Modelos de perfil de velocidad para evaluación de consistencia del trazado en carreteras de la provincia de Villa Clara, Cuba Speed profile models for evaluation of design consistency in road of the province of Villa Clara, Cuba

Among the aspects that influence road accidents, geometric design is the most relevant. The most used method for evaluating the design all over the world is based on the design consistency with speed profile models of operation. Cuba does not have proprietary models that consider the characteristics of the roads and drivers, so it is necessary to develop predictive models for the evaluation of design consistency. The development of operating speed profile prediction models for different alignment conditions on rural roads with two lanes in the context of Cuba is made from the geometric characteristics and point speeds with statistical analysis of the main variables related with the operating speed. Once models are developed they are applied to a section of road designated as an accident concentration section (TCA) of the province of Villa Clara located in central Cuba, these results confirm the validity of the models developed to determine the operating speeds, thus evaluating the design consistency, with the aim of detecting the locations of greater difficulties with respect to the geometric design.


Introduction
In Cuba the accident rate is mainly concentrated in urban areas.The predominance of human factor is recognized as the primary reason for accidents (Albentosa, 2006), although the roads geometric characteristics also influence the accident rate.
In Cuba the causes of accident rate related to highways are higher than the ones reported in other countries, due to roads conditions, present status of elements comprising them and the pavement surface characteristics (García, 2010).
Presently there is a strong worldwide tendency to evaluate road safety based on road consistency.This is defined as the relationship between the road geometrical characteristics and the ones expected by the driver travelling on a roadway (Leisch and Leisch, 1977).Several researchers have proposed models allowing the determination of operating speed profiles on two-lane highways.Some of them are listed on Table 1.Fitzpatrick et al., (2000) included in the IHSDM 2004 (Interactive Highway Safety Design Model) proves the roads inconsistency for a high percentage of segments lengths; due to differences between speed design and operation design.Above, because models employed in this assessment were obtained for another conditions and they do not reflect the real operating speed in Villa Clara´s highways (Raoul 2009).

The experience of roads consistency assessment in Cuba, developed by the Universidad Central de Las Villas (UCLV) by means of expressions by
Based on this situation and considering that the percentages of national interest two-lane rural roads represent a 71.6% of total Villa Clara province, in addition to the high accident and severity rates, it was decided to develop speed predictive models for these kind of rural highways in order to evaluate the roads consistency.

Development
The general procedure followed in this research is divided into two stages.The first consists of a bibliographic analysis and the determination of speed profile models.The second stage evaluates the roads consistency for national interest two-lane rural roads.These stages include the following aspects:
( • Definition of fixed parameters to be researched. Highways fixed parameters are the characteristics that do not change throughout time, where preservation measures are not applied.The most significant geometric characteristics are slope and horizontal curvature radius, which are determined at selected locations."Site" is considered as the group of one or several curves with similar geometrical characteristics under the same condition, horizontal curve, vertical curve or the combination of both (Fitzpatrick et al., 2000).General criteria used to select locations are: rural area, lower functional classification of arterial lane, speed limit between 50 and 90 km/hr, plane and undulated ground, traffic volumes between 100 and 4,000 vehicles/day, carriageway width between 2.75 and 3.75 meters, non-restricted horizontal curves length and, vertical curves length between 40 and 320 meters.These parameters were selected as they represent the most common features of rural highways in the country.

• Determination of selected sites. The selection of sites is developed based on the elements that counteract with the effect of centrifugal force in horizontal curves (cant, transverse friction and horizontal radius), which depend on the speed at horizontal curves (Expression 1).
Where: Radiuses intervals are determined based on the highway category and ground type.Afterwards the amount of sites is defined by considering that speed values dot not exceed dispersion values, which were assumed in ±2.5 km/hr.
Donde: Número existente de sitios \ número real de sitios para el desarrollo de modelos \ número de sitios para la validación de los modelos.
Where: number of existing sites / actual number of sites for the development of models / number of sites for validating the models (2) In the case of vertical curves the algebraic difference of slopes is considered, which is conditioned to the curve location at the top or depression, for convex and concave cases thus defining two sites: one for each condition.
Once radiuses intervals are established for each site, it is necessary to determinate their existing amount per condition and which ones are required for models development.Calculation of samples number is carried out by using Formula 2, which is recommended when the population size is already known.
Where: n sample size Z confidence level p positive variability q negative variability N population size E accuracy or error The amount of sites in two-lane rural highways is obtained from a detailed analysis on these kinds of highways in Villa Clara province, where all alignment combinations are present.Afterwards, sites are defined where models are validated.In order to determinate the number of sites required for the development of operating speed predictive models Expression 2 is applied, because the total number of existing sites in the studied rural highways is available per condition and interval radiuses.Results are shown in Table 3.
The determination of specific speed samples number analyzed for every single site under study, in order to calculate operating speed, is obtained by Expression 3 (Radelat, 2003), which is used when the population size is unknown.The result obtained from the normal distribution parameter, assumed standard variation and the error delivered by measurements is 23 samples.

• Completion of information obtained in the field.
Data completion required for the elaboration of operating speed predictive models is carried out by means of direct measurements taken from the longitudinal slope field and the horizontal curves radiuses, in case of lacking of information on CPV and CPIT files or when there are doubts about the information reliability.
• Field work carried out in selected sites.Speed samples are taken from free-flow travelling light weight vehicles, at day, on dry and well conditions asphalts by using a laser gun.Speed studies shall be developed at the curve site where the operating speed is increased (Fitzpatrick et al., 2000).According to developed studies, these sites are located in the centerline of horizontal curves and vertical curves.
• Development of speed predictive models.Once measurements and checking of fixed parameters and speed are completed, the normality, homogeneity and independency of data groups are tested in order to conduct a parametric test and variance analysis.
Now the operating speed is calculated by considering two variables per sites (radius and speed), which are employed for models development.
Operating speed prediction profiles for two-lane rural highways are obtained by the application of regression techniques.The statistical processing of the variables employed is developed by the SPSS 16.0.1 software.Models development considers logarithmic, exponential and linear regressions including several variables.The most fitted models are the linear ones that speed and radius for horizontal curves (1, 2, 3, 4, 5, and 6).As unique independent variable, the inverse radius was introduced in the specific case of horizontal curves and, for the case of horizontal curves the slopes algebraic difference was considered.
Table 4 shows the results from statistical tests, obtained by employed variables (inverse radius, slope algebraic difference and operating speed).There are no self-correlation, multiple co-linearity and significance levels lower than 0.05, with adjustments of curves higher than 0.693; therefore, it can be concluded that these are high quality models.From the verification of statistical results and models quality, the equation for each condition is established as well as the number of sites where tests were applied for models development.The results are shown in Table 5.

Roads consistency assessment
• Developed models cross-check.Models crosschecking is performed by measuring speeds on the field site and later applying the corresponding expression at the laboratory.Difference must be approximately of ±2.5 km/h to prove the model efficiency.The cross-checking number is defined in Table 3. Results are satisfactory for all conditions.
• Roads consistency assessment.Roads consistency assessment is developed in accordance with Table 6, based on the difference of operating speed obtained when applying the speed profile together with design speed and, the difference of operating speed among consecutive elements.The results assess the roads consistency in accordance with criteria proposed by Lamm and Choueiri, 1987, Intervalo/ Interval Clasificación de la consistencia/ Consistency qualification Comparando con la velocidad de diseño (V d )/ Comparing to design speed (V d ) V 85 : velocidad de operación en un punto dado de la vía (km/h)/ operating speed at a given road point (km/h) V d : velocidad de diseño (km/h)/ design speed (km/h) ΔV 85 : diferencia de velocidad de operación entre dos elementos consecutivos (km/h)/ speed difference two consecutive elements (km/h) Tabla 6. Intervalos y calificación de la consistencia del trazado Table 6.Intervals and qualification of roads consistency which are still in force and have been employed by several researchers (FHWA; Castro and Sanchez, 2008;and Sanchez, 2008).
The obtained results define the sites having difficulties regarding roads consistency, provoked by one or maybe by two causes.Therefore, actions are focused to such critical points so as to eliminate the potential accident causes.

• Analysis of results obtained by the consistency assessment.
Roads consistency assessment is developed on a two-lane rural highway segment, called Santa Clara-Hatillo.This segment was rated as the most dangerous in the country.
The segment under analysis is a national interest two-lane road, belonging to Santa Clara -Sitiecito highway, located at the southeast of Santa Clara City, which is the entrance to the provincial capital from Cifuentes, Sagua la Grande, Quemado de Guines and Coralillo city councils and it holds strong pendulum-like-movements among population settlements.From above, the social and economic relevance is deduced for the segment to be assessed (Figure 1).
The ground plant and cross section of highway segment are now available, as well as speed design (60 km/hr), determining its alignment conditions, which are used in order to apply operating speed predictive models.
Tables 7 and 8 show the design of an Excel sheet created for the calculation of roads consistency assessment, where different characteristics of ground plant and cross section alignments are depicted for the studied segment.Besides, an operating speed graph is obtained as well as operating speed differences between consecutive elements (Figures 2 and 3), which enable us to notice the most critical points for both circulation directions.The summarized results of design consistency assessment are shown on Table 9, for Santa Clara -Hatillo segment, considering both traffic directions.
In Santa Clara -Hatillo traffic direction, roads consistency assessments deliver poor and regular results for both concepts, in four alignments totalizing 349.86 meters, which represent a 3.5% of total segment length.Contrarily, in the opposite direction, the results of five alignments totalizing 442.55 meters represent a 4.4% of total segment length.Poor and regular consistency assessment remains for both criteria, same traffic direction, for one single condition, with 80.59 meters; which represent a 0.8% of total segment length.Obtained results have proven that there is a higher amount of locations wrongly assessed due to operating speed and project speed differences.Above, because the allowed limit speed is determined according to vehicles potential speed without considering geometric characteristics of analyzed segments.

Conclusions
Specific operating speed predictive models are developed for alignment conditions existing in Santa Clara province, for two-lane rural highways of national interest.
The application of such models enables the localization of roads weakness points as well as the determination of roads consistency assessment for a highway segment with two circulation directions.
In a simple way, the elaboration of an Excel sheet allows determining roads consistency assessment by using operating speed predictive profile models developed for two-lane rural highways in Villa Clara province.
It is proven that in Santa Clara -Hatillo segment there is a road safety risk factor represented by roads consistency assessment for both traffic directions, thus proposing measurements that contribute to decrease accident rate becomes necessary.

Table 1 .
Expressions to estimate operating speed

Table 2 .
Number of sites

Table 4 .
Statistical tests summary

Table 5 .
Operating speed predictive models

Table 9 .
Summary of poor road consistency assessment on Santa Clara -Hatillo segment