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Page 1: Impact of highway consistency on capacity utilization of two-lane rural highways

Impact of highway consistency on capacityutilization of two-lane rural highways

Gamal M. Gibreel, Ibrahim A. El-Dimeery, Yasser Hassan, and Said M. Easa

Abstract: Consistent highway design is expected to provide safe, economical, and smooth traffic operation. Severalstudies have been performed to investigate the effect of highway consistency on traffic safety. However, the relationshipbetween design consistency and highway capacity and level of service has not been addressed in current research workand design practices. In addition, the effect of the three-dimensional (3D) nature of highway alignments was notconsidered, and design consistency was studied based solely on two-dimensional (2D) analysis of highway horizontalalignments. This paper presents a methodology to determine the effect of highway design consistency on highwaycapacity utilization based on 3D analysis. This methodology will help road designers to estimate highway capacitymore accurately. The study was performed on two-lane rural highways in Ontario, where two types of 3D combinationswere considered: a horizontal curve combined with a sag vertical curve (sag combination) and a horizontal curvecombined with a crest vertical curve (crest combination). An additional adjustment factor that reflects the effect ofhighway design consistency on capacity utilization was developed. Different statistical models are introduced toestimate this factor based on geometric or traffic data. In addition, typical values of the consistency factor weredeveloped based on an overall consistency evaluation criterion and can be easily used in capacity analysis.

Key words: three-dimensional, alignments, capacity, geometric design, operating speed, design consistency.

Résumé : Il est supposé que la conception routière uniforme permet une circulation sûre, économique et régulière. Denombreuses études ont été faites pour examiner les effets d’uniformité routière sur la sécurité de la circulation.Cependant, la relation entre l’uniformité de conception et la capacité et le niveau de service routier n’a pas été traitéedans les travaux de recherche et les pratiques de conception actuels. De plus, l’effet de la nature en trois dimension(3D) d’alignements routiers n’a pas été considéré, et l’uniformité de conception a été étudiée uniquement sur based’analyses à deux dimensions (2D) des alignements horizontaux. Cet article présente la méthodologie pour déterminerl’effet de conception routière uniforme sur l’utilisation de capacité routière basé sur une analyse 3D. Cetteméthodologie va aider les concepteurs de routes dans l’estimation plus précise de capacités routières. L’étude a étéeffectuée sur une route rurale à deux bandes en Ontario, où deux types de combinaisons 3D ont été considérés : unecourbe horizontale combinée avec une courbe d’affaissement verticale (combinaison affaissement) et une courbehorizontale combinée avec une courbe verticale de crête (combinaison crête). Un facteur d’ajustement supplémentaire aété développé qui reflète les effets de l’uniformité de conception routière sur l’utilisation de capacité. De plus, desvaleurs typiques du facteur d’uniformité ont été développées à base d’un critère d’évaluation d’uniformité global etelles peuvent être utilisées facilement dans l’analyse de capacité.

Mots clés : trois dimension, alignement, capacité, conception géométrique, vitesse opératoire, uniformité de conception.

[Traduit par la Rédaction] Gibreel et al. 798

Introduction

Achieving highway design consistency is an importantgoal for highway planners and designers to ensure safe, eco-nomical, and efficient traffic operation. The lack of geomet-ric design consistency may result in unnecessary accident

risk (Al-Masaeid et al. 1995). Many studies have addressedthe relationships between geometric design consistency, op-erating speed, and safety. Most previous research work ondesign consistency has been based on two-dimensional (2D)analysis of highway horizontal alignments and has not ac-counted for the effect of the three-dimensional (3D) natureof highways (Gibreel et al. 1999a, 1998a). In addition, thiswork has not addressed the interaction between design con-sistency and highway capacity, driver comfort, or sight dis-tance.

Speeds on a highway with consistent design are expectedto be uniform without any sharp or abrupt reduction, andhence traffic delays are reduced; thus, a consistent highwaydesign would enhance the highway capacity utilization. It isimportant to develop a reliable methodology for investigat-ing the relationship between design consistency and highwaycapacity based on 3D analysis of combined highway align-ments. The following sections investigate the effect of de-

Can. J. Civ. Eng. 26: 789–798 (1999) © 1999 NRC Canada

789

Received January 13, 1999.Revised manuscript accepted June 9, 1999.

G.M. Gibreel and S.M. Easa. Department of CivilEngineering, Lakehead University, Thunder Bay, ONP7B 5E1, Canada.I.A. El-Dimeery. Ain Shams University, Cairo, Egypt.Y. Hassan. Public Works Department, Cairo University,Egypt.

Written discussion of this article is welcomed and will bereceived by the Editor until April 30, 2000 (address insidefront cover).

Page 2: Impact of highway consistency on capacity utilization of two-lane rural highways

sign consistency on service flow rate at daytime under goodweather conditions on two-lane rural highways, using datacollected on 3D alignments involving sag and crest verticalcurves in Ontario. The results of this research should helphighway engineers and researchers deal with capacity analy-sis more accurately.

Study approach

To investigate the effect of design consistency on capacityutilization, an experimental program was proposed to com-pare actual service flow rate obtained from field measure-ments on several highway sections with the theoretical flowrate that is calculated based on highway capacity analysis.The steps of the study were1. Collection of geometric design, traffic, and traffic con-

trol devices data on selected highway sections. The geo-metric design data would include the design data ofhorizontal and vertical alignments and cross section.The traffic data would include the operating speed pro-file, traffic volume, percentages of heavy vehicles, andpercent of time delay. The traffic control devices dataare mainly the percentage of no-passing zones.

2. Determination of the measured and calculated serviceflow rates. The measured service flow rate would becalculated from the measured traffic volumes. The cal-culated service flow rate would be determined based onthe volume-to-capacity ratio and the relevant adjustmentfactors using the procedures provided by the HighwayCapacity Manual (TRB 1998).

3. Developing of the consistency factor as the ratio be-tween the measured and calculated service flow rates.

4. Testing the consistency factor to examine whether or notthere is a true difference of its population from unity.

5. Based on the measured and calculated service flowrates, the consistency factor would be modeled in termsof geometric and speed parameters. The models deter-mine the accurate drop in the service flow rate due todesign inconsistencies on a specific roadway section.

6. Based on the consistency evaluation, typical values ofthis factor would be established to provide an approxi-mate estimation loss in the service flow rate if exacttraffic and geometric data are not available.

Data collection

Site selectionHighway 61 and Highway 102 in Ontario were selected

for the purpose of this study. Two types of 3D alignmentcombinations were used: (a) sag combination (a sag verticalcurve combined with a horizontal curve) and (b) crest com-bination (a crest vertical curve combined with a horizontalcurve). The selection of the study sites was limited to thosesections that satisfied the following general conditions:

1. No influence of intersections.2. No influence of other adjacent sections.3. No physical features or activities adjacent to, or in the

course of, the roadway that may create an abnormalhazard such as narrow bridges, schools, factories, orrecreational parks.

4. Roadway pavement is marked and shoulders are paved.

5. Pavement width ≥ 7.5 m and shoulder width ≥ 1.8 m.6. Grades ≤ 6%.7. Sections are protected by guardrails when the embank-

ment height exceeds 3 m.8. AADT ≤ 10 000 vehicles/day.9. Design speed ≤ 110 km/h.

10. Directional split factor ranges from 50/50 to 70/30.The site selection process resulted in 9 sections of the sag

combinations and 10 sections of the crest combinations lo-cated on Highway 61 and Highway 102.

Geometric design dataThe geometric design data of the selected highway sec-

tions were extracted from the plan-profile drawings, whichwere obtained from the Planning and Design Section, Minis-try of Transportation of Ontario (MTO). The data includedall information concerning highway cross section, grades,horizontal alignment, and vertical alignment. Table 1 showsthe minimum and maximum limits of the geometric designdata for the selected sites.

Operating speed dataOperating speed data were collected at five points located

along each travel direction at each roadway section to estab-lish a speed profile along the 3D alignment combination.Based on the geometry of horizontal curves, the positions ofthese points were defined for each travel direction as follows(Gibreel et al. 1998b, 1999b):1. Point 1 is about 60–80 m on the approach tangent be-

fore the beginning of the spiral curve.2. Point 2 is the beginning of horizontal curve (spiral-to-

curve point, SC).3. Point 3 is the mid-point of horizontal curve (MC).4. Point 4 is the end of horizontal curve (curve-to-spiral

point, CS).5. Point 5 is about 60–80 m on the departure tangent after

the end of the spiral curve.Speed radar gun devices (Muni-Quip T-3) were used to

collect speed data. Based on a pilot survey that was per-formed before starting the data collection, the speed datacollection started at 9:00 am for 1 h for each individual pointat each travel direction. The data were collected for all vehi-cles in the traffic stream under free-flow conditions. Basedon the recommendations by Poe et al. (1996) and TRB(1998), the free-flow conditions were taken as the isolatedvehicles with a minimum headway of at least 5 s or vehiclesheading a platoon. The observers were located on the side ofthe roadway in a setup that would minimize the cosine effectof the measurement angle without influencing the vehiclespeeds. The collected speed data were downloaded to thecomputer and a spreadsheet computer program was used todetermine the 85th percentile operating speeds.

Traffic volume dataThe objective of the traffic volume data collection was to

determine the hourly volume, service flow rate, and LOS oneach section. Traffic volume count, with vehicle classifica-tion, was done in 1 day separately for the two traffic direc-tions of each individual highway section. Because the trafficcharacteristics on the days preceding or following weekends,or on the weekends themselves, are different from the nor-

© 1999 NRC Canada

790 Can. J. Civ. Eng. Vol. 26, 1999

Page 3: Impact of highway consistency on capacity utilization of two-lane rural highways

mal characteristics, the counting was always done on Tues-days, Wednesdays, and Thursdays.

To determine the time period during which the peakhourly volume would occur, a pilot survey was done on aroadway section on each of Highway 61 and Highway 102.The survey was conducted on two different days for a 10-hour period, each starting at 8:00 am and ending at 6:00 pm.Volumes were counted for 15-min intervals as this is theshortest interval during which stable flow can exist (Garberand Hoel 1996). The patterns of variations in the 15-minvolumes, as shown in Fig. 1, indicated that there was alwaysa single daily peak occurring between 10:00 am and1:00 pm. Thus, traffic volumes were measured for only 5 hfor each travel direction at each highway section. The mea-suring time started at 9:00 am and ended at 2:00 pm to coverthe daily peak.

After the data collection was completed, the count formswere downloaded to the computer, and a spreadsheet pro-gram was used to prepare the data for the modelling stage.The measured service flow, percentage of trucks, percentageof buses, percentage of recreational vehicles, and the direc-tional split factor were then calculated as follows:

[1] SF V= 4 h

[2] T V V= ×( / )T t 100

[3] B V V= ×( / )B t 100

[4] RV V V= ×( / )RV t 100

[5] d V V= dir t/

where SF = measured service flow rate (vehicles/h), Vh =highest 15-min traffic volume in both travel directions dur-ing the 5-h counting interval (veh), T = percentage of trucks(percent), VT = volume of trucks in both travel directions inthe 5-h counting period (veh), Vt = total traffic volume inboth travel directions in the 5-h counting period (veh), B =

percentage of buses (percent), VB = volume of buses in bothtravel directions in the 5-h counting period (veh), RV =percentage of recreational vehicles (percent), VRV = volumeof recreational vehicles in both travel directions in the 5-hcounting period (veh), d = directional split factor, Vdir =highest directional traffic volume in the 5-h period (veh).

No-passing zonesThe calculations of service flow rate, based on the HCM,

require determining the percentage of no-passing zonesalong the studied sections, taken as the average percentageof no-passing zones in both traffic directions. The no-passing zones are established at vertical curves, horizontalcurves, or their combination, and elsewhere on two-lanehighways where passing must be prohibited (MTO 1995). Ano-passing zone is defined as any section of a highwaywherein the available passing sight distance is equal to orless than 450 m (TRB 1998).

To obtain representative values of the percentage of no-passing zones for the different highway segments of thestudied sections, a segment length of 5 to 10 km was takenas a base for calculation. The percentage of no-passingzones was calculated in three steps. First, the length of thesolid barrier line representing the no-passing zones alongeach traffic direction was measured within each specifichighway segment using a car odometer with a precision of±25 m (the measuring wheel was not used because this pre-cision was sufficient for this type of analysis). Second, theaverage length of no-passing zones in both travel directionswas determined for each segment. Third, the percentage ofno-passing zones for any highway section located in a spe-cific highway segment was calculated as follows:

[6] NPZ L L= ×N seg/ 100

© 1999 NRC Canada

Gibreel et al. 791

0

5

10

15

20

25

30

35

40

45

50

55

60

65

8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00

Time (h)

Traf

ficvo

lum

e(v

eh)

Highway 61

Highway 102

Fig. 1. Fifteen-minute traffic volume patterns on Highway 61and Highway 102.

Type of 3D alignment combination

Geometricelementa

A sag vertical curveand a horizontal curve

A crest vertical curveand a horizontal curve

r 575–900 425–1800∆c 5–40 5–55E 4.4–5.5 2.9–6.0Ls 45–65 30–75G ≤6.00 ≤6.00Lv 80–180 80–320A 1.15–6.00 1.00–7.10L0 42.9–186.0 5.9–170.0X ≤150 ≤210Lw 3.75 3.75Lsh 2.00 2.00

ar = radius of horizontal curve (m), ∆c = deflection angle of horizontalcurve (degree), E = rate of superelevation (percent), Ls = length of spiralcurve (m), G = grade (percent), Lv = length of vertical curve (m), A =algebraic difference in grades (percent), L0 = distance between thehorizontal and vertical points of intersections (m), X = shared portion ofthe lengths of horizontal and vertical curves in the same combination (m),Lw = lane width (m), and Lsh = shoulder width (m).

Table 1. Limits of geometric design data.

Page 4: Impact of highway consistency on capacity utilization of two-lane rural highways

where NPZ = percentage of no-passing zones of a highwaysegment (percent), LN = average length of no-passing zonesin both travel directions (km), and Lseg = actual length of thehighway segment (km).

Preliminary analysis

Measured service flow rateThe studied segments on Highway 61 and Highway 102

have no points of fixed interruptions and therefore, in capac-ity analysis procedures, these segments were treated as unin-terrupted flow facilities. Two types of service flow rateswere determined for each highway section, which are themeasured service flow (SF) and the calculated service flow( )SFcal . As explained earlier, the values of measured SF weredetermined based on eq. [1]. The values of SF ranged from163 to 689 vehicles/h for the sections of sag combinations,while they ranged from 144 to 464 vehicles/h for the sec-tions of crest combinations.

Calculated service flow rateCalculated service flow rate, SFcal, represents the com-

puted flow rate of the roadway segments for the existinglevel of service and prevailing roadway, traffic, and environ-mental conditions. Several traffic data were needed to deter-mine the SFcal at these sections including the type of terrain,average percent time delay (PTD), percent of no-passingzones (NPZ), volume to capacity ratio (v/c), and the adjust-ment factors for directional distribution (Fd), narrow laneand restricted shoulder width (Fw), and heavy vehicles (FHV).The longitudinal grades on the studied highway sectionswere either less than 3% and shorter than 800 m, or morethan 3% and shorter than 400 m, and therefore the sectionswere treated as general terrain segments (TRB 1998). Thus,the adjustment factor for the effect of grades was not neededin the analysis. The SFcal was determined for the differentsections using the following formula of the general terrainsegment on two-lane rural highways (TRB 1998):

[7] SF v c F F Fcal d w HV= 2800( / )

According to the HCM (TRB 1998), the adjustment factorfor directional distribution of traffic, Fd , was determined foreach section based on the traffic split factors. As the pave-ment width was >7.2 m and shoulder width was >1.8 m forall study sections, the adjustment factor for narrow lane andrestricted shoulder width, Fw, was found to equal 1. The ad-justment factor for the presence of heavy vehicles, FHV, wasdetermined for each highway section using the formulagiven by the HCM as follows:

[8] FP E P E P E

HVT T B B RV RV

=+ − + − + −

11 1 1 1[ ( ) ( ) ( )]

where PT, PB, and PRV = percentages of trucks, buses, andrecreational vehicles in the traffic stream, respectively (deci-mal), and ET, EB, and ERV = passenger car equivalent fortrucks, buses, and recreational vehicles, respectively.

Passenger car equivalent on a specific highway sectioncan be determined depending on the type of terrain and levelof service of the section. According to the HCM, the topog-raphy of the studied highway sections with longitudinal

grades ≤2% was classified as level terrain, and the topogra-phy of those with longitudinal grades >2% was classified asrolling terrain. The validity of this classification was con-firmed by the observation that the average speed of heavyvehicle on the studied sections was very close to that of pas-senger cars (average heavy vehicle speed = 94% of averagepassenger car speed).

The level of service on a specific roadway section is de-termined based on the PTD on this section, which can be es-timated as the percent of vehicles travelling at headway≤5.0 s (TRB 1998). After the level of service on each sectionwas determined, the value of the NPZ on that section wasused to find the v/c ratio. The values of SFcal were obtainedby substituting in eq. [7] with the values of v/c, Fd , Fw, andFHV. The graphical representations for the values of SF andSFcal for both sag and crest combinations are shown inFigs. 2 and 3, respectively. Based on these figures, it can beclearly noticed that the values of SFcal were always greaterthan those of SF for all highway sections of both combina-tion types. Since the values of SF and SFcal at each highwaysection should be the same, it can be argued that the effectof a specific additional factor has been ignored.

Consistency factor

As stated earlier, the values of SFcal were always higherthan those of SF for all study sections. This indicated thatthe actual traffic stream was affected by an additional factorbesides those included in eq. [7]. This factor may be attrib-uted to the effect of geometric design consistency of thehighway sections of the sag and crest combinations; it wascalled consistency factor Fc ≤1. The factor was defined asthe ratio of SF/SFcal and ranged from 0.74 to 0.98 with amean of 0.90 for all study sections. A test of hypothesis wasperformed on the population sample of Fc to test whetherthere was a true difference of this population from 1.00 orwhether the difference was caused by random errors in thefield measurements and computations. The summary of thetest elements is as follows:(a) The null hypothesis (H0): Fc = 1.00.(b) The alternative hypothesis (Ha): Fc < 1.00.(c) The average and standard deviation of the Fc sample are

0.903, and 0.015, respectively.(d) The level of significance, α, is 0.05 (one-tailed test).(e) The calculated t-statistic is –6.28.(f) The tabulated t-statistic is −1.734 (α = 0.05) and −3.922

(α = 0.0005).

[9] SF v c F F F Fcal d w HV c= 2800( / )

Based on this summary, the probability of Type I error(rejecting the null hypothesis, Fc = 1.00, when it is true) wasless than 0.05%. Thus, the values of Fc were significantlylower than 1.00 and the differences between SF and SFcalcannot be attributed to random errors. Thus, eq. [7] wasmodified as follows:

Modelling consistency factor

Fc and geometric elementsThe relationship between Fc and geometric design param-

eters was investigated for both sag and crest combinations.

© 1999 NRC Canada

792 Can. J. Civ. Eng. Vol. 26, 1999

Page 5: Impact of highway consistency on capacity utilization of two-lane rural highways

Multiple regression analysis was used for model estimationtaking into account three conditions: (a) the coefficient ofdetermination R2 must be significant at the 0.95 confidencelevel, (b) each of the independent variables used in themodel must have a regression coefficient that is significantlydifferent from zero at the 0.95 confidence level, and (c) thealgebraic sign of the coefficients of the independent vari-ables must have a logical explanation. Different geometricparameters were examined for use as independent variables,but only three parameters were found to have significant ef-fect on Fc: the radius of horizontal curve, r; the rate of verti-cal curvature, K; and the distance between point of verticalintersection (PVI) and point of horizontal intersection (PHI),L0. In addition, several modelling trials were performed toestablish the appropriate equation form and determine thevariable coefficients. The final models to estimate Fc for sagand crest combinations can be represented, respectively, by

[10] Fr K

Lc-sag 0.317 0.170= + + +

+

ln

( )( )( )

1 110

0 7.

,

R2 = 0.59

[11] Fr K

Lc-crest 0.383 0.302= + + +

+

ln

( )( )( )

1 110

0 3.

,

R2 = 0.54

where Fc-sag and Fc-crest = consistency factor for sag andcrest combinations, respectively.

The coefficients of determination of the models, R2 , weresignificant at the 0.95 confidence level and had moderatevalues (0.54 and 0.59). The most probable reason for thismoderate range was the limited number of available datapoints, which was 9 and 10 points for sag and crest combi-nations, respectively. The coefficients of the independentvariables were also significantly different from zero at the0.95 confidence level. The positive sign of the regression co-efficients for r, K, and 1/L0 indicates that Fc increases as ei-ther the horizontal or vertical curve becomes flatter (greaterr or K), and decreases as L0 increases. This increase in L0can be interpreted as an increase in the section complexity asthe position of PVI is further shifted from the position ofPHI.

The models of eqs. [10] and [11] can be used to establishdesign charts that can be easily used. For example, Fig. 4

© 1999 NRC Canada

Gibreel et al. 793

(a)

(b)

1.00

0.90

0.80

0.50

0.70

0.60

0 40 16080 120 200

Lo (m)

r = 1800 m

r = 1300 m

r = 800 m

r = 100 m

r = 400 m

Fc

Fc

1.00

0.90

0.80

0.700 40 16080 120 200

Lo (m)

Fig. 4. Estimation of Fc based on geometric parameters: (a) sagcombinations (K = 40 m); and (b) crest combinations (K =40 m).

0

100

200

300

400

500

600

700

800

1 2 3 4 5 6 7 8 9

Study sections

SFcal

SF

SF

and

(veh

/h)

cal

SF

Fig. 2. Comparison between SF and SFcal values on sagcombinations.

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10

Study sections

SFcal

SF

SF

SF

and

(veh

/h)

cal

Fig. 3. Comparison between SF and SFcal values on crestcombinations.

Page 6: Impact of highway consistency on capacity utilization of two-lane rural highways

shows the charts for estimating Fc for K = 40 m on sag andcrest combinations, respectively. The value of Fc corre-sponding to the sharpest r (100 m) for crest combinationswas always higher than the similar value for sag combina-tions. Also, the value of Fc corresponding to the flattest r(1800 m) for crest combinations was generally lower thanthe similar value for sag combinations. The combined effectof these two differences in Fc is an increase in the band-width of Fc (the change in Fc caused by a change in r from100 to 1800 m) on sag combinations relative to crest combi-nations. This can be attributed to either or both of the fol-lowing reasons:1. On sag combinations, the sag curve does not obstruct

the daytime sight distance, and so the entire effect ofsight distance is reflected only in r. On the other hand,for crest combinations both the crest vertical curve andhorizontal curve can obstruct the sight distance, hence rcontributes only partly to the effect of sight distance.Therefore, the effect of r is reduced.

2. On sag combinations, the driver can see the entire hori-zontal curve, while on crest combinations, the driver’sview is limited to a portion of the horizontal curve de-pending on the values of r and K. Therefore, the driverwill be less intimidated by sharp horizontal curves andless encouraged by flat ones.

Fc and speed variationsThe operating speed changes and the differences between

operating and design speeds on a 3D combined alignmentare affected by the status of geometric design consistency ofthis alignment (Gibreel et al. 1999a, 1999b). The relation-ships between Fc and such variables as the change in operat-ing speed and the difference between operating and designspeeds were investigated for both sag and crest combina-tions. Multiple regression analysis was used to estimate themodels, taking into account the three conditions that havebeen previously considered in modelling Fc and geometricparameters.

To determine the change in operating speed, the speedprofiles for both travel directions of each highway sectionwere created using the measured 85th percentile operatingspeed (V85). The change in operating speed was taken as themaximum reduction in operating speed between the highestand lowest operating speed values along the combination.For sag combinations, the highest values of V85 along thelength of the combination were located at point 2, while thelowest values were located at point 1. Regarding crest com-binations, the highest values of V85 along the length of thecombination were located at point 5, while the lowest valueswere located at point 3.

When dealing with the maximum difference between op-erating and design speeds, only the operating speed valuesalong the length of horizontal curve (which involves all or aportion of vertical curve length) were considered (i.e., speedat points 1 and 5 were not included). For sag combinations,the highest value of V85 along the length of horizontal curvewas located also at point 2. For crest combinations, the high-est values of V85 along the length of horizontal curve werelocated either at point 2 or point 4. As for determining thedesign speed, since the design speed of a sag vertical curveis based on nighttime sight distances (while this study is

based on daytime measurements), the design speed of thehorizontal curves was taken as the control design speed inthe case of sag combinations.

For crest combinations, the minimum of either horizontalcurve design speed or vertical curve design speed was takenas the control design speed. The horizontal curve designspeed was determined based on either the radius of the curveand rate of superelevation, or the radius of the curve and lat-eral clearance according to Table B.3.1.4.b or Fig. B.3.3.3bprovided by the Transportation Association of Canada (TAC1986), respectively. The minimum of these two values wastaken as the design speed of the horizontal curve. The designspeed of the crest vertical curve was determined for mini-mum stopping sight distance based on the rate of verticalcurvature according to Table B.4.2.2 provided by TAC(1986). Numerous model experiments were performed to es-tablish the model forms and the coefficients of independentparameters, and the best models are as follows:

[12] F V V V ec-sag m dHz max0.002= − − + +1 1 2( )[ln( )] ,∆R2 = 0.52

[13] F V V V ec-crest max m d0.002= − + − +1 1 0 6 3[( ) ][ln( )] ,.∆R2 = 0.52

where Vm = maximum 85th percentile operating speed alongthe horizontal curve (km/h), VdHz = design speed of horizon-tal curve (km/h), ∆Vmax = maximum reduction in the 85thpercentile operating speed along the 3D combination (km/h),Vd = minimum of either horizontal curve design speed orvertical curve design speed (km/h), and e = 2.7183.

The resulting values of R2 were significant at the 0.95confidence level, but the limitation of data points may havecaused these values to be moderate (0.52). The regressioncoefficients of independent variables were significantly dif-ferent from zero at the 0.95 confidence level and have logi-cal algebraic signs. The negative signs of these coefficientsindicate that capacity utilization decreases with the increasein either operating speed reduction or the difference betweenoperating and design speeds or both.

It should be noted that current design speed values givenby TAC (1986) and the American Association of State High-way and Transportation Officials (AASHTO 1994) are cal-culated based on 2D considerations of vehicle stability,driver comfort, and sight distance. The effect of 3D sightdistance and 3D vehicle stability on design speeds have beenconsidered in other studies (Hassan et al. 1998; Kontaratoset al. 1994), whereas the effect of 3D driver comfort on de-sign speed has not been yet considered. Therefore, upon es-tablishing the 3D design speed models that will consider theprevious three criteria, it will be more accurate to use theminimum design speed based on these models in future anal-ysis.

Typical values of FcBased on operating and design speeds, design consistency

of the different combinations was evaluated using the twoconsistency evaluation criteria suggested by Lamm et al.(1995). These criteria are as follows:(a) Good design: ∆V85 10≤ km/h or V V85 10− ≤d km/h.(b) Fair design: 10 km/h < ∆V85 20≤ km/h or 10 km/h <

V V85 20− ≤d km/h.

© 1999 NRC Canada

794 Can. J. Civ. Eng. Vol. 26, 1999

Page 7: Impact of highway consistency on capacity utilization of two-lane rural highways

(c) Poor design: ∆V85 > 20 km/h or V85 – Vd > 20 km/h.where V85 = 85th percentile operating speed (km/h), ∆V85 =reduction in the 85th percentile operating speed along thecombination (km/h), and Vd = design speed (km/h).

Operating speed reductions and operating and designspeed differences were determined for both travel directionsincluded in each combination. The average values for bothdirections were then computed and checked against the pre-vious consistency evaluation criteria. Table 2 shows the eval-uation of design consistency on sag and crest combinationsbased on the two evaluation measures. It should be notedthat the two evaluation measures did not provide the sameevaluation result for a specific roadway section as the reduc-tion in operating speed did not necessarily match the differ-ence between operating and design speeds. Therefore, it wassuggested to include the effect of these two evaluation mea-sures together in an overall criterion that reflects the effectof different speed variations on capacity utilization in termsof Fc.

Based on the models of eqs. [12] and [13], the effect ofspeed variations on Fc for sag and crest combinations can berepresented graphically as shown in Fig. 5a and b, respec-tively. This figure shows the different ranges of Fc based onthe combined effect of the two evaluation criteria. It shouldbe noted that the two figures parts are very similar, and thedifference between the two in estimating Fc is small. How-ever, the bandwidth of Fc on sag combinations was slightlylarger than that on crest combinations (bandwidth of Fc onsag combinations was about 1.2 times that on crest combina-tions). This can also be attributed to either or both of the tworeasons mentioned earlier.

Based on the two consistency evaluation criteria men-tioned earlier, typical values of Fc that reflect the designevaluation can be developed. These values were establishedto correspond with the different evaluation classes included

© 1999 NRC Canada

Gibreel et al. 795

Operating speed Operating and design speeds

Type of 3Dcombination

Highwaysection

Reductiona

(km/h) EvaluationDifferencea

(km/h) Evaluation

Sag combinations 1 6.1 Good design 19.1 Fair design2 3.8 Good design 15.3 Fair design3 3.3 Good design 10.3 Fair design4 3.3 Good design 9.5 Good design5 4.8 Good design 14.6 Fair design6 4.6 Good design 14 Fair design7 3.0 Good design 13 Fair design8 5.0 Good design 17 Fair design9 2.0 Good design 12.5 Fair design

Crest combinations 1 10.1 Fair design 18.6 Fair design2 5.5 Good design 12.9 Fair design3 6.5 Good design 16.9 Fair design4 3.5 Good design 17.5 Fair design5 2.9 Good design 14.0 Fair design6 5.0 Good design 14.0 Fair design7 7.3 Good design 12.5 Fair design8 4.9 Good design 19 Fair design9 6.5 Good design 9.1 Good design

10 6.0 Good design 11.9 Fair designaAverage of both travel directions.

Table 2. Evaluation of design consistency of the 3D alignment combinations.

F c

(a)

D = 30 km/hVmax

D = 20 km/hVmax

D = 10 km/hVmax

D = 0 km/hVmax

G-FG-P

F-P

P-P

P-F

F-F

G-G

F-G

P-G

F c

(b)

G-FG-P

F-P

P-P

P-F

F-F

G-G

F-G

P-G

G = Good DesignF = Fair DesignP = Poor Design

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20200 10 30

V Vm dHz= (km/h)

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20200 10 30

V Vm dHz= (km/h)

Fig. 5. Estimation of Fc based on speed differences: (a) sagcombinations; and (b) crest combinations.

Page 8: Impact of highway consistency on capacity utilization of two-lane rural highways

in each measure. The minimum and maximum Fc values forany area that represents a specific combined evaluation arethose values corresponding to the lower and upper cornersof the area, respectively. A summary of different Fc rangescorresponding to different evaluation results for sag andcrest combinations is shown in Table 3. In addition, the av-erage Fc value corresponding to the centre of gravity of eachevaluation area is included in parentheses.

Table 3 shows that the corresponding ranges of Fc forboth sag and crest combinations are very close. For example,when the two design evaluations were both good, Fc was ap-proximately ≥0.85 and when the two design evaluationswere both poor, Fc was approximately <0.60. In addition, theranges were also close to and interfere with each other fordifferent evaluation classes within any combination type.Therefore, it would be easier for practicing highway engi-neers to group the Fc ranges included in Table 3 in a briefform that reflects the general overall consistency evaluationof the roadway section. This overall design consistency eval-uation, which is applicable to both sag and crest combina-tions, was developed as follows:

1. The lower limit of the Fc range of the area that has agood–good design (Fc = 0.85) and the upper limit of theFc range of the area that has a poor–poor design (Fc =0.60) were taken as initial limits for the overall evalua-tion as a good and poor design, respectively.

2. If the average Fc of a specific area lay within any ofthose two ranges, this area would be considered to havean overall good or poor design, respectively.

3. The area whose average Fc did not lie within the previ-ous two ranges was considered to have an overall fairdesign.

4. The final lower limit of the Fc range of the overall gooddesign was considered equal to the average of the lowerlimits of the Fc ranges of the areas that have a good de-sign.

5. The final upper limit of the Fc range of the overall poordesign was considered equal to the average of the upperlimits of the Fc ranges of the areas that have a poor de-sign.

6. The final Fc range of the overall fair design would be setbetween the lower limit of the overall good design andthe upper limit of the overall poor design.

Based on this procedure, it was found that the overall de-sign consistency evaluation can be set as good when thecombined evaluation of both measures (reduction in operat-

ing speed and difference between operating and designspeeds) is good–good, good–fair, and fair–good, respec-tively. The overall evaluation is poor when the combinedevaluation of both measures is poor–poor and fair–poor, re-spectively. Otherwise, the design is fair. The typical Fcranges corresponding to the suggested overall evaluationwere determined as shown in Table 4. These ranges providean approximate estimation of the reduction in capacity utili-zation due to the consistency of the geometric design of aspecific 3D combination.

Design implications

It is important to account for the effect of the status ofgeometric design consistency in capacity analysis due totheir significant influence on the service flow rate. Ignoringthe effect of Fc would result in inaccurate service flow ratesthat do not represent the reality. For example, for a specificlevel of service, the reduction in the service flow rate due tothe effect of design status might reach 20% on a 3D combi-nation with a good design depending on its geometric data.For a combination with a fair design, the reduction in theservice flow rate will be more than 20% and might reach33%. Ultimately, if the design is poor, the reduction will ex-ceed 33%. Therefore, it is important to pay attention to im-proving design consistency to increase capacity utilizationon the critical sections.

In brief, to determine the range of the expected loss inservice flow rate due to design inconsistency, the followingprocedure can be applied to any 3D alignment that containscombined vertical and horizontal curves:1. Determine the 85th percentile operating speed values ei-

ther from field data or from the 3D operating speed con-sistency models by Gibreel et al. (1999b).

2. Determine the design speed from the design guidesbased on the type of combination and the geometric de-sign data.

3. Determine the maximum reduction in operating speed inaddition to the difference between operating and designspeeds.

© 1999 NRC Canada

796 Can. J. Civ. Eng. Vol. 26, 1999

Design consistency evaluationmeasure Operating speed reduction (∆Vmax) criterion

Good Fair Poor

(a) Sag combinations(Vm – VdHz) Good Fc ≥ 0.85 0.78 ≤ Fc < 0.97 (0.86) 0.74 ≤ Fc < 0.97 (0.82)

Fair 0.74 ≤ Fc < 0.98 (0.88) 0.58 ≤ Fc < 0.85 (0.76) 0.49 ≤ Fc < 0.78 (0.64)Poor 0.60 ≤ Fc < 0.96 (0.82) 0.40 ≤ Fc < 0.74 (0.55) Fc < 0.58

(b) Crest combinations(Vm – Vd) Good Fc ≥ 0.86 0.80 ≤ Fc < 0.98 (0.87) 0.73 ≤ Fc < 0.98 (0.82)

Fair 0.75 ≤ Fc < 0.96 (0.87) 0.62 ≤ Fc < 0.86 (0.74) 0.53 ≤ Fc < 0.80 (0.65)Poor 0.64 ≤ Fc < 0.93 (0.82) 0.48 ≤ Fc < 0.73 (0.62) Fc < 0.62

Table 3. Typical values of Fc for sag and crest combinations.

Good design Fair design Poor design

0.80 ≤ Fc ≤ 1 0.67 ≤ Fc < 0.80 Fc < 0.67

Table 4. Final typical values of Fc for sag and crestcombinations.

Page 9: Impact of highway consistency on capacity utilization of two-lane rural highways

4. Estimate the value of Fc using the models in eqs. [12]and [13] or Fig. 5.

5. If the operating speed cannot be accurately estimated ormeasured, use Tables 3 and 4 to obtain a general guide-line for the expected range of Fc.

Numerical exampleAn illustrative example is introduced to show the effect of

changing the design status on capacity utilization using a sagand a crest combinations. Consider a sag combination thathas r = 875 m, E = 2.4%, G1 = –2.5%, G2 = 1%, Lv =120 m, L0 = 82 m, and K = 34 m, and a crest combinationthat has r = 875 m, E = 2.4%, G1 = 2.25%, G2 = –0.9%, Lv =280 m, L0 = 138 m, and K = 89 m. Using the 3D models byGibreel et al. (1999b) and Tables B.3.1.4.b and B.4.2.2 pro-vided by TAC (1986), Vm, VdHz, and ∆Vmax are 102, 60, and2 km/h on the sag combination, while Vm, Vd , and ∆Vmax are98.5, 60, and 11.5 km/h on the crest combination. Accord-ingly, V Vm dHz− and V Vm d− equal 42 and 38.5 km/h, for sagand crest combinations, respectively. Thus, based on theoverall consistency evaluation, the design of both combina-tions was evaluated as fair and poor, respectively.

Assume that an improvement of vehicle stability anddriver comfort has occurred on these sections. This can takeplace as a result of increasing the superelevation rate ofthese sections (for example, E = 4.5% instead of 2.4%)while all other geometric parameters have not changed. Sim-ilarly, using the models and tables mentioned earlier, Vm,VdHz, and ∆Vmax are 103.5, 94, and 3.3 km/h on the sag com-bination, while Vm, Vd , and ∆Vmax are 99, 90, and 6.5 km/hon the crest combination. Consequently, Vm – VdHz and Vm –Vd equal 9.5 and 9 km/h, for sag and crest combinations, re-spectively. Thus, the design of both combinations was evalu-ated as good based on the overall consistency evaluation.

Definite values for the drop in the service flow rate can beobtained using the models of eqs. [12] and [13]. The dropsin the service flow rate of the sag and crest combinationsdue to the original geometric design are 21 and 47%, respec-tively, while those calculated after the improvement has beenoccurred are 7 and 10%, respectively. Thus, an increase inthe superelevation rate of about 46% of its original value hascaused the service flow rate on the sag and crest combina-tions to gain additional 14 and 37% of its value, respectively.

As an alternative, the overall consistency evaluation of thesag combination, due to E equal to 4.5 and 2.4%, is goodand fair, respectively, while the overall evaluation of thecrest combination, due to the same values of E, is good andpoor, respectively. Based on Table 4, the expected loss inservice flow rate can reach 20% (with E = 4.5%) and 33%(with E = 2.4%) for the sag combination. Also, the expectedloss in service flow rate for the crest combination can reach20% (with E = 4.5%) and will exceed 33% (with E = 2.4%).In other words, the improvement in the superelevation ratecan produce a maximum gain in the service flow rate of33% in the case of the sag combination, while it can producea minimum gain in the service flow rate of 13% in the caseof the crest combination. These results totally conform withthe previous results obtained when using the models ineqs. [12] and [13]. This numerical example illustrates theimportance of the effect of design inconsistency on reducingcapacity utilization in terms of service flow rate.

Conclusions

Among the points that have not been covered in the previ-ous research work on highway design consistency is the re-lationship between highway design consistency and capacity.This paper presents a methodology based on 3D analysis ofcombined highway alignments to investigate the interactionbetween highway consistency and capacity. The study wasperformed on two-lane rural highways using data collectedat daytime in Ontario. The results of this study should proveuseful to highway design and traffic engineers in evaluatingthe cost effectiveness of a more consistent geometric designto extend the service life of two-lane highways. Based onthis study, the following comments are offered.1. The inconsistency of highway geometric design has a

negative effect on highway capacity utilization, andtherefore ignoring its effect will produce inaccurate val-ues of the service flow rate. In other words, the more in-consistent the highway design, the higher the loss in theservice flow rate.

2. The effect of highway design consistency on the serviceflow rate has been reflected by including an additionaladjustment factor, called consistency factor (Fc), in theconventional service flow formula. The consistency fac-tor should be used, in addition to other adjustment fac-tors for directional distribution, narrow lanes andrestricted shoulders, and heavy vehicles, to estimate thetrue service flow rate under a specific level of service on3D alignment combinations.

3. Two statistical models were developed to estimate theconsistency factor for the sag and crest combinationsbased on geometric design data. Three geometric pa-rameters were found to have a significant effect on theestimation of Fc: radius of horizontal curve, rate of ver-tical curvature, and distance between point of verticalintersection and point of horizontal intersection. Twoadditional models were also developed to estimate Fcbased on the change in operating speed and the differ-ence between operating and design speeds along sagand crest combinations. Consequently, accurate valuesof the consistency factor can be obtained from thesemodels to determine the expected loss in the serviceflow rate due to design inconsistencies.

4. The models of the consistency factor showed logical ex-planations for the effect of each independent variable onthe prediction of Fc. All the coefficients of the inde-pendent variables were significant at the 0.95 confidencelevel.

5. An overall consistency evaluation criterion was pro-posed based on speed variations, according to whichtypical values of Fc were obtained. These typical valuescan be used to determine the approximate loss in serviceflow rate if available speed data are not accurate.

6. This study was limited to two types of 3D combinedalignments on two-lane rural highways: a sag verticalcurve combined with a horizontal curve and a crest ver-tical curve combined with a horizontal curve. Future re-search work should consider other types of 3Dalignment combinations so that the effect of design in-consistency on capacity utilization can be determinedfor any pattern of 3D alignment combination. The pre-

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Gibreel et al. 797

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798 Can. J. Civ. Eng. Vol. 26, 1999

sented methodology can also be applied to the data al-ready collected by other researchers for 2D horizontalalignments.

It is recommended that future research include more datapoints along the various highway combination sections todetermine whether the resulting coefficient of determinationcan be improved. Future research may also focus on deter-mining the cost effectiveness of highway design consistencyimprovements in extending the service life of two-lane ruralhighways.

The developed methodology for the consistency factor as-sumes that other adjustment factors in the service flow for-mula are correct. A more comprehensive research approachis needed to examine all the adjustment factors that affectservice flow on two-lane highways, with possible consider-ation of factorial design. Until such a comprehensive analy-sis is done, caution is needed in applying the developedconsistency factor in practice.

Acknowledgments

This research was financially supported by the EgyptianGovernment and the Natural Sciences and Engineering Re-search Council of Canada.

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