In order to reduce road fatalities as maximum as possible, this paper presents a new methodology toevaluate road safety in both design and redesign stages of two-lane rural highways. This methodology isbased on the analysis of road geometric design consistency, a value which will be a surrogate measure ofthe safety level of the two-lane rural road segment. The consistency model presented in this paper is basedon the consideration of continuous operating speed profiles. The models used for their construction havebeen obtained by using an innovative GPS-data collecting method, based on continuous operating speedprofiles recorded from individual drivers. This new methodology allowed the researchers to observe theactual behavior of drivers and to develop more accurate operating speed models than those which arebased on spot-speed data collection. This means a more accurate approximation to the real phenomenon,and thus a better consistency measurement.
Operating speed profiles were built for 33 Spanish two-lane rural road segments, and several consis-tency measurements based on the global and local operating speed were checked. The final consistencymodel takes into account not only the global dispersion of the operating speed, but also some indexes
that consider both local speed decelerations and speeds over posted speeds.
For the development of the consistency model, the crash frequency for all sites was considered, obtain-ing a model directly related to safety. This allows estimating the number of crashes of a road segmentby means of the calculation of its geometric design consistency. Consequently, the present consistencyevaluation method becomes an innovative tool that can be used as a surrogate measure to estimate road
safety of a road segment.
. Introduction
Road safety is one of the most important problems in our society.very year 1.2 million of people are killed and between 20 and0 million people are injured in road accidents. If current trendsontinue road traffic accidents are predicted to be the third leadingontributor to the global burden of disease and injury by 2020. Inpain approximately 78.5% of rural road accident fatalities occur onwo-lane rural roads.
Three factors may have influence on the appearance of a roadccident: human factor, vehicle factor and road infrastructure fac-
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
or. Some research pointed out that the infrastructure factor isehind over 30% of road crashes (Treat et al., 1979). In fact, pre-ious research has shown that collisions tend to concentrate at
certain road segments, showing that road characteristics play amajor role at some accidents. One of the main reasons of accidentoccurrence can be the lack of geometric design consistency. Roadgeometric consistency can be defined as how drivers’ expectanciesand road behavior fit. A road with a good consistency level showsa high similarity between drivers’ expectations and road behav-ior, so road users will not be surprised while driving along it. Apoor consistency means bad fitting, surprising events and also ahigh speed variability along different road segments and among dif-ferent drivers, increasing the likelihood of crashes. Self-explainingroads are those ones designed to be easily interpreted by driversand hence to induce adequate drivers’ behavior. Although the con-cept of consistency or self-explaining roads is not widely spread,most guidelines include ways for producing better and more con-sistent roads (Weber and Matena, 2008).
Most of the research and development of design consistencymeasures focuses on four main areas: operating speed, vehicle sta-
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
bility, alignment indices and driver workload (Ng and Sayed, 2004;Awata and Hassan, 2002).
Operating speed evaluation is the most commonly used criteriato evaluate highway design consistency (Gibreel et al., 1999). The
2 F.J. Camacho-Torregrosa et al. / Accident Analysis and Prevention xxx (2012) xxx– xxx
Table 1Thresholds for a determination of design consistency quality. Lamm’s criteria I & II.
Consistency rating Criterion I (km/h) Criterion II (km/h)
Good |v85 − vd| ≤ 10∣∣v85i
− v85i+1
∣∣ ≤ 10∣ ∣
osmcborttaoo(aai
ctsca
cards
|emdoT
ac
tgs(ssta
wfiwmmbc
v
Table 2Thresholds for a determination of design consistency quality.
Design consistency quality (m/s) C = e−0.278·[Ra·�/3.6]
Good Acceptable Poor
Fair 10 < |v85 − vd| ≤ 20 10 < ∣v85i− v85i+1
∣ ≤ 20
Poor |v85 − vd| > 20∣∣v85i
− v85i+1
∣∣ > 20
perating speed, often defined as the 85th percentile speed (v85) of aample of vehicles under free-flow conditions, can be estimated byeans of operating speed models. This specific measure of speed
an be used for consistency evaluation by examining disparitiesetween design speed (vd) and operating speed or examining theperating speed decrement between successive elements of theoad (�v85). Tangent-to-curve transitions are the most critical loca-ions when considering safety measures. In fact, it is estimatedhat more than 50% of all fatalities on rural highways take placet curved sections (Lamm et al., 1992). Consistency models basedn operating speed evaluation are the most widely used becausef the large amount of operating speed models existing worldwidea summary can be seen at Transportation Research Board, 2011nd Fitzpatrick et al., 2000). These models are a powerful tool toccurately estimate drivers’ operating speed profiles and thus fordentifying sudden decelerations or important speed dispersion.
Leisch and Leisch (1977) recommended a revised design speedoncept that included guidelines on both operating speed reduc-ions and differentials between design and operating speeds. In theame way, Kanellaidis et al. (1990) suggested that a good designan be achieved when the difference between v85 on the tangentnd the following curve does not exceed 10 km/h.
However, the most commonly used method to evaluate roadonsistency was developed by Lamm et al. (1999) based on meanccident rates. They presented two design consistency criteriaelated to operating speed, which include the difference betweenesign and operating speed and the difference between operatingpeeds on successive elements.
The difference between operating speed and design speedv85–vd| is a good indicator of the consistency at a single geometriclement, while the speed reduction between two successive geo-etric elements (�v85) indicates the inconsistency experienced by
rivers when traveling from one geometric element to the nextne. Consistency thresholds for Criteria I and II are summarized inable 1.
Although most consistency criteria give thresholds for good, fairnd poor design consistency, other authors (Hassan, 2004) suggestontinuous functions as a better tool for designers.
The consistency criteria previously presented allow evaluatinghe design consistency and estimating road safety only in a roadeometric element or in a transition between two of them. Othertudies, such as the one carried out by Polus and Mattar-Habib2004), used continuous speed profiles to determine the globalpeed variation along a road segment. In this case, a single con-istency value for the whole road segment is obtained. Moreover,heir design consistency index is a continuous function instead of
threshold-based methodology.They developed two new consistency measures. The first one
as the relative area bounded between the operating speed pro-le and the average weighted operating speed (Ra). The second oneas the standard deviation of the operating speeds at every geo-etric elements along the whole road segment (�). This additionaleasure was used in order to complement the first one because Ra
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
y itself provided similar results for somewhat different geometricharacteristics in a few cases.
The final consistency model was developed based on both pre-ious indicators. Thresholds for good, acceptable, and poor design
C > 20 1 < C ≤ 2 C ≤ 1
consistency of any road segment were proposed (Table 2). The Ra
and � on several test sections provided a similar assessment ofconsistency as Lamm’s measures.
The geographic environment at which consistency variables andtheir relationships to crash rates are obtained is also important.Extrapolation must be carried out carefully. For example, furthertest for the applicability of Lamm’s criteria revealed that a 20 km/hlimit for poor design is applicable to Korea (Lee et al., 2000), but adifferent limit was recommended for Italy (Cafiso, 2000).
Other method to evaluate geometric design consistency is theanalysis of vehicle stability. When insufficient side friction is pro-vided at a horizontal curve, vehicles may skid out, rollover or beinvolved in head-on accidents. According to this statement, loca-tions that do not provide enough vehicle stability can be consideredas inconsistent.
In this context, Lamm et al. (1999) presented a design consis-tency criterion which includes the difference between the assumedside friction provided by the curve and the side friction demandedby vehicles. The difference between assumed side friction (fRA, thatdepends on the design speed) and the demanded one (fRD, thatdepends on the operating speed), denoted as �fR, was used to rep-resent vehicle stability at Lamm’s criterion III. According to thiscriterion, consistency is considered good when �fR is higher than0.01, fair when its value is between 0.01 and −0.014, and poor when�fR is lower than −0.04.
A simpler approach to evaluate design consistency is by meansof the use of alignment indices (Hassan, 2004). They are quanti-tative measurements of the general character of a road section’salignment. Examples of alignment indices include average radius(AR), ratio between maximum and minimum radius (RR), averagerate of vertical curvature (AVC) and CRR (defined as the ratio ofradius of a single horizontal curve to the average radius of theentire section). Analyses of collisions on two-lane rural highwayshave shown that a significant relationship exists between collisionfrequency and alignment indices (Hassan, 2004).
The last approach for evaluating geometric design consistencyis by means of drivers’ workload. Driver workload is defined asthe rate of time at which drivers must perform a given amountof driving tasks. It increases as long as the complexity in highwaygeometric features increases (Gibreel et al., 1999). Driver workloadmay be a more appealing approach for identifying inconsistenciesthan operating speed because it is an indicator of the effort thatthe roadway requires from drivers; whereas the operating speedis only a measurable output of the driving task (Ng and Sayed,2004). Several methods and approaches have been tried to modeldriver workload including visual demand (VD) and workload rating(Hassan, 2004). However, drivers’ workload evaluation is much lessused than other consistency evaluation methodologies because ofits higher difficulty for measuring.
Several research have studied the effect of geometric designconsistency on road safety. Anderson et al. (1999) analyzed therelationship between design consistency and safety using loglin-ear regression models. They developed two models that relatedaccident frequency to traffic volume, curve length, and speed reduc-
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
tion (�v85). A separate model relating accident frequency to curvelength and CRR was also obtained.
Ng and Sayed (2004) investigated the effects of several designconsistency measures on safety. These variables were v85 − vd,
v85, �fR, CRR and visual demand. They also developed some mod-ls for estimating road safety depending on such indicators.
Finally, it is worth to highlight the study carried out by Cafisot al. (2007). They presented a methodological approach for theafety evaluation of two-lane rural highway segments combiningwo different procedures based on design consistency evaluationnd safety inspection processes.
They developed a safety index (SI) that measured the relativeafety performance of a road segment. The SI is combined threeisk components: the exposure of road users to road hazards, therobability of a vehicle to be involved in a road accident and theesulting consequences of such accident.
They performed several comparisons between SI and EB (Empir-cal Bayes) safety estimations. Both results were comparable, hencealidating their new indicator.
. Objectives
Different studies show that improving design consistency leadso safer roads. The objective of this study is to develop a new designonsistency model that may be used as a surrogate measure for roadafety evaluation for two-lane rural roads.
A set of 65 two-lane rural road segments was selected in Spain.eometry data, crash data and traffic volumes were obtained for
hose road segments.The design consistency parameter will be based on continuous
perating speed models, developed in previous research through annnovative technique that uses GPS devices placed on actual drivers’ehicles. Thus, operating speed profiles are more accurate, bettereflecting actual drivers’ behavior.
Several measures will be obtained based on operating speedrofiles, with the aim of obtaining a single consistency value forhe whole road segment instead of focusing only on individual oronsecutive road geometric elements.
The crash frequency will also be considered in the developmentf the model. Consequently, a relationship between consistencynd crash rate will be obtained, being an important tool to assistngineers to design safer roads.
Finally, a road segment with consistency problems is shown,howing the estimated number of crashes. A redesigned road seg-ent is proposed, with a better consistency value and a lower
mount of estimated accidents.
. Data description and methodology
.1. Data description: road segments characteristics, trafficolume, crash data
A set of 65 two-lane, rural road highway segments was selectedn the Valencian Region of Spain. All road segments were 2–5 kmong. None of the road segments presented curves with radiusower than 70 m. Longitudinal grades were lower than 5%. Nonef the selected road segments presented important intersectionshat could dramatically vary their traffic volume or their operat-ng speed. Some of the requirements are because of the operatingpeed model later applied.
Traffic data volume was downloaded from the official website ofhe Valencian local government. It consisted on traffic data duringast 15 years for all road segments. This large database was verymportant for the research, but it had to be handled with care,
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
ecause of the possible presence of redesigned road segments dur-ng this period of time. Traffic volumes for all road segments werenalyzed in order to determine irregular variations of the AADTlong years. The history of building works for all road segments was
PRESSsis and Prevention xxx (2012) xxx– xxx 3
also examined. Thus, some specific years or road segments were nolonger considered in the analysis.
Crash data was also provided by the Valencian local government.It consisted on a list of all reported crashes during last 13 years,characterized by location, date and time, daylight conditions, crashseverity, vehicle type, driver characteristics, external factors, causesof the accident and other conditions. Considering all data, a filteringprocess was performed, discarding all accidents that presented atleast one of the following issues:
• Crashes that took place during years not considered in the trafficvolume data.
• Property damage only (PDO) accidents. In order to prevent biasdue to underreporting problems, only accidents with victimswere considered.
• The causes for all accidents were examined, taking out from theanalysis those related to external factors (e.g. due to previousillness of the driver, or animals crossing the road), or intersections(because the consistency model does not consider this type ofaccident). Although the most frequent consistency-related typeof accident is run-of-the road accidents, all accident types wereconsidered in order to not bias the results.
3.2. Operating speed models
The operating speed profiles were obtained using the operat-ing speed models developed by Pérez et al. (2010). This operatingspeed profile model consists of two operating speed models: onefor horizontal curves and other for tangents. The final operatingspeed profile is built by means of some construction rules and anacceleration and deceleration rates. These rates are calculated bytwo additional models.
This operating speed model presents the advantage that it wasobtained by considering continuous speed profiles from individualdrivers, by using GPS devices. It allowed to accurately determinethe starting and ending points of all speed transitions, and alsothe actual maximum and minimum speeds for the different roadgeometric elements. A procedure was also carried out in order toensure that drivers were not biased by the presence of GPS devices.
The operating speed model for curves uses the radius as explana-tory variable. Two different models were developed, for radiushigher or lower than 400 m (the minimum radius is 70 m).
v85 = 97.4254 − 3310.94R
; 400 m < R ≤ 950 m (1)
v85 = 102.048 − 3990.26R
70 m < R ≤ 400 m (2)
where v85: operating speed on curve (km/h); R: radius (m)An operating speed model for tangents was also developed,
considering the length of the tangent and the operating speed ofthe previous curve. It was noticed that all drivers tended to reach adesired speed, set to 110 km/h. However, depending on the lengthof the tangent they could accelerate more or less departing from theoperating speed of the previous curve. Thus, the higher the lengthof the tangent, the closer its operating and the desired speeds are.
v85T = v85C + (1 − e−�.L) · (vdes − v85C ) (3)
where � = 0.00135 + (R − 100) · 7.00625 × 10−6; v85C: operatingspeed on previous curve (km/h); v85T: operating speed on tangent(km/h); vdes: desired speed (110 km/h); R: horizontal curve radius(m); L: length of the tangent (m)
Deceleration rates were obtained by Pérez et al. (2011), while
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
acceleration rates have been obtained in this research using thesame methodology. Most previous operating speed models giveconstant rates, regardless of the characteristics of the adjacentcurves. One exception is the operating speed model presented by
Table 3Negative binomial model of accident frequency.
Independent variable Coefficient t-statistics
Intercept −4.9462 <.0001Log of the length of road segment (km) 0.8645 0.0021Log of AADT per lane 0.7683 <.0001Rmin/AR −0.7285 0.0842Overdispersion 0.1519Number of sections 43Log likelihood at zero 167.8662Log likelihood at convergence −94.5553
ARTICLEAP-2915; No. of Pages 10
F.J. Camacho-Torregrosa et al. / Acciden
archionna and Perco (2008), where the radius of the preceding orhe following curves are considered. Like in this case, two modelsre presented for determining the deceleration and decelerationates depending on the adjacent curve radius. In both cases, theadius of the preceding or the following curve are considered (Eqs.4) and (5)).
These deceleration and acceleration rates were obtained byonsidering individually each driver, selecting the specific pointst which speed variations started and ended, instead of consid-ring the same speed transition length for all drivers. Thus, thecceleration and deceleration rates reflect better drivers’ behavior.
.3. Operating speed profiles construction
A computer program was developed in order to calculate theperating speed profile for each road segment, both in forwardnd backward directions. In order to do so, it was first necessaryo obtain the horizontal alignment for all road segments. Geom-try data consisted of the GPS coordinates of the axis of all roadegments. The procedure for determining the horizontal alignmentas described at Pérez et al. (2010). This methodology is performed
n two steps:
The first one takes the successive points of the axis and deter-mines the local curvature. This calculation is performed not onlywith three but more points at each location. Thus, the resultsattained are much more accurate. Finally, an unprocessed curva-ture diagram is obtained.The second step takes the previous curvature diagram and trans-forms it into a final diagram, composed by straight segments thatrepresent the successive tangents, spiral transitions and circularcurves.
fter processing all road segments, some of them were found tohow errors in their coordinates, so they were removed from thenalysis. Therefore, the final number of road segments was reducedrom 65 down to 43.
Once the horizontal alignment was determined for all road seg-ents, their operating speed profiles were plotted, by using the
perating speed model presented above.
. Development
The consistency model was calibrated by means of relating itsalue to the crash rates for all road segments. Thus, the numberf road crashes had to be determined. Once the operating speedrofiles were plotted for all road segments, some indicators werextracted from them in order to analyze their relationship to theirrash rate.
.1. Determination of the number of crashes
For almost all road segments, accident data was available for3 years. In order to improve the accuracy of the model, a Safetyerformance Function for estimating the number of accidents at
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
wo lane rural road segments for a 10 years period of time waseveloped. A logistic, negative binomial regression was calibrated,onsidering exposure units (length and AADT) and one alignmentndex (Table 3).
Pearson �2 38.9802AIC 199.1107
Four alignment indices were obtained for all road segments:Average Radius (AR), Curvature Change Ratio (CCR), Ratio betweenmaximum and minimum radius of the road segment (RR), and ratiobetween the minimum radius and the average radius of the roadsegment (Rmin/AR). Different regressions were performed consid-ering the exposure and each one of the alignment indices. Finally,only the last one showed a significant effect over safety, so it wasincluded in the final form of the Safety Performance Function:
where Yi, 10: estimated number of crashes in 10 years for the roadsegment; L: length of the road segment (km); AADT: mean valueof average annual daily traffic for 10 years (veh/day); Rmin: min-imum radius of the road segment (m); AR: average radius of theroad segment (m).
Considering the expected number of accidents by the SPF andthe actual number of accidents that took place at the different roadsegments, the Empirical Bayes method was used to estimate thefinal number of accidents for each road segment. Crash rates (acci-dents with victims per 106 veh-km) were determined for each roadsegment. The overdispersion parameter of the safety performancefunction was � = 0.1519. Then, k = 1/� = 6.5832. As expected, thenumber of accidents increased and the accident rate decreased asthe AADT did (Weber and Matena, 2008).
The Empirical Bayes Method is formulated as follows:
E(
�
r
)= ̨ · � + (1 − ˛) · r (7)
where ̨ = 1/(1+�/k); �: number of accidents estimated by the safetyperformance function; r: number of observed crashes for the spe-cific site.
4.2. Analysis of the operating speed profiles
The operating speed profiles were developed for all road seg-ments considering both directions. Some measures relating speeddispersion and deceleration performance were obtained, in orderto resume the drivers’ behavior. Speed limits for all road segmentswere also examined, and some variables considering the speed dis-persion and the speed limit were also evaluated. The final amountof variables analyzed was 14.
The average value (v̄85) and the standard deviation (�85) of everyoperating speed profile were obtained in first place. The first onewas determined in order to be an indicator of the overall speedalong the road segment, whereas the second one was for deter-mining the global dispersion of the operating speed. The higher thedispersion is, the more inconsistent the road segment is expected to
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
be. Both measures were obtained after building the operating speedprofile, also considering the speed transitions. Calculations wereperformed meter-by-meter, for both directions and not consideringindividually each geometric element of the road segment.
Considering the operating speed profiles, average speed andosted speed, some derived indicators were obtained:
Ra (m/s). First introduced by Polus and Mattar-Habib (2004), itmeasures the area bounded by the operating speed profile andthe average operating speed of each road segment, divided bythe road length. Thus, it is an indicator of the global variabilityof the speed, presenting higher values as the speed variabilityincreases.Ea,10 (m/s). It is also a measurement of the speed dispersion. Likethe previous measure, it is the area bounded by the operatingspeed profile and the average operating speed profile plus andminus 10 km/h. It is finally divided by the length of the roadsegment.Ea,20 (m/s). Similar to the previous indicator, but considering20 km/h.L10. Length of the road segment at which the absolute differencebetween the operating speed and the average operating speed ishigher than 10 km/h divided by the length of the road segment.L20. Like the previous variable, but using 20 km/h.
By means of the operating speed profiles, it was also easy todentify and analyze all the speed decrement transitions. They wereetected for all road segments, calculating the speed differentialkm/h) in absolute value (�v85), and the distance (m) used for eachpeed transition (L�v85
). All decelerations lower than 1 km/h wereot considered, because users might not perceive them. Some roadegments presented very few decelerations. Those road segmentsere also taken out from the analysis, because they behaved in a
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
ery different way than the others. Thus, the final number of roadegments to be analyzed was 33. Table 4 shows the main charac-eristics of alignment, traffic volume and crash data for each roadegment.
PRESSsis and Prevention xxx (2012) xxx– xxx 5
Considering all deceleration processes for each road segment inboth directions, the following variables were obtained:
• Average speed reduction (�v85). Average value of all speed reduc-tion processes at each road segment. Road segments are expectedto be more inconsistent as long as this variable increases, becauseof the higher speed reductions.
• Standard deviation of speed reductions (��v85). It measures the
standard deviation of the speed reductions for each road segment.Drivers’ behavior is expected to be more disperse with highervalues of this variable, reducing the consistency level of the roadsegment.
• Deceleration average distance (L�v85). Average value of the dis-
tances used for reducing speed in a road segment. Due toacceleration and deceleration rates are obtained from geome-try relationships, similar speed differentials could be achieved bymeans of different distances. Thus, this measure could add morevariability to the average deceleration value in its relationship tocrash rates.
• Speed reduction intensity (d�v85). For all individual speed reduc-
tion processes, the speed reduction amount was divided by itscorresponding length, determining the individual speed reduc-tion intensity (d�v85
, km/h/m). This variable represents theaverage value for each road segment.
• Deceleration length rate (Ld). It is an indicator of the distanceat which the road segment’s speed profile is under decelerationconditions. It is obtained by adding the individual decelerationlengths on a road segment and dividing it by its total length.
Considering the speed limits for all road segments, two newvariables were determined:
• Difference between the average operating speed and the speedlimit (�v85−l). The speed limit has been obtained considering alldifferent posted speed limits with their corresponding lengths. Itis intended to be an auxiliary variable for helping other indicatorsto add correlation to the final model.
• Ea,1 (m/s). As Ea,10 and Ea,20, this variable is the area bounded bythe operating speed and the speed limit for the road segment. Itis finally divided by the road segment length.
5. Results and discussion
Some indicators obtained above were correlated among them,showing some interesting relationships. For instance, the averagespeed reduction and its standard deviation were highly correlated:higher speed reduction values usually present higher variability.
Fig. 1 shows the average standard deviation value of operat-ing speed of all road segments plotted against the average value ofoperating speed. Different colors show different crash rates. Bothvariables are correlated, since their values increase together. More-over, higher values of both variables yield to more hazardous roads,validating previous assumptions.
Ra also presented a high correlation with the average oper-ating speed. The hypothesis is that, at road segments composedby sharp curves and short tangents, drivers are constrained bythe road geometry and they cannot develop their desired speed,usually leading to lower operating speeds and a small speed disper-sion. Thus, the Ra variable, which measures the speed variability,presents a low value. At road segments where the geometry doesnot constrain drivers, operating speeds are higher, resulting into
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
lower speed variability and thus, into lower Ra values. So, the max-imum values of Ra are reached with medium operating speeds. Agraphical representation is shown in Fig. 2. Maximum crash ratesare also related to higher values of Ra.
6 F.J. Camacho-Torregrosa et al. / Accident Analysis and Prevention xxx (2012) xxx– xxx
deviat
oprgs
Fig. 1. Average value vs. standard
Considering all 14 variables, a correlation analysis was carriedut in order to determine which variables represented the samehenomena. The correlation matrix is shown in Table 5. High cor-elations (coefficients higher than 0.70) are highlighted in dark
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
ray, while medium correlations (coefficients higher than 0.50) arehown in light gray.
The following correlations are found:
Fig. 2. Ra vs. average o
ion of operating speed reductions.
• �85, Ra, L10, L20, Ea,10, Ea,20 and ��v85present high correlation val-
ues. Ra was previously used by Polus and Mattar-Habib (2004) asa way to quantify the speed dispersion. Compared to the rest ofthe variables, it presented a slightly higher correlation and behav-
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
ior with road accidents than other variables. Thus, this variable isselected for further research.
Table 6Calibrated models for ECR by individual variable.
Variable Model R2
Ra ECR = 12.22562+5.46248/Ra
30.9%
ECR = e−1.00383 · e−0.988661/Ra 24.9%
ECR = e−1.89911 · R0.497538a 24.4%
v85 ECR = 1
2.00006+0.000429405·v285
31.7%
ECR = e−0.915549 · e−0.0000860305·v285 31.3%
ECR = e1.81969 · v−0.7576385 25.8%
Ld ECR = 13.16716+27.9187·L2
d
10.6%
ECR = e−1.23859 · e−3.65402·L2
d 4.5%
ECR = e−1.70654 · L−0.186688d
1.5%
�v85ECR = 1
0.524925+46.9038/�v8530.9%
ECR = e−0.675934 · e−8.72905·�v85 26.3%
ECR = e0.407621 · �v854.51153
25.9%
Ea,l ECR = 0.292265 − 0.0196406 · Ea,l 5.7%
ECR = e−1.31034 · e−0.0692368·Ea,l 4.7%
ECR = e−1.42202 · E0.0448093a,l
2.7%
Table 7Final calibrated models for ECR.
Model number Expression R2
1 ECR = 12.65897+(0.0570069/(Ra/v̄2
85))
39.8%
2 ECR = 1
3.00826+0.00056031/Ra/v285
42.3%
3 ECR = e0.00516932 ·(
Ra
v85
)0.43191935.8%
4 ECR = 13.18601+33.4686/Ra ·v85
32.8%
5 ECR = 1
3.11287+0.0273507·v85/�v852 45.7%
6 ECR = e−0.866762 · e−0.085472· v85
�v8540.1%
7 ECR = 1
3.36708+0.0000029176·(v285/�v85)
2 48.2%
d�v85−0.975 0.447 0.437 0.415 0.369 0.409
�v85−l 0.691 −0.067 −0.048 −0.031 0.004 0.001
Ea,l 0.453 0.21 0.228 0.266 0.247 0.263
L�v85, d�v85
and v̄85. They present high correlation values, so onlythe operating speed average value is considered for further anal-yses. The other two variables are more difficult to be determinedand they may be also very variable depending on the operatingspeed model.�v85. It is medium-correlated with other variables. As the cor-relation is medium, it is suggested to be maintained for furthersteps.Ld. This variable is not correlated to any other variable, so it ismaintained.Limit speed related variables are correlated among them, and alsoa medium correlation is found with the average operating speed.Then, Ea,1 is suggested for consideration.
Hence, the variables that will be chosen for the next step are theollowing:
Ra
Average operating speed (v̄85)Percentage of road segment under deceleration conditions (Ld).Average speed reduction (�v85).Ea,1
It is important to point out that the Global Consistency Modeleveloped by Polus and Mattar-Habib (2004) consists on a com-ination of Ra and �. As stated above, both variables are highlyorrelated. Then, it is suggested to use only one of them andombine it with another indicator, probably obtaining a highertatistical significance.
Considering the previous variables, several models werehecked in order to analyze the relationship between the Estimatedrash Rate (ECR) and all variables separately. Those models arehown in Table 6.
As can be seen in Table 6, variables with higher correlation torash Rate are Ra, v̄85 and �v85. The other variables presented aeak relationship to crash rate and were not considered for fitting
he final models.Considering only the best variables, additional models were
hecked, always combining them into a single indicator. Thoseodels are shown in Table 7.The strongest correlation to the crash rate is given by the divi-
ion of the squared average operating speed and the average speededuction value. Once the main expression was obtained, severalttempts were carried out to add any of the two variables that wereaken out from this step, but no good results were achieved.
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
Thus, the proposed design consistency index is the following:
= v285
�v85(8)
8 ECR = 1
2.40939+0.00403287·v285/�v85
46.3%
The speed average value is given in km/h, and also is the averagespeed reduction value. Thus, the final index is given in km/h.
Analyzing its composition, road segments presenting loweraverage speed reduction values lead to higher consistency values,due to their more homogeneous speed. Higher operating speedaverage values are associated to better, more consistent roads for
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
the same speed reduction values.It is worth to point out that this model considers both
the average speed and its variability. As a difference to other
8 F.J. Camacho-Torregrosa et al. / Accident Analysis and Prevention xxx (2012) xxx– xxx
sh rat
ci
iSrAhstr
TH
Fig. 3. Estimated cra
onsistency models, only decelerations are considered, representedn the standard deviation of the operating speed.
After determining the composition of the consistency model,t is now necessary to determine its relationship to safety.ince the consistency model has been fitted according to crashates, the expressions are already obtained (models 7 and 8).s can be seen in Table 6, the model 7 presents a slightlyigher correlation than model 8, but for low-consistent road
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
egments model 8 behaves slightly better. Both models are plot-ed in Fig. 3, but model 8 is finally chosen for estimating crashates.
able 8orizontal alignments for the initial road segment and the proposed redesign.
In Fig. 3, the estimated crash rates for all road segments areplotted as a function of their consistency index.
6. Practical example
In order to show how to use this new consistency model, anexample is shown. It consist on a road segment of about 1.7 km
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
long, which presents some safety problems. A redesign has to becarried out. In this example, one solution is presented and its safetylevel calculation is performed.
Table 8 shows the horizontal alignments for both road segments.
F.J. Camacho-Torregrosa et al. / Accident Analysis and Prevention xxx (2012) xxx– xxx 9
Fig. 4. Operating speed profiles for the exis
Table 9Estimation of the crash rate for both road segments.
v̄85 �v̄85 C ECR
n
trlA
0rcot
7
stdf
ts(
sostmidp
Before 81.23 16.63 396.75 0.24941After 86.93 8.05 938.25 0.16146
Fig. 4 shows the operating speed profiles for both alignments,ecessary for determining the consistency evaluation.
Fig. 4 only shows one direction of travel, but both of them haveo be considered. The average operating speed and average speededuction are calculated for both road segments. The consistencyevel is finally obtained, which allows us to estimate the crash rate.ll results are shown in Table 9.
In this case, the expected number of accidents is reduced from.249 to 0.161 accidents with victims per 106 vehicles-km, whichepresents a moderate increase of road safety. This result can beonsidered in the selection of alternatives stage, together withther considerations (benefit/cost ratio, environmental impacts ofhe solution, etc.).
. Conclusions
Road fatalities are one of the most important problems in ourociety, causing thousands of victims every year. To contribute withhe improvement of the road safety, this paper presents a newesign consistency model that may be used as a surrogate measureor road safety evaluation of two-lane rural roads.
The consistency model has been obtained analyzing the rela-ionship between crash data and operating speed measures ofeveral two-lane rural road segments in the Valencian RegionSpain).
The variables considered are not only related to the operatingpeed, but also to the deceleration behavior and the posted speedf road segments. All of them have been obtained from operatingpeed profiles built considering operating speed and decelera-ion/acceleration models developed in previous research. Those
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
odels were calibrated with continuous speed data recorded by annnovative technique that uses GPS devices for monitoring actualrivers’ behavior. Thus, operating speed profiles are more accurate,resenting better approximation to the actual behavior of drivers.
ting road and the redesign proposal.
In order to determine the number of crashes, a Safety Per-formance Function was calibrated, showing an overdispersion of0.1519. Then, based on this parameter and the observed crashes,the Empirical Bayes methodology was applied to estimate moreaccurately the number of accidents and thus the crash frequencies.
14 variables were obtained from analyzing the operating speedprofiles and speed limits for all road segments. A correlation analy-sis was carried out in order to reduce the final amount of parametersdown to five. Some interesting relationships were also foundamong variables, such as higher crash rates reached when operat-ing speed variability presents a medium value, or high correlationbetween this parameter and the operating speed deviation.
After the statistical analysis, the proposed model for relatingcrash data to road geometry results as:
ECR = 12.40939 + 0.00403287 · C
(9)
where C is the design consistency index, calculated as follows:
C = v285
�v85(10)
The development of the new model and consistency index leadsto a new design consistency measure for a whole road segment.Moreover, since the model presents the relationship between con-sistency and crash rate, it is possible to use that parameter as asurrogate measure to evaluate road safety and estimate the num-ber of accidents with victims. Consequently, the results of thisresearch can be an innovative tool for assisting engineers at designor redesign stages. According to this methodology, engineers mayevaluate the consistency and road safety of several possible solu-tions and choose the safest one. Besides, the presented model canbe also applied to the estimation of crash rates of an existing roadwhere accident data is not available.
Further research is proposed to analyze the sensibility of themodel and also to establish consistency thresholds. Once the
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
consistency model and the consistency index are defined, thethresholds for the consistency measure should be proposed afterdetailed crash data observation. Thus, taking into account the rela-tionship between this index and the estimated crash rate, the
dequacy of the road to drivers’ expectancies will be able to beeasured also from the value of this road safety parameter.This paper examines the crash rate, but does not consider the
everity of those crashes. Further research is needed in order tonclude this variable in the analysis, yet higher values of operatingpeeds lead to lower crash rates, but they might be more severe.
Some other operating speed models have to be developed, inrder to consider the vertical alignment or the presence of inter-ections. Drivers’ behavior may vary at these new kinds of roadegments, so the consistency model should vary to consider newndings.
cknowledgements
Authors would like to thank Center for Studies and Experimen-ation of Public Works (CEDEX) of the Spanish Ministry of Public
orks that partially subsidized the research. We also wish to thanko the Infrastructure and Transportation Department of the Gen-ral Directorate of Public Works of the Valencian Government, tohe Valencian Provincial Council and to the Ministry of the Inte-ior, especially to General Directorate of Traffic of Spain, for theirooperation in field data gathering.
eferences
nderson, I.B., Bauer, K.M., Harwood, D.W., Fitzpatrick, K., 1999. Relationship tosafety of geometric design consistency measures for rural two-lane highways.Transportation Research Record 1658, 43–51.
wata, M., Hassan, Y., 2002. Towards establishing an overall safety-based geometricdesign consistency measure. In: 4th Transportation Specialty Conference of theCanadian Society for Civil Engineering.
Please cite this article in press as: Camacho-Torregrosa, F.J., et al., New gefor road safety evaluation. Accid. Anal. Prev. (2012), http://dx.doi.org/10.10
afiso, S., 2000. Experimental survey of safety condition on road stretches with align-ment inconsistencies. In: Proceedings of the 2nd International Symposium onHighway Geometric Design, Mainz, Germany, pp. 377–387.
afiso, S., La Cava, G., Montella, A., 2007. Safety index for evaluation of two-lane ruralhighways. Transportation Research Record 2019, 136–156.
PRESSsis and Prevention xxx (2012) xxx– xxx
Fitzpatrick, K., Elefteriadou, L., Harwood, D.W., Collins, J.M., McFadden, J., Ander-son, I.B., Krammes, R.A., Irizarry, N., Parma, K.D., Bauer, K.M. and Passetti,K., 2000. Speed Prediction for Two-Lane Rural Highways. Report FHWA-RD-99–171. FHWA, U.S. Department of Transportation.
Gibreel, G.M., Easa, S.M., Hassan, Y., El-Dimeery, I.A., 1999. State of the art of high-way geometric design consistency. Journal of Transportation Engineering 125,305–313.
Hassan, Y., 2004. Highway design consistency: refining the state of knowledge andpractice. Transportation Research Record 1881, 63–71.
Kanellaidis, G., Golias, J., Efstathiadis, S., 1990. Driver’s speed behaviour on rural roadcurves. Traffic Engineering and Control 31 (7/8), 414–415.
Lamm, R., Choueiri, E.M., Mailaender, T., 1992. Traffic safety on two continents—aten year analysis of human and vehicular involvements. In: Proceedings of theStrategic Highway Research Program (SHRP) and Traffic Safety on Two Conti-nents, pp. 18–20.
Lamm, R., Psarianos, B., Mailaender, T., 1999. Highway Design and Traffic SafetyEngineering Handbook. McGraw-Hill Companies, Inc., New York, USA.
Lee, S., Lee, D., Choi, J., 2000. Validation of the 10 MPH rule in highway designconsistency procedure. In: Proceedings of the 2nd International Symposium onHighway Geometric Design, Mainz, Germany, pp. 364–376.
Leisch, J.E., Leisch, J.P., 1977. New concepts in design-speed application. Transporta-tion Research Record 631, 4–14.
Marchionna, A., Perco, P., 2008. Operating speed profile prediction model for two-lane rural roads in the italian context. Advances in Transportation Studies 14,57–68.
Ng, J.C.W., Sayed, T., 2004. Effect of geometric design consistency on road safety.Canadian Journal of Civil Engineering 31 (2), 218.
Pérez Zuriaga, A.M., García García, A., Camacho Torregrosa, F.J., D’Attoma, P., 2010.Modeling operating speed and deceleration on two-lane rural roads with globalpositioning system data. Transportation Research Record 2171, 11–20.
Pérez Zuriaga, A.M., García García, A., Camacho Torregrosa, F.J., 2011. Study oftangent-to-curve transition on two-lane rural roads with continuous speed pro-files. In: Transportation Research Board 90th Annual Meeting, Washington, DC.
Polus, A., Mattar-Habib, C., 2004. New consistency model for rural highways and itsrelationship to safety. Journal of Transportation Engineering 130 (3), 286–293.
Transportation Research Board, 2011. Modeling Operating Speed – Synthesis Report.TRB Research Circular EC151.
ometric design consistency model based on operating speed profiles16/j.aap.2012.10.001
R.L., Castellan, N.J., 1979. Tri-level study of the causes of traffic accidents: Finalreport – Executive summary. Bloommington. Institute for Research in PublicSafety. [REPORT No. DOT-HS-034-3-535-79-TAC(S)].
Weber, R., Matena, S., 2008. RIPCORD-ISEREST – Final Report. http://ripcord.bast.de/pdf/ripcord iserest deliverable d14 final.pdf
