Three-Dimensional Virtual Highway Model for Sight-Distance Evaluation of Highway Underpasses

The provision of adequate sight distance on highways is of utmost importance not only in the design phase but also during the operation of such roadways. The three-dimensional (3D) nature of highways admittedly requires a 3D approach for the sight-distance estimation. Highway administrators have acknowledged the difficulties involved in estimating unbiased sight distance on in-service roadways. Possible sources of bias in sight-distance estimation are many and varied. The most significant include the use of two-dimensional (2D) models instead of 3D models, inaccurate 3D highway models, and the overlooking of structures and roadside elements. Furthermore, the available sight distance (ASD) is closely related to the signposting of speed limits and the design of passing zones, which are fundamental for the safe and efficient operation of highways.

Sag vertical curves do not usually present sight-distance issues in daytime; however, in standards, the design of them is conditioned, to some extent, by nighttime driving performance (Ministerio de Fomento 2016; AASHTO 2011). Nevertheless, a significant sight restriction may be created by overpasses at or near sag curves (Easa 1992). The elements used as inputs in 3D sight-distance models do not always permit the re-creation of overhanging structures. Moreover, 3D methods avoid the need to rely on closed-form models typically devised from analytical 2D approaches (Ismail and Sayed 2007).

This paper first describes the computational process of 3D modeling of roadways and related elements and sight-distance estimations of them with an overpassing structure. This model was then applied to a case study to analyze in full detail the effects of such a structure and the road geometry on the sight-distance conditions where the required stopping and passing sight distances are assessed.

Most highway standards proposed 2D sight-distance estimation procedures (Ministerio de Fomento 2016; AASHTO 2011). In daylight, sight-distance restrictions are typically made on crests and curves. However, overpass structures may limit sight distance on certain sections. Easa (1992) formulated a 2D analytical method to calculate the sight distance on highways with noncentered overpasses where the underpassing roadway profile conformed to a grade–sag–grade sequence. Easa (2009) presented a model to optimize the ASD in the design of underpasses. Other closed-form methods were available in design guides (AASHTO 2011). These methods assumed that the deck of the overpass structure lays horizontal and somewhat perpendicular to the underpassing road. Existing 2D models may overestimate or underestimate the ASD (Hassan et al. 1996). Particularly, the validity of 2D procedures is limited because deviations from those assumptions may arise (e.g., nonperpendicular overpass structures or more complex layouts in highway alignment), affecting the sight-distance results.

Although the current Spanish design standard, which has recently been enforced (Ministerio de Fomento 2016), obliged designers to check that no significant sight restriction was created where an overpass was present for the underpass traffic, the standard did not propose a method for this verification.

Over the last few years, several 3D sight distance estimation methods have gained importance. These methods had varying features. A first distinction related to whether the evaluating algorithm was based on view sheds or on sight lines. In the former, the procedure evaluated the field of vision from the driver’s position and the length of the highway the driver sees (Jha et al. 2011; Castro et al. 2011). With regard to sight line–based routines, Hassan et al. (1996) drew up an analytical method to compute 3D sight distances based on theoretical alignments, for which sight lines were evaluated with a finite-element model representing the highway and surrounding environment. The model was able to incorporate diverse sight obstructions, such as lateral obstructions and overhanging elements, modeled by means of additional finite elements. The capabilities of this method were used in an additional study for determining passing and no-passing zones (Hassan et al. 1997). Then, in a similar manner, Ismail and Sayed (2007) devised a 3D method that determined the ASD with high precision by iteratively reducing the element size near the tangential or obstruction point. Other authors applied 3D sight-distance estimation techniques to in-service facilities. Data collected using light detection and ranging (LiDAR) equipment, either terrestrial or aerial, were necessary to re-create the roadway and related roadsides (Bassani et al. 2016). Aerial and terrestrial LiDAR data could supplement each other for a more complete model where landscape elements were not captured by either type of sensor. With respect to alignment re-creation, Easa (1999) proposed a method to fit vertical alignments to a given set of surveyed points.

Elevation models derived from LiDAR data were proposed in several sight-distance studies on highways. On the one hand, digital terrain models (DTMs) depict the bare ground surface, ignoring any additional feature in the landscape. Nonetheless, the evaluation of sight distance requires that all potential visual obstructions are taken into account. On the other hand, digital surface models (DSMs) comprise relevant landscape elements above the terrain surface. In either case, the sight-distance evaluation procedures typically verified whether the lines of sight were intercepted by such elevation models. Castro et al. (2016) discussed the use of DTMs and DSMs from different sources for highway sight-distance studies. Khattak and Shamayleh (2005) identified locations with potential stopping and passing sight-distance issues from aerial LiDAR data in a geographic information system (GIS), validating the results by means of a field visit. Castro et al. (2014a) developed software for the evaluation of sight distance on highways in a GIS. The algorithm used launched lines of sight iteratively along a defined path. Charbonnier et al. (2010) compared a method for sight-distance evaluation using LiDAR with another method that was based on photogrammetric restitution of roadway perspectives and with field verification using vehicles. To model the terrain and landscape features, a raster elevation model may be used (Castro et al. 2011; Gargoum et al. 2018). Otherwise, a triangular irregular network (TIN) could be created from the point clouds, thereby building a surface of nonoverlapping triangles that connected the points. The nonoverlapping surface limitation, however, did not allow for fully 3D landscape features and may have distorted the assessment of sight distance on in-service facilities, leading to inaccurate sight-distance outputs where overhanging structures were present. Hence, these models were often referred to as 2.5D. As an alternative, 3D virtual models have been proposed by several authors. The modeling techniques for the 3D geometry of highway tunnels were described by Lam and Tang (2003), who defined the surface of the tunnel by a mesh of triangles. Iglesias-Martínez et al. (2016) proposed a method for calculating a highway sight distance that incorporates overhanging features, and thus, overcame the problem; this method used a geoprocessing model in a GIS. The overhanging features that may obstruct vision had to be sketched and fitted into the model as multipatches. Chmielewski and Lee (2015) analyzed visibility in urban areas, modeling the landscape by combining an elevation model and multipatches. Bassani et al. (2015) created a model to evaluate the ASD in urban areas that also used a GIS and multipatches.

Unlike for the previous studies described herein, Campoy-Ungria et al. (2012) devised a technique for evaluating sight distance without relying on TIN surfaces to re-create the roadway and roadside features; instead, they used LiDAR point clouds directly. This approach overcame the limitations of the elevation models, where no overhanging features could be re-created. Nonetheless, it often tended to overestimate sight distance because polyhedral sight lines often slipped through among the points in the cloud even where the corresponding real area was solid. Iglesias et al. (2016) also broached the sight-distance evaluation scanning obstructions in a LiDAR point cloud at the driver’s eye height, thereby generating a horizontal field of vision as output. However, information regarding sight obstructions outside that horizontal plane remained unknown. Jung et al. (2018) proposed the use of 3D voxels in sight-distance evaluations to represent the objects captured by the LiDAR survey.

An additional application of 3D sight-distance evaluation techniques was the detection and analysis of sight-distance-related design issues. In this regard, the most relevant issues for highway safety were known to be hidden horizontal curves and sight-hidden dips (Zimmermann and Roos 2005; Kuhn and Jha 2011). Several studies have sought to characterize sight-hidden dips and the potential effects of them on safety (De Santos-Berbel and Castro 2016; Castro et al. 2015a). Moreover, Castro et al. (2014b) quantified the parameters of sight-hidden dips using measurements taken from photographs. Easa et al. (1996) presented a 2D analytical method for evaluating sight distance on complex highway vertical alignments, which took into account sight-hidden dips and overpasses. Nonetheless, a completely 3D analysis of sight distance on complex highway alignments in the vicinity of underpasses has not been conducted nor has the effect of sight-hidden dips and overpasses on the sight distance been adequately researched.

This study was based on an enhanced version of the geoprocessing model in a GIS presented by Iglesias-Martínez et al. (2016). Additional features for output display and analysis were added to this application, ensuring compatibility with an add-in previously devised by the authors (Castro et al. 2014a). This software launched sight lines iteratively from each driver’s eye position toward target positions ahead to a maximum given distance. The algorithm checked whether the elevation model (DTM or DSM), or other features in the model, obstructed these sight lines. Overhanging 3D structures could be re-created and incorporated into the highway model in addition to the usual elevation model. On the one hand, the DTM used consisted of a surface built up from a point cloud arranged in a 1-m grid derived from an aerial LiDAR survey (IGN 2010). Castro et al. (2015b) explained the convenience of selecting a small grid size, which showed the roadway and roadside shape in greater detail. The selected format for the elevation model was a TIN. On the other hand, a multipatchfeatureclass (or shapefile) was the required format for additional inputs in the GIS. A multipatch feature was a GIS object that stored a collection of patches to represent the boundary of a 3D object (ESRI 2018). The interchange file format used to insert these features in a GIS was called collaborative design activity (COLLADA). The resulting 3D virtual model was a combined model that comprised the TIN surface and the multipatch features.

An essential input was the path over which the sight distance was evaluated. The observer and target, namely the ends of the line of sight, were sequentially placed on the path. To evaluate sight distance, two different paths were used for each driving direction: the roadway centerline and a trajectory parallel to the centerline at an offset of 1.5 m. The former was used to compare the ASD and the required stopping sight distance according to the Spanish standard (Ministerio de Fomento 2016). The latter was adopted to evaluate whether a sufficient passing sight distance was available because the Spanish standard (Ministerio de Fomento 2016) specified that the passing sight distance must be measured along the highway centerline, which is also in accordance with AASHTO (2011) guidelines. The ability to incorporate diverse trajectories also proved the versatility of the method with regard to adjusting to different requirements.

In addition, different observer and target heights were simulated in the sight-distance evaluations. With regard to stopping sight distance, the Spanish standard proposed 1.1 m as the observer’s eye height (Ministerio de Fomento 2016), which corresponded to that of a driver in a passenger car. The lowest observer and target height values are typically assumed to provide safe sight-distance design criteria, which may be valid on vertical crests and horizontal curves. However, considering low observer and target height values may make the design unsafe on vertical sags where overhanging sight restrictions are present because low observer and target heights represent the most favorable assumption for the evaluation of sight distance on these sites. Therefore, higher observer and target height values must be assumed. In this respect, an observer’s eye height of 2.5 m is commonly used to simulate visibility conditions for heavy trucks (Fambro et al. 1997; VSS 1991). In addition to the two height values described, the intermediate driver’s eye height values were set at 1.5 and 2.0 m. The target height was set at 0.5 and 1.1 m, as applicable, to analyze stopping sight distance or passing sight distance, respectively, as proposed by the Spanish standard (Ministerio de Fomento 2016). In standards, the lowest target height represented a potential obstruction on the roadway, whereas the highest targets represented an oncoming vehicle traveling in the opposite direction. In the case of sight distance at underpasses, Easa et al. (1996) affirmed that, although the target height could be theoretically set to zero, a specific value greater than zero was preferred.

The case study consisted of a two-lane highway (N-603) underpass and a motorway (AP-61) overpass located in Segovia, Spain. The horizontal alignment was almost straight, whereas the profile adjusted to a dip in the topography with a complex sequence of crests and sags (Fig. 1). Above the lower sag (between Stations at 407 and 640 in Fig. 1), two overpassing structures bridged the gap to connect both buttresses. A crest vertical curve (between Stations 656 and 741 in Fig. 1) was present near the lower sag because the highway underpass also overpassed a country lane. There was no junction connecting the two highways in the vicinity of the underpass. Therefore, this analysis corresponded to a linear segment, not to an intersection. The actual view of the section of the case study is presented in Figs. 2(a and b).

An overpass is a structure consisting of standardized features that is sketched with ease in 3D modeling software once the dimensions and geometric layout are known. The 3D models were represented by shells, and the software could assemble as many components as the structure comprised. For an accurate 3D modeling of the spot, it was also necessary to re-create each roadway geometry. Fig. 1 shows that the bottom sides of the decks were not contained to a horizontal plane because the structures fitted the geometry of these roadways. Both motorway roadways were curved by the plan with a superelevation rate of 5.66%, and the grade in the profile was −2.67% on the spot. The digital elevation model facilitated the extraction of the highway geometric features.

The overpass structures had a rhomboidal shape on the horizontal projection, which spanned 15.2 m; however, the skewness angle between the centerlines of the two-lane highway and the motorway at the structure was 48.31 grads. The total width of each deck was 13 m. In addition, the structure model incorporated the vehicle parapets existing on the structure (Figs. 1 and 3).

This method was validated on site by means of 11 photographs taken at several fixed positions, all of them at a height of 1.75 m above the road surface. Two of these photographs are shown in Figs. 2(a and b). As can be seen in the photographs, either the roadway or the overpass was the element that limited sight distance. Two hundred and five targets distributed along a length of 840 m were selected on easily identifiable points on the road centerline markings. The locations of the photographs and targets were mapped on the orthophoto in the GIS, and the corresponding shape-file path was created. The pertinent lines of sight were launched with the geoprocessing model on the highway virtual model, which included the TIN surface and the overpass multipatch model. The visibility from every position where each photograph was taken was reproduced in the geoprocessing model by using the height above the road where the photographs were taken and a theoretical height of 0.01 m for the road markings. To validate all the modeling inputs included in the procedure, the lines of sight obstructed by the roadway and those obstructed by the overpasses were considered separately in the evaluation. The results from the geoprocessing model and the road markings visible in the photographs (i.e., the sight line evaluated as “seen” or “unseen” in the model and the road markings evaluated as “seen” or “unseen” in the photograph) were compared. Next, the agreement between the two procedures, in terms of lines of sight correctly evaluated, was estimated through the accuracy and the coefficient, κ (Cohen 1960), for which κ is defined aswhere p₀ = relative agreement between procedures; and p_e = likelihood of chance agreement. When the procedures produced completely identical outcomes, κ equaled 1, whereas they showed no agreement at all for low κ values close to 0. Table 1 shows the sight lines evaluated as well as the accuracy and κ coefficients obtained in the evaluation of the procedure. The values were taken from photographs for which the sight obstruction was the terrain (the TIN in the model) and the overpass (the multipatches in the model), and the total of both were also presented. We observed that the accuracy values and κ coefficients were, in all cases, very close to 1, thus revealing the validity of the method.

In the case study presented, the required stopping and passing sight distances were examined to identify potential issues. With regard to the stopping sight distance, the results of the outward direction are described and were analyzed under a single assumption for the observer and target with and without the overpassing structure. With reference to passing sight distance, both traveling directions were analyzed, and several assumptions were contemplated for the observer and target heights. Table 2 shows the summary of the assumptions made in the case study, with the inputs and the parameter values for each sight-distance computation. The combinations of all parameters and inputs yielded 18 series of sight-distance results, 2 for the assessment of stopping sight distance and 16 for the passing sight distance.

The 3D modeling of overpasses through multipatch features has been shown to be an effective solution for the evaluation of highway sight distance. The results of the assessments of stopping sight distance and passing sight distance are presented, respectively, in the two following subsections.

This paper presents the validation and application of a fully 3D methodology for sight-distance evaluation on an in-service roadway underpass. It incorporated additional features and tools compared with work previously completed by the authors. The comprehensiveness of the methodology proposed was proven because many factors affecting sight distance were contemplated simultaneously. A 2D approach required certain assumptions that may not accurately represent the geometric layout of the site, thus giving rise to uncertainty about the validity of the results for sight-distance evaluation. Such issues were resolved with the fully 3D procedure used and described herein; it was capable of reproducing the roadway and the roadside elements. The capacity to add overhanging and overpassing structures permitted the estimation to consider any item that restricts sight distance better than can be done due to difficulties inherent in the use of surface models, which revealed the need for a fully 3D approach. Furthermore, the procedure used LiDAR data acquired from the air to re-create in-service highways and related features accurately. However, a lifelike representation of the multipatch features was required to obtain accurate sight-distance output.

Highway standards normally oblige designers to take into account the presence of overhanging elements and overpasses in sight-distance evaluations, yet few guidelines have been provided in these respects. The method presented herein resolves this problem. To analyze stopping sight distance, three speeds were assumed: the theoretical design speed, the posted speed, and the operating speed. These assumptions permitted the detection of inconsistencies between design, posted, and operating speeds in the case study. The ASD requirement was found to be fully compliant for the design speed only. Moreover, the analysis detected and considered poor 3D alignment coordination between the plan and profile. As it is not always possible to remove them due to a range of constraints, at least the potential effects of such design shortcomings on safety should be studied.

Furthermore, higher driver’s eye and targets were shown to reduce the ASD at or near underpasses, which contrasts to typically assumed highway designs. Where overhanging or overpassing structures were present, lower target heights can be considered for passing sight distance because they were found sufficient for observing oncoming traffic at these particular spots. However, a higher observer’s eye should be considered in both stopping and passing sight distance because the passing vehicles could be trucks or buses, which do not have such advantageous visibility in these places; on this basis, a driver’s eye height of 2 m or higher is recommended.

Finally, the existing passing zones were evaluated by means of the results obtained. The beginnings and ends of the currently existing passing zones did not match those expected according to standardized criteria, thereby revealing possible deficiencies when establishing passing zones.

Several future lines of research are suggested. First, because of the differences found between design, posted, and operating speeds, a speed study where such inconsistencies are found could further understanding about how the operating speed relates to the design speed and the posted speed limit. It could also be used to examine the potential effects of these differences on safety with regard to sight distance. Second, this 3D methodology can be applied to study the effects on the ASD for building brand new overpasses and optimizing the location and layout of the overpasses with respect to the sag vertical curve.

The authors gratefully acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (FEDER) for research project TRA2015–63579-R (MINECO/FEDER).