly th sam way. Figur 4 shows a drivd probability distribution of th latd xtnt of ncroachmnts using such approach. Sinc shouldr width is usd to stimat th probability, th distribution is good for lvld or flat roadsid conditions (with no slops). This stimatd distribution can b sn to b quit consistnt with AASHTO's distributions for roads with a dsign spd of 56 mi/h (896 km/h). On th othr hand, it is vry diffrnt from th distributions drivd from Hutchinson and Knndy's ncroachmnt data. Not that th basis of AASHTO's distributions is not clar from its Roadsid Dsign Guid paily t al., n addition, th stimation of a singl distribution for a dsign spd has bn controvrsial; it has bn suggstd that multipl distributions for diffrnt sidslop ratios ar ncssary. n thory, this distribution could b conditional on sidslop,

15 Miaou, S.P., July shouldr typ (.g., pavd vs. unpavd, with or without rumbl strips), dnsity of roadsid hazards, travld path, or vn ncroachd angl. Th radrs ar rfrrd to Daily t al. [19941 amd Mak and Bligh [1996] for mor discussion. Th drivd probability distribution of th latral xtnt of ncroachmnts from th proposd mthod can srv as a basis to obtain mor laboratd distributions undr diffrnt roadsid conditions. 5. DSCUSSONS Th illustration abov shows that th mthod dscribd in this papr can b a viabl approach to stimating ncroachmnt frquncy Without actually collcting th ncroachmnt data that can b vry costly. Most importantly, it is straightforward using such an approach to stimating ncroachmnt fkquncis for various mainlin traffic and dsign conditions,.g., AADT, lan Width, horizontal curvatur, and vrtical grad. Th only prmis is that a sound accidnt prdiction modl b dvlopd. Th bttr th accidnt prdiction modl, th bttr th stimat of roadsid ncroachmnt fiquncy can b xpctd. n thory, th proposd mthod can b usd for roadway classs othr than th twolan undividd roads illustratd in this papr. t is, howvr, not clar whthr th xtnsion of th proposd mthod to RORA at intrsctions is straightforward. Mor rsarch to xplor th intrrlationship btwn th accidntbasd approach and ncroachmntbasd approach can hlp dvlop viabl and costffctiv ways of quantifying roadsid safty. Th illustration providd in this papr is a good xampl. ACKNOWLEDGEMENTS This papr is basd on th rsults of a rsarch projct sponsord by th Offic of Safty and Traffic Oprations R&D, Fdral Highway Administration (FHWA). Th opinions xprssd in this papr ar, howvr, solly thos of th author.

16 Miaou, SP., July REFERENCES Amrican Association of Stat Highway and Transportation Officials (AASHTO). Roadsid Dsign Guid. Washington, DC; Coopr, P. Analysis of Roadsid Encroachmnts Singl Vhicl RunOfRoad Accidnt Data Analysisfor Fiv Provincs. B.C. Rsarch, Vancouvr, Canada, March 198. Daily, K.; Hughs, W.; McG, H. Exprimntal Plans for Accidnt Studis of Highway Dsign Elmnts: Encroachmnt Accidnt Stud$ Prpard for FHWA; April Glnnon, J.C. Roadsid Safty mprovmnt Programsfor Frways4 Cost Efctivnss Priority Approach. NCHRP Rport 148, Transportation Rsarch Board. Washington, DC; Hutchinson, J.W.; and Knndy, T.W. Mdians of Dividd Highways Frquncy and Natur of Vhicl Encroachmnts. Enginring Exprimnt Station Bulltin 487, Univrsity of llinois, Jun McFarland, W.F., and H.E. Ross., Jr. Dvlopmnt of dsign critria for safr luminair supports. Board. National Cooprativ Highway Rsarch Program (NCHm) Rport 77, Transportation Rsarch Board. Washington, D.C., Mak,K.K. and Sicking, D.L. Dvlopmnt of Roadsid Safty Data Collction Plan, Tchnical Rport, Txas Transportation nstitut, Txas A&M Univrsity Systm, Collg Station, Txas; Maycock, G.; and Hall, R.D. Accidnts at 4arm Roundabouts. Transport and Road Rsarch Laboratory Rport 1 12; Miaou, S.P. "Th Rlationship Btwn Truck Accidnts and Gomtric Dsign of Road Sctions: Poisson Vrsus Ngativ Binomial Rgrssions." Accidnt Analysis & Prvntion 26(4): ; Miaou, S.P.Masuring th GoodnssofFit of Accidnt Prdiction ModZs. FHWARD964, forthcoming (Sptmbr 1996). Miaou, S.P.; Hu, P.S.; Wright, T.; Rathi, A.K.; Davis, S.C. "Rlationships Btwn Truck Accidnts and Highway Gomtric Dsign: A Poisson Rgrssion Approach." Transportation Rsarch Rcord. 1376:lO18; Miaou, S.P., Hu, P.S., Wright, T., Davis, S.C., Rathi, A.K. Dvlopmnt of Rlationship Btwn Truck Accidnts and Gomtric Dsign: Phas, Publication No. FHWARD ; Miaou, S.P.; Lum, H. "Modling Vhicl Accidnts and Highway Gomtric Dsign Rlationships." Accidnt Analysis and Prvntion 25(6):68979; National Highway Traffic Safty Administration (NHTSA), Tra@c Safty Facts 1992, Rvisd, March Transportation Rsarch Board. Dsigning Safr Roads Practicsfor Rsurfacing, Rstoration, and Rhabilitation. TRB Spcial Rport 214. Washington, DC; Vinr, J.G. Harmful Evnts in Crashs. Accidnt Analysis & Prvntion. 25(2): 13915; Vinr, J.G. Rollovrs on Sidslops and Ditchs. Accidnt Analysis & Prvntion. 27(4): ; 1995.

17 Miaou, S.P., July Zgr, C.V.; Hummr, J.; Rinfurt, D.; Hrf, L.; Huntr, W. Safty Efcts of CrossSctionDsign for TwoLan Roads. Volums and 11. Chapl Hill: Univrsity of North Carolina; Zgr, C.V.; Stwart, R.; Rinfurt, D.; Council, F.; Numan, T.; Hamilton, E.; Millr, T.; and Huntr, W. CostEfctiv Gomtric mprovmntsfor Safty Upgrading of Horizontal Curvs. Volums. Final Rport. Chapl Hill: Univrsity of North Carolina; 199.

18 Miaou, S.P., JU) Tabl 1. Estimatd rgrssion cofficints of som tstd ngativ binomial rgrssion modls and associatd statistics for shglvhid runoffthroad accidnts. Estimatd Paramtr Valut Covariat and Paramtr (M.46;2.62) P1 Dummy intrcpt (=1).676 (M.12;4.92) P2 Dummy variabl for Michigan (l=michigan; kthrwis).4218 (M.13;3.16) P3 Dummy variabl for Washington (l=washington; hthrwis).1783 (&.4;4.57) P4 AADT pr lan (in 1CV).1411 (M.4;3.43) PS Lan width (in ft).1375 (M.7;1.97) Pa Mdian clar roadsid rcovry distanc (in ft) P Pavd shouldr width (in ft).881 (M.14;638) PS Earth, grass, gravl, or stabilizd shouldr width (in ft).692 (M.45;1.54) P9 Mdian sidslop (.g., 3:l and 7:l slops ar rcordd as 1b.33 & U74.14, rspctivly. ) PlO Trrain typ (*flat;.2939 (M.9;335) l=monntainous+rolling) P11 P12 Postd spd limit (in mph) Numbr of intrsctions pr mil.129 (M.6;2.33) P3 Yumbr of drivways pr mil P14 Yumbr of bridgs pr mil Disprsion paramtr of th NB modl (a) L(a,P) (=logliklihood function) 4kaik nformation Critrion Valu ExDctd vs. obsrvd total numbr of accidnts.216 (M.95;2.13) 3988 (M.36;ll.O) ,79. vs 4,632. Nots: (1)596 rural 2lan undividd road sctions; total lngth=1,788 mi; about 5 yars of accidnt data ( ). (2) Valus in parnthss ar asymptotic standard dviation and tstatistics of th cofficints abov. (3) indicats "not includd in th modl." (4) 1 mil = 161kw 1 ft = 348 m.

19 Miaou, S.P., J u b 1996 m U d / ~ s i' 4: W.H t D c. 2 D n n i 2 d co E Q= W d c

20 !.. d r' *.. 4 \o * t b Q\ * r' m W cd +., d) 8 2 * N.. 4 d # \ 1 # i. t 8*.. + rn a v)... d c\l *m 2 c,

21 sr \ Knndy and Hutchinson.C19.66]:...r.:... Rural & Urban 4Lan wighway, 7& j \*. : : * j *H... :.... Coopr w b l : 4Lan Highbay, mi/h... #**!... i ~~... \ :...*...&\.... ' ' J...,... (1 mi = 1.61i km; 1 ft =.348 m) Annual Avrag Daily Traffic (in 1,s) 25 Figur 3. Comparison of th drivd roadsid ncroachmnt frquncy from th accidnt prdiction modl dvlopd in this study and obsrvd frquncis &om arlir studis. l l 3

22 Miaou, S P., July 1996.f 1 i 9 8 E :c' cw t Latral Extnt of Encroachmnt (ft) Figur 4. Comparison of various probability distributions of th latral xtnt of ncroachmnts. 5