New Consistency Index Based on Inertial Operating Speed

Transcription

1 New Consistency Index Based on Inertial Operating Speed Alfredo García, David Llopis-Castelló, Francisco Javier Camacho-Torregrosa, and Ana María Pérez-Zuriaga The occurrence of road crashes depends on several factors, with design consistency (i.e., conformance of highway geometry to drivers expectations) being one of the most important. A new consistency model for evaluating the performance of tangent-to-curve transitions on two-lane rural roads was developed. This model was based on the inertial consistency index (ICI) defined for each transition. The ICI was calculated at the beginning point of the curve as the difference between the average operating speed on the previous 1-km road segment (inertial operating speed) and the actual operating speed at this point. For the calibration of the ICI and its thresholds, 88 road segments, which included 1,686 tangent-tocurve transitions, were studied. The relationship between those results and the crash rate associated with each transition was analyzed. The results showed that the higher the ICI was, the higher the crash rate; thus, the probability of accidents increased. Similar results were obtained from the study of the relationship between the ICI and the weighted average crash rate of the corresponding group of transitions. A graphical and statistical analysis established that road consistency might be considered good when the ICI was lower than 10 km/h, poor when the ICI was higher than 20 km/h, and fair otherwise. A validation process that considered 20 road segments was performed. The ICI values obtained were highly correlated to the number of crashes that had occurred at the analyzed transitions. Thus, the ICI and its consistency thresholds resulted in a new approach for evaluation of consistency. Road crashes have three general categories of contributing factors: human, vehicle, and road infrastructure. Previous research has indicated that the infrastructure factor is responsible for more than 30% of road crashes (1). Collisions tend to concentrate on certain road segments; this tendency highlights the major role that road characteristics play in some accidents. The influence of the geometric characteristics of roads increases when the level of geometric design consistency, which may be defined as how drivers expectations and road behavior fit, is low. An inconsistent road design surprises drivers and leads to anomalous behavior and possible collisions. Most related research and developed design consistency models focus on four main areas: operating speed and its variations, vehicle stability, alignment indexes, and driver workload (2, 3). Among those models, the most universally used criteria for evaluation of road Highway Engineering Research Group, Universitat Politècnica de València, Camino de Vera, s/n, Valencia, Spain. Corresponding author: A. García, agarciag@ tra.upv.es. Transportation Research Record: Journal of the Transportation Research Board, No. 2391, Transportation Research Board of the National Academies, Washington, D.C., 2013, pp DOI: / design consistency are based on evaluation of operating speed, which is often defined as the 85th-percentile speed (V 85 ) of the distribution of speeds selected by drivers in free-flow conditions (4). This measure of speed can be used in evaluation of consistency by examining the differences (a) between design speed (V d ) and V 85 or (b) in V 85 between successive road elements, especially between horizontal curves and previous tangents. Tangent-to-curve transitions are considered the most critical locations because estimates indicate that more than 50% of the total fatalities on rural highways take place on curved sections (5). Leisch and Leisch recommended a revised design speed concept that included guidelines on both operating speed reductions and differentials between design and operating speeds (6). In the same way, Kanellaidis et al. suggested that a good design can be achieved when the difference between V 85 on the tangent and on the following curve does not exceed 10 km/h (7). However, the most commonly used method to evaluate road consistency was developed by Lamm et al., on the basis of the mean accident rates observed at several alignment configurations (8). They presented two design consistency criteria related to operating speed: the difference between design and operating speeds (Criterion 1) and the difference between operating speeds on successive elements (Criterion 2). Criterion 1, the difference between operating speed and design speed ( V 85 V d ), allows identification of road alignment elements whose design does not fit the general road alignment. It is a good indicator of the consistency on a single element. Criterion 2, the reduction in operating speed between two successive elements (ΔV 85 ), indicates the surprises experienced by drivers that make them reduce their speed when traveling from one element to the next. Table 1 summarizes the consistency thresholds for Criteria 1 and 2. These thresholds are an approach to the thresholds that determine the need for redesign. However, other authors have suggested continuous functions instead of consistency thresholds as a better tool for designers (9). The consistency criteria previously presented allow evaluation of design consistency on a single road element (the horizontal curve) or at tangent-to-curve transitions. They are usually called local consistency models. Such models try to identify road inconsistencies by considering that drivers expectations are thwarted when operating speed is much higher than design speed or by assuming that drivers are surprised when the operating speed in a road element is much lower than the previous one. Thus, drivers expectations are assumed to be characterized by the design speed of the whole road segment or by the operating speed in the previous element. While, in the first case, the road segment 105

2 106 Transportation Research Record 2391 TABLE 1 Thresholds for Determining Quality of Design Consistency: Lamm s Criteria 1 and 2 Consistency Rating immediately preceding the inconsistency is not taken into account, in the second one, only the previous element is considered. However, no previous research has determined the road segment length necessary for producing ad hoc expectations that may be compared with road design geometry. Other studies, such as those by Polus and Mattar-Habib (10), Cafiso et al. (11), and Camacho-Torregrosa et al. (12), are based on continuous speed profiles. They studied the global speed variation along a road segment as a function of several indexes and determined a single consistency value for the whole road segment. Moreover, their design consistency index is a continuous function instead of being based on ranges. Those global consistency models are less used than local ones because of the difficulty of estimating continuous operating speeds. Furthermore, each consistency model was calibrated at a specific geographic environment, and driver behavior may change from one region to another. Therefore, the extrapolation of those models or thresholds should be carefully implemented. Further tests of the applicability of Lamm s criteria revealed that a 20 km/h limit for poor design is applicable for Korea (13), but a different limit was recommended for Italy (14). By taking into account the considerations itemized above, this paper presents a new model for evaluation of the consistency two-lane rural roads. This model is based on the comparison of ad hoc drivers expectations and road design geometry and therefore establishes a better approach to defining road design consistency. Objectives and Hypotheses The main objective of this study is the development of a new index for evaluation of the design consistency of two-lane rural roads that allows the inclusion of drivers expectations within the analysis. This development is based on the hypothesis that drivers expectations at every point can be estimated as the average operating speed at the previous road segment. This speed parameter is called inertial operating speed (V 85inertial ). According to this hypothesis, the difference between inertial operating speed and actual operating speed shows the discordance between drivers expectations and road alignment. Data Description Threshold (km/h) Criterion 1 Criterion 2 Good V 85 V d 10 V 85i V 85i+1 10 Fair 10 < V 85 V d < V 85i V 85i+1 20 Poor V 85 V d > 20 V 85i V 85i+1 > 20 Tangent-to-curve transitions are the most conflictive points of a road alignment. Lamm et al. estimated that more than 50% of fatal accidents occur on rural roads at those locations (5). This high fatality percentage is why the proposed consistency model is focused on those transitions. For development of the model, 88 two-lane rural road segments from the Valencia region of Spain were evaluated and 1,686 tangentto-curve transitions were identified. The length of the road segments ranged from 2.0 to 15.5 km, with their longitudinal grades being between 3% and 3%. None of the selected segments presented important intersections that could significantly alter traffic volumes, operating speeds, or number of crashes. Traffic Volume Traffic volume data were downloaded from the official website of the local Valencian road administration. They consisted of annual average daily traffic data for the last 15 years, but only data from 2001 to 2010 were used to avoid consideration of data belonging to road segments that were redesigned or improved during that period. The highest traffic volume considered was 25,015 vehicles per day, while the road segment with the lowest annual average daily traffic presented only 363 vehicles per day. Crash Data Crash data were also provided by the local Valencian road administration. They consisted of a list of all reported crashes during those years characterized by point station, date and time, lighting conditions, crash severity, type of vehicle, characteristics of the driver, external factors, causes, and other conditions. While all data were considered, a filtering process discarded all property-damage-only accidents to avoid bias attributable to underreporting problems. Accidents caused by external factors, such as illness of the driver or animals crossing the road, were also removed from the analysis. Because of data characterization, crash locations and driving directions were identified. However, the accuracy of crash locations was 100 m, so the relationship of the crashes to their corresponding tangentto-curve transition could not be determined directly. The authors therefore assumed that each accident could have been produced within a range (±50 m) of its reported location. An accident is generally considered transition related if its actual location occurs within or, because of kinematic effects, 100 m beyond the curve. Because of the uncertainty of the accident location in the current data, an accident was considered to be transition related if its reported location was somewhere between 50 m before and 150 m after the corresponding curve. Profiles of Continuous Operating Speed Operating speed profiles were based on operating speed models developed by Zuriaga et al. (15). The operating speed model for curves uses the radius as an explanatory variable (Equations 1 and 2). V 85 C V 85 C = m < R 950 m (1) R = m < R 400 m (2) R where V 85C is the operating speed (km/h) on the curve and R is the horizontal curve radius (m). This model does not consider radii smaller than 70 m. However, doing so was not necessary because none of the road segments presented any curve with a radius smaller than 70 m.

3 García, Llopis-Castelló, Camacho-Torregrosa, and Pérez-Zuriaga 107 The developed model for estimating operating speed on tangents considers the length of the tangent and the estimated operating speed of the preceding curve (Equation 3). λil ( ) i ( C ) V = V + 1 e V V (3) 85T 85C des 85 where λ = (R 100) , V 85T = operating speed on tangent (km/h), V des = desired speed (110 km/h), and L = tangent length (m). The operating speed profiles were built, both in forward and backward directions, for all road segments by considering these models. Some construction rules and deceleration and acceleration rates estimated by Equations 4 and 5 also had to be considered in their construction. Those models were calibrated by Zuriaga et al. (15) and Camacho-Torregrosa et al. (12), respectively. d a = = R R where d 85 is the deceleration rate (m/s 2 ) and a 85 is the acceleration rate (m/s 2 ). (4) (5) The representative index of the proposed model is the difference between inertial operating speed (V 85inertial ) as an estimation of drivers expectations and operating speed (V 85 ) as an estimation of the performance of the road geometry. This new index is called the inertial consistency index (ICI). V 85inertial was defined as the average operating speed of the previous road segment for each point of the road. It was first necessary to identify the length that should be used for constructing this index. This was accomplished by means of a sensitivity analysis. The aim of this study was to determine the road segment length that better reflects drivers behavior, so several road segment lengths were evaluated. The use of road segment lengths shorter than 1,000 m led to an inertial operating speed profile slightly smoother than the corresponding operating speed profile, without significant contributions compared with the operating speed profile. In contrast, road segment lengths greater than 1,000 m resulted in a profile that was too smooth, hiding significant speed variations. After this evaluation, the authors concluded that the most suitable road segment length for this kind of study was 1,000 m. Thus, V 85inertial was finally defined as the 1,000-m moving-average value of the operating speed. Figure 1 shows an example of inertial operating speed profile, in both forward and backward directions. The next step was to calibrate the relationship between the new consistency index and the corresponding crash rate. The consistency index was determined at the beginning of the curve of each tangentto-curve transition. To establish consistency thresholds, the ICI was also grouped into several intervals and the average crash rates were obtained for all of them. Development Road safety is highly correlated with consistency in road design, so every design consistency model should be calibrated by considering its relationship to crashes. Crash Rate Versus ICI The crash rate of each tangent-to-curve transition was calculated as the quotient between the number of crashes and the total traffic volume in each transition. The ICI was also determined for each tangent-to-curve FIGURE 1 Example of inertial operating speed profile.

4 108 Transportation Research Record 2391 FIGURE 2 Crash rate versus ICI (veh = vehicles). transition. The relationship between those variables is shown in Figure 2. Figure 2 shows a clear relationship between crash rate and the ICI: the higher the ICI is, the higher the crash rate. However, it was not possible to obtain general conclusions from this graph because of the large amount of data without crashes that may bias results and conclusions. Weighted Average Crash Rate Versus ICI The second analysis was based on consideration of the relationship between the ICI and the weighted average crash rate (WACR). Two kinds of graphs were used in this part of the analysis. The first one is shown in Figure 3. ICI values were put into groups of 5 km/h. For each group, the weighted average crash rate was calculated as the quotient between the total number of crashes with a certain interval of ICI, and the total traffic volume of them. Light gray columns reflect the calculated WACR from considering all the curves, and the dark gray ones correspond to the WACR (with the transitions with no accidents having been previously removed). This data treatment was performed because of the large amount of data without crashes that could have a serious influence on the results of the analysis. Because, from a statistical standpoint, crashes are rare, random, and discrete events, they should be adjusted to a Poisson or a negative binomial distribution. However, distribution does not correctly fit to data when the number of zeros in the data is high. In this case, zero-crash tangent-to-curve transitions may be associated with a safe transition or with the randomness of the crash phenomenon. Some methodologies, such as Bayesian analyses, differentiate between the two data groups and therefore improve the results of the analysis. Nevertheless, this analysis is useful only when a large data sample is available. In this case, the data set was not sufficient to perform this calculation, so a different methodology was used. Two calculations, with and without consideration of blank transitions, were performed. The real result was assumed to be between the two solutions. A similar graph setting the ICI into groups of 10-km/h intervals was plotted (Figure 4). Both graphs (at 5- and 10-km/h intervals) show that WACR increases as the ICI does. Because the proportion of curves without crashes (blank transitions) was high for each interval, its percentage was compared with the total number of transitions (Figures 5 and 6). These figures show a decreasing trend in the percentage of blank transitions with the ICI. This result emphasizes that the proportion of curves with accidents increases as the difference between inertial operating speed and actual operating speed also increases. That relationship leads to the conclusion that the ICI is strongly related to road safety. Therefore, the increase in the ICI is related to a higher probability of crash occurrence in the tangent-to-curve transition. Threshold Analysis Once the relationship between the ICI and road safety was demonstrated, the authors had to establish intervals of values of ICI for which FIGURE 3 WACR versus ICI at 5-km/h intervals.

5 García, Llopis-Castelló, Camacho-Torregrosa, and Pérez-Zuriaga 109 FIGURE 4 WACR versus ICI at 10-km/h intervals. This analysis revealed significant statistical differences with a 95% confidence level between tangent-to-curve transitions with ICIs less than 10 km/h and those with ICIs of 10 to 20 km/h (Figure 7, a and b) and between those with ICIs of less than 10 km/h and those with ICIs of greater than 20 km/h (Figure 7, e and f ). These results were obtained both by considering all the curves (with blank transitions) and by omitting blank curves (without blank transitions). However, tangent-to-curve transitions for which the ICI ranges from 10 to 20 km/h and greater than 20 km/h seem to belong to the same population (Figure 7, c and d). This result is attributable to a small data sample for this interval (15 nonblank tangent-to-curve transitions) and causes higher crash rate dispersion. Therefore, future research on this topic should use a larger sample. the influence of the road design consistency index on road safety could be considered the same. The WACR represented in Figure 3 clearly shows a generally increasing trend, divided into two minor trends: the first one ranging from 2.5 to 12.5 km/h and the second from 12.5 to 27.5 km/h. Figure 4 shows the differences in trends more clearly, with the trend remaining almost horizontal from 10 to 10 km/h and dramatically increasing in the interval for 10 to 20 km/h. The interval from 20 to 30 km/h shows an even greater increase. To confirm those thresholds, a statistical analysis was conducted by using intervals of least significant difference (Figure 7) that compared the different ICI intervals. Two ICI ranges can be assumed to belong to different populations (i.e., different tangent-to-curve behaviors) when their intervals do not overlap. Proposed Geometric Design Consistency Model As noted earlier, the ICI is related to safety and may be used for analyzing safety at tangent-to-curve transitions. Threshold values are defined in the following table, as obtained earlier: ICI Value from Proposed Model Design Consistency [V 85inertial V 85 (km/h)] Good 10 Fair >10 to 20 Poor >20 As demonstrated earlier, a higher difference between inertial operating speed (i.e., drivers expectations) and operating speed FIGURE 5 Percentage of blank transitions versus ICI at 5-km/h intervals. FIGURE 6 Percentage of blank transitions versus ICI at 10-km/h intervals.

6 110 Transportation Research Record 2391 (a) (b) (c) (d) (e) (f) FIGURE 7 Intervals of least significant difference (at 95% confidence interval) for determination of model thresholds [without blank transitions (left) and with blank transitions (right)]: comparison of tangent-to-curve transitions with (a and b) ICIs < 10 km/h and ICIs of 10 to 20 km/h, (c and d) ICIs of 10 to 20 km/h and ICIs > 20 km/h, and (e and f) ICIs < 10 km/h and ICIs > 20 km/h. (i.e., road geometric design) results in a lower consistency and, therefore, a higher crash probability. validation of Proposed Model The proposed model for evaluation of the consistency of geometric design was validated by applying it to 20 other two-lane rural road segments that included 370 tangent-to-curve transitions. Empirical operating speed profiles were used for validation. The corresponding empirical operating speed profiles were obtained by applying the data collection methodology developed by Zuriaga et al. (15). This methodology consisted on asking drivers to install a Global Positioning System device with strong magnetic points between two checkpoints belonging to each road segment. Drivers were encouraged to drive as they usually do. This method allowed collection of continuous speed data along a road segment from a great number of drivers. Additional tests were performed to ensure that drivers were not biased by the presence of the checkpoints or the device (15). As expected, tangent-to-curve transitions identified as inconsistent by the ICI model presented a higher crash concentration than the rest within the same road segment. Figure 8 shows the evaluation of road consistency and the location of crashes for one road segment. To improve the validation analysis, a graph comparing the ICI with the WACR was drawn (Figure 9); it includes all tangent-to-curve transitions located at the 20 road segments used in this process. Light gray columns correspond to WACR that consider all the transitions and the dark gray ones to WACR that consider only transitions with accidents.

7 García, Llopis-Castelló, Camacho-Torregrosa, and Pérez-Zuriaga V 85 inertial - V 85 (km/h) Distance (m) Forward Backward FIGURE 8 Example of road segment validation identifying inconsistencies in tangent-to-curve transitions and showing crash locations. Figure 9 shows an increasing trend of the WACR with a corresponding difference between inertial operating speed and operating speed. The differences in WACR between the intervals of ICI values are even higher than in the model calibration process. The inflection points clearly correspond to the thresholds identified for the consistency model. Conclusions Road safety (especially fatal crashes) is one of the most important problems affecting society today. The infrastructure factor is found in 30% of road crashes occurring on two-lane rural roads. Collisions tend to concentrate on certain road segments, with road characteristics playing a major role in some accidents. Furthermore, tangent-to-curve transitions are considered the most conflictive points, as more than 50% of crashes occur on those sections. To improve road geometric design and evaluation of road safety, this paper presented a new model of design consistency for evaluating the quality of tangent-to-curve transitions on two-lane rural roads. The proposed model is based on the hypothesis that design consistency may be defined as the difference between drivers expectations and road alignment behavior. The road alignment behavior at one station may be estimated by means of the operating speed at that point. Drivers expectations may be estimated by the inertial operating speed, defined as the average operating speed of the previous 1 km road segment, at the same point. The difference between those two parameters, the ICI, results in a new approach to the evaluation of road consistency. The ICI and the associated consistency thresholds were developed by studying the operating speed profiles of 88 two-lane rural road segments and considering both driving directions, which included 1,686 tangent-to-curve transitions. V 85inertial V 85 was calculated at the beginning point of the curve of each transition. The relationship between those results and the crash rate associated to each transition from 2001 to 2010 was examined. This relationship highlighted that higher crash rates corresponded to higher ICI values. Therefore, a high ICI is linked to a higher crash probability. Both a graphical and a statistical analysis were performed to establish the thresholds of the consistency model. According to those 8 WACR (Crashes/veh 10 7 ) [-10; 0] [0; 10] [10; 20] [20; 30] V 85 inertial V 85 (km/h) with 0 without 0 FIGURE 9 WACR versus ICI at 10-km/h intervals for road segments used for validation.

8 112 Transportation Research Record 2391 analyses, the consistency of road alignment at every location may be considered good when the ICI is lower than 10 km/h, fair when it is between 10 and 20 km/h, and poor when it is higher than 20 km/h. The proposed consistency model was validated through its application to the empirical operating speed profiles of 20 road segments that included 370 tangent-to-curve transitions. The ICI values obtained were correlated to the number of crashes that occurred at the studied transitions. The validation process revealed that the transitions with a higher ICI value presented more collisions. Acknowledgments The authors thank the Center for Studies and Experimentation of Public Works of the Spanish Ministry of Public Works, which partially subsidized the data collection, for obtaining the empirical operating speed profiles used in the validation process. The authors also thank the General Directorate of Public Works of the Infrastructure and Transportation Department of the Valencian government, the Valencian Province Council, and the General Directorate of Traffic of the Ministry of the Interior of the Government of Spain for their cooperation in data gathering. References 1. Treat, J. R, N. S. Tumbas, S. T. McDonald, D. Shinar, R. D. Hume, R. E. Mayer, R. L. Stansifer, and N. J. Castellan. Tri-Level Study of the Causes of Traffic Accidents: Final Report Executive Summary. DOT-HS TAC(S). Institute for Research in Public Safety, Indiana University, Bloomington, Ng, J. C. W., and T. Sayed. Effect of Geometric Design Consistency on Road Safety. Canadian Journal of Civil Engineering, Vol. 31, No. 2, 2004, pp Awata, M., and Y. Hassan. Towards Establishing an Overall Safety-Based Geometric Design Consistency Measure. Presented at 4th Transportation Specialty Conference of the Canadian Society for Civil Engineering, Montreal, Quebec, Canada, Gibreel, G. M., S. M. Easa, Y. Hassan, and I. A. El-Dimeery. State of the Art of Highway Geometric Design Consistency. Journal of Transportation Engineering, Vol. 125, No. 4, 1999, pp Lamm, R., E. M. Choueiri, and T. Mailaender. Traffic Safety on Two Continents a Ten-Year Analysis of Human and Vehicular Involvements. Proc., Strategic Highway Research Program (SHRP) and Traffic Safety on Two Continents, Gothenburg, Sweden, Statens väg-och transport forskningsinstitut, Linköping, Sweden, 1992, pp Leisch, J. E., and J. P. Leisch. New Concepts in Design-Speed Application. In Transportation Research Record 631, TRB, National Research Council, Washington, D.C., 1977, pp Kanellaidis, G., J. Golias, and S. Efstathiadis. Driver s Speed Behaviour on Rural Road Curves. Traffic Engineering and Control, Vol. 31, No. 7 8, 1990, pp Lamm, R., B. Psarianos, and T. Mailaender. Highway Design and Traffic Safety Engineering Handbook. McGraw-Hill, New York, Hassan, Y. Highway Design Consistency: Refining the State of Knowledge and Practice. In Transportation Research Record: Journal of the Transportation Research Board, No. 1881, Transportation Research Board of the National Academies, Washington, D.C., 2004, pp Polus, A., and C. Mattar-Habib. New Consistency Model for Rural Highways and Its Relationship to Safety. Journal of Transportation Engineering, Vol. 130, No. 3, 2004, pp Cafiso, S., A. Di Graziano, G. Di Silvestro, G. La Cava, and B. Persaud. Development of Comprehensive Accident Models for Two-Lane Rural Highways Using Exposure, Geometry, Consistency and Context Variables. Accident Analysis and Prevention, Vol. 42, No. 4, 2010, pp Camacho-Torregrosa, F. J., A. M. Pérez-Zuriaga, J. M. Campoy-Ungría, and A. García García. New Geometric Design Consistency Model Based on Operating Speed Profiles for Road Safety Evaluation. Accident Analysis and Prevention (forthcoming). 13. Lee, S., D. Lee, and J. Choi. Validation of the 10 MPH Rule in Highway Design Consistency Procedure. Proc., 2nd International Symposium on Highway Geometric Design, Mainz, Germany, 2000, pp Cafiso, S. Experimental Survey of Safety Condition on Road Stretches with Alignment Inconsistencies. Proc., 2nd International Symposium on Highway Geometric Design (R. A. Krammes, ed.), Mainz, Germany, FGSV, Cologne, Germany, 2000, pp Zuriaga, A. M. P., A. G. García, F. J. C. Torregrosa, and P. D Attoma. Modeling Operating Speed and Deceleration on Two-Lane Rural Roads with Global Positioning System Data. In Transportation Research Record: Journal of the Transportation Research Board, No. 2171, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp The Traffic Flow Theory and Characteristics Committee peer-reviewed this paper.