《高等路面设计理论》课程授课教案（讲义）Formulation Of Analytical Wet Weather Safety

FORMULATION OFTHEANALYTICALWETWEATHER SAFETYINDEXAnalyticalThe analytical formulation of a Wet Weather Safety Index (wwSla) isdefined by the flow diagram (Figure 17),the definition of terms (Table2)and the equation 1isting (Table 3 ).It is a systematic organization oftheoretical, analytical and empirical work that has been accomplished inthe areas of vehicle handling and stability, tire-pavement interaction anddriver performance over the past 20 years.References are given by eachequation in Table 3.Basic to the formulation of a wwsi is the need to have an indicator ofaccident probability during dry weather and accident probability in wetweather.The indicators selected and formulated are discussed on pages 27through 37.They are summarized here as (1)TF,the traffic conf1ict factorwhich is present during either wetand dry weather, and is based on thespectrum of vehicle speeds and confiicts between all these vehicles withothers in the traffic pattern as weli as with vehicles seeking access oregress from the traffic stream; and(2)wF,thewet weather conf1icts factor,a factor which is present only when rain is falling or the pavement is stillwet.The value of wF calculated is dependent on the differences between thecomputed maximum safe speed for traffic and the frequencies of vehiclesmoving at higher speeds.Although the logic behind the development of these two factors wasexplained previously,the way in which they are put together to form theRHI (Road Hazard Index) and the WWSI (Wet Weather Safety Index) wii1 betreated here.TTI Res Rpt 22/-1FNovember 1977

CalculateChoose LargerCatculate spCalculateCaleulatowpENPUT,BATAXSPRAYt0Sru11ergfsDam1gP;10:T80DorNOEeuatlon9Equat1on17tquetton 10- MDS: L: MO,: 50,R;eS,iV,tM,ENSaitSHAo*PA,-VA,PA,"VA,TheSoullerCalculate FM,of't, Pr..'.qustlon 1Yandy,Pv,. "'v,.-Py,. 'y,and.SoeuaCAN; CTM; CH;VCalcutate rs,CalculatoTCalculateEquatlon12Equation2Calculate FiSTARTwerageFN,FHFMPROGRANTesandFRCalculateFn,TestCalculateEquatten 131svO0.017CALCULATEO FACTORSEeuat1otp, s, fr."tye.Vv, wCalculate FH,Fm,.Fn,.e.fpEeuatfons14,15,$16F,.TF, ME.CalcwlateRHRHF,WSTteuatfon 21CalculateTnEquattons5,6&Calculate WSI,Equation 22Tigure 17,Plow ChartferOeteminutton orws1

TABLE2.DEFINITIONOFTERMS.INPUTDATA1. Ig, Design rainfall intensity (in./hr)2.P,Design tire pressure (1b/in.2)3.TD, Design tread depth (32nds of an in.)4.TxD,Surface texture(in.)5. s, Surface slope (in./in.)6.L,Drainage path length (ft)7.WDa,Puddling water depth (in.)8.SDg,Geometric sight distance (ft)9.VT50 Percentile truck speed (mph)5010.fr, Average truck spacing (ft)11.R, Road curve radius (ft)12.e, Curve superelevation (in./in.)13.Sr, Reverse crown slope (in./in.)14.W,,Road lanewidth (ft)15.W,,Paved shoulder width (ft)16.Wt,Track width (ft)17.SN40, Skid number at 40 mph (dimensionless)(i=1+n), Matrix of normalized vehicle frequency and18.Pv.,VvVicorresponding velocities (dimensionless and miles/hr)19.PA,VA, (i-1+k), Matrix of normalized automobile frequency andcorresponding velocities (dimensioniess and miles/hr)20.Pr,,Vt.(j=1+m),Matrix of normalized truck frequency and1corresponding velocities (dimensioniess and miles/hr)21.CH, Critical vehicle frequency (vehicles/hr)(DHv may be used to approximate CV)22.CAH, Critical automobile frequency (vehicles/hr)23.CTH, Critical truck frequency (vehicles/hr)24. V, First assumption of critical vehicle speed (miles/hr)25. T(w), Decimal portion of time road is wet (dimensionless)

TABLE 2.DEFINITION OF TERMS.(continued)CALCULATED FACTORS1.SSD,Sight distance(ft)2.SDw, Climatic sight distance (ft)3.WD,water depth (in.)4.V, Final estimate of critical speed (miles/hr)5.Yy，Hydroplaning speed (miles/hr)6.V.,Critical wet weather speed (miles/hr)7.W,Availablesidespace(ft)8.FN,Available friction number (dimensionless)9.FNs,Stopping distance friction number (dimensionless)10.FNc,Cornering friction number (dimensionless)11.FNp, Passing friction number (dimensionless)12.FN,Emergency correction friction number (dimensionless)13.KSPRAY, Reduction of sight distance due to truck spray (dimensionless)14.TF,Traffic confiict factor15.WF,Wet surface speed conflict factor16.RHF,RoadHazardFactor17.wwSI,Wet Weather Safety Index19.FNvThe average friction number of FNs,FNc, FNp,and FNeavg

TABLE3.EQUATIONS(continued)ReferenceNumber10,11LOFN,= 100(a,SN40 + by)a, = 1.14 × 10-6 (v2 - 10v + 3530)106by = -7.44 × 10~5(v2 - 10V - 3000)107Definitionft = VT-。 × 5280/CTH8'50V2WD/2 cVH150New Dev.9KSPRAY =14.5×106(4500-15001g)KSPRAY12*,13*10SD..68rNew Dev.+0.8]IdL27v?14,1511FN, " 0.3(SD - 3.67V)v214,16120. 08R + 40 - 100 eFNc"v214,1713FN.220 - 100 S,SP100v2(1- cos e)14,1514FNe " T5(00V(.47 0S10) + 2New Dev.15W = 0.8 W.+ 51516e = 0.2 W.+38rTxD0.11_0.43,0.5913WD = 0.00338 [17- TXDs0.42* Equation 5 was developed from information presented in these studies

TABLE3.EQUATIONS.(continued)NumberReference18Vμ = 1. 1p0.3 (TD + 1)0. 06 A *19A=_10.419+3.519WD0.0629207.8) TxD0.14A=[19-WD0.06nnCVH2TF =62QV1NNew Dev.2j=i+1jnm-PL,[v?WF=[v- v214CAH2QACTHN3New Dev.AAi=c'jj=cj21RHF = TF(1 - T(w) + IFE + T() × 40 + WF × T(w)New Dev.FNavgTF22WWSI,New Dey.40-TFNa+ WFavg* Use the smaller value of A given by equations 19 and 20

TheRoad Hazard Index is defined in terms of wF, TF,T(w), 40, andFNavg as40 T(w) + NF(T(w)RH TF(1 - T(0) + FA%gTerm l,TF(1 -T(w)),is the indicator of potential traffic conflictsin terms of both conflict probability and severity during dry weather.Note T(w) is the decimal proportion of time rain is falling in a particulararea so 1 -T(w) is the decimal proportion of time rain is not falling,i.e., an indicator of the relative amount of dry weather.FAo T(w), is the indicator of potential traffic confictsTerm 2, TF FNavgduring wet weather with a modifying factor of 40/FNavg Forty is the amountof friction in percent generaliy considered usable by traffic during dryweather. FNavg is the average friction demand in the performance of anumber of specific maneuvers when traveling at the critical speed. Thisvalue decreases with decreases in SNao and with water depth on the pave-ment since these factors influence the critical speed. If FNavg is con-siderably below 40, the result is an increase in the Term 2 value due toa decrease in the capability of traffic to avoid the conflicts which occur.The third term, WF(T(w)), indicates the contribution of the wetweather speed conflicts on the overali accident history of the highway.Note this conflict factor is modified by T(w), the proportion of time whenwet weather is occurring.The Analytical Wet Weather Safety Index is defined by the same terms asthe RHI, but formulated in a different way.TFi.e.,WWSIa40+ WFTFFNavg

The numerator of this ratio is proposed as the indicator of accidentprobability during dry weather, and the denominator the indicator ofaccident probability during wet weather.If these two indicators havevirtue, the wsI should correlate with theratio of accident rate duringdry weather and accident rate during wet weather. When it becomes justas safe wet as dry the WwsI should approach some 1imiting upper value.As wet weather safety goes down, i.e., the denominator gets larger, thewwsIwill decrease.The main thing that has yet to be shown is the determination of V,Vh and Vc, three velocities that relate to vehicle controllability.These speeds are, respectively, V, the speed above which a given segment oftraffic should not be able to perform a selected group of maneuvers dueto the maneuvers requiring greater than available friction; Vy, the speedat which hydroplaning will occur for a given segment of automobiles; and,finally, Vc, the lower of the two previously defined speeds, V and Vh.These speeds are calculated by the WwSI, program as follows: Theinput data is selected as defined in Table 2 including geometric, pave-ment and traffic characteristics as well as a value of design rainfallintensity.To begin the computation procedure, a value of y is arbitrarilyassumed, usually 40 mph. Using this value and an input value of SN4o, avalue of available friction is calculated by Equations 5, 6 and7

The amount of water layer buildup on the pavement due to the designrainfall intensity is calculated and is used along with the assumed vehiclespeed to calculate the sight distance during rainfall.This sight dis-tance is a function of both the rainfall and the spray created by traffic.The computed sight distance is compared to the geometric sight distance,andthe lowerselected.This sight distance is then used in Equation ll to determine thefriction required for stopping, FNs. The roadway curvature, superelevationand V are used in Equation12 to calculate the friction required for cornering,FNc. The road lane geometrics and assumed speed, V, are used to determineFNp, the friction required for passing (Equation13). Finally, the lanedimensions, shoulder dimensions and assumed speed, V, are used to calculateFNe (Equation 14), the amount of friction needed in emergency directioncorrectionmaneuvers.The average of these values, FNs,FNc, FNp or FNe, is then selectedand compared to FNa. In other words the average required friction is comparedto the available friction. If the required friction is greater than theavailable friction the assumed value of v is too large,and it will bedecreased for the next iteration. If the required friction is lower thanthe available friction, the assumed value of V is too smail. It will thenbe increased for the next iteration. By successive iteration, a value ofV is found where average required friction is fundamentally equal to availablefriction. This value of V is then called the critical value for that segmentof traffic assumed for design.The next velocity which must be computed is Vh, the velocity at whicha certain segment of traffic wili hydroplane.This speed can be calculated

directly by Equations 18,19,and 20 since water depth has been previouslycomputed and the other governing factors, texture, tread depth and tirepressure, are part of the input data. Note "design" values of tread depthand tire pressure must be selected. The minimum legal tread depth,2/32nds of an inch was selected along with 18 psi,the low 7 percentiletire pressure.Any vehicle with tread depths and/or tire pressures lowerthan this would be expected to hydroplane at slightly lower speeds. Withrespect to automobiles, the 1ower of v or Vy would be denoted Vc, thecritical automobile speed. Since trucks generally carry tire pressurestoo high to allow dynamic hydroplaning, Vh is not considered for trucks,and Vc is equated to V, the speed where available and required friction areequal.This is probably a conservative estimate for trucks since most of thevalues of required values of friction are based on observations of auto-mobiles.With the possible exception of stopping maneuvers,it is the authors'opinion that most of the maneuvers attempted by truck drivers are of a lessextreme nature than those attempted by automobile drivers.Once the critical wet weather speeds for automobiles and trucks aredetermined, it is then possible to calculate the factors WF,TF, RHI andWWSI