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ekmekcieffectsroadwidthradii2024.md

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category: literaturenote citekey: ekmekcieffectsroadwidthradii2024 title: "Effects of road width, radii and speeds on collisions at three-arm priority intersections" authors: "Ekmekci, Mustafa; Woods, Lee; Dadashzadeh, Nima" year: 2024 date: 2024-00-00 2024 doi: 10.1016/j.aap.2024.107522 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2024.107522" zotero_key: 4EJRG565 zotero_storage: BP4JZH48 collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Ekmekci, Mustafa"

status: converted

Contents lists available at ScienceDirect

Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Effects of road width, radii and speeds on collisions at three-arm priority intersections

Mustafa Ekmekci a,1,* , Lee Woods b,2 , Nima Dadashzadeh c,3

  • a School of Civil Engineering and Surveying, University of Portsmouth, Portsmouth PO1 3AH, UK
  • b Faculty of Technology, Portland Building, University of Portsmouth, Portsmouth PO1 3AH, UK
  • c Future Mobility Centre, Huddersfield Business School, University of Huddersfield, Huddersfield HD1 3DH, UK

ARTICLE INFO

Keywords: Visibility Priority intersection Safety Collisions 20 mph speed limit 30 km/h speed limit piecewise Structural Equation Modelling

ABSTRACT

Simulation and observational studies have identified the importance of intersection geometries and vehicle speeds in collisions. However, the causal mechanisms of such collisions in low-speed areas and for different collision types remain unclear. This observational study investigates the complex relationships between geometries, speeds, visibilities, and road traffic collisions in the context of low-speed urban areas. Data were collected from 120 three-arm priority intersections in Portsmouth, UK. In 2007, Portsmouth became the first city in the UK to adopt a 20mph speed limit on all residential streets. The city has also adopted the UK's Manual for Streets (MfS) as the design standard for all new priority intersections in low-speed residential areas. Piecewise structural equation models (pSEM) were developed to represent the causal mechanisms that relate to geometries, speeds, speed limits and collisions. Findings indicate the role of combinations of approach lane width, corner radii, speed limit, and type of collision. The interaction of wider approach lanes on the minor arm and larger radii of turns for left-turning vehicles (left-hand driving perspective) was associated with higher numbers of road traffic collisions for right-turning vehicles. It is posited here that this is due to the orientation of the left-turning vehicle blocking the left visibility of the right-turning vehicle. These results give weight to the introduction of the 20mph speed limit zone in Portsmouth and some of the changes brought about by MfS. However, the combined effect of approach width and radii on collisions is novel and could form the basis of further guidance on reducing specific types of collisions at three-arm priority intersections.

1. Introduction

Globally, there is a growing awareness of the importance of road safety and the high number of road collisions leading to fatalities and severe injuries. According to the World Health Organisation (WHO, 2018), 1.35 million people worldwide are killed in road collisions. Among young people aged 15–29, road collisions are the leading cause of death (WHO, 2015). According to the Federal Highway Administration (FHWA, 2018), just under 37,000 fatal collisions occurred on the roads of the United States in one year. More than 50 % of the total fatal and injury crashes occur at or near intersections (FHWA, 2024). Furthermore, 18 % of the fatal collisions happen in unsignalized intersections, with 14 % involving pedestrians and 3 % cyclists.

Intersections, at-grade or grade-separated, are locations of high collision concentration among European countries, 40–60 % of the total (European Commission, 2024). In the UK, 49 % of collisions in urban areas happen at priority control intersections, of which 59 % occurred at T or staggered intersections (statistic calculated from STATS19 (Department for Transport, 2022) dataset using ArcGIS). These collisions are responsible for many casualties, 66 % of whom were drivers, cyclists or motorbike riders; 19 % passengers; and 15 % pedestrians.

Priority intersection design standards and guidance have evolved in the UK from 1946 (Design & Layout of Roads in Built-Up Areas) (Cook, 1946) to the most recent guidance published in Manual for Streets and Manual for Street 2 (Department for Transport, 2007; CHIT, 2010). MfS has been adopted as the design standard by many highway authorities

* Corresponding author.

E-mail addresses: mustafa.ekmekci@port.ac.uk (M. Ekmekci), lee.woods@port.ac.uk (L. Woods), n.dadashzadeh@hud.ac.uk (N. Dadashzadeh). 1 ORCID: 0000-0003-2636-1739. 2 ORCID: 0000-0002-8336-4939. 3 ORCID: 0000-0001-5425-0572.

when designing new priority intersections, particularly in lower-speed urban areas. There was a recognition in MfS that providing excellent visibilities to drivers through Design Manual for Roads and Bridges (DMRB) (Highways Agency, 1994) and Design Bulletin 32 (DB32) (Department of the Environment, 1992) standards had a counterintuitive effect on safety. With excellent visibility, drivers' perceptions of risks reduce, which leads to increased vehicle speeds, less concentration, and greater risk-taking behaviours (Henson et al., 1992). Rather than improving the intersections' safety, it is suggested that excessive visibility reduces the safety of intersections. As such, MfS reduces the minimum visibility requirements at priority intersections alongside guidance on reducing the geometric dimensions of these intersections. MfS also promotes the use of 20mph speed limits in built-up areas. Portsmouth in the UK became the first city where a 20mph city-wide speed limit was introduced across residential areas (Bunce, 2009).

This study sets out to investigate the traffic safety of low visibility priority intersections at 120 locations in Portsmouth. This paper examines the effect of visibility distance, approach width, radii and speeds on road traffic collisions. Although many studies in the literature look at the effect of geometrical variables on road traffic collisions, these studies did not look at the combined effect of geometrical variables in the context of low-speed/low-speed-limit priority intersections.

The remainder of this paper is structured as follows: Section 2 reviews the existing literature on contributory factors of road traffic collisions (RTC) at priority intersections, human factors of RTC, and visibility issues at priority three-arm intersections. Section 3 describes the study area, data collection and analytic methods. Results and discussions are presented in Section 4, followed by the conclusions and suggestions for further work in Section 5.

2. Review of literature

2.1. Contributory factors of road traffic collisions

A considerable body of literature exists on the causes of road traffic collisions, including several studies related to priority intersections in the UK and globally. It is essential to understand what kind of variables affect intersection safety in order to be able to discern the effects of visibilities, radii and approach width from the effects of all other variables likely to impact the numbers and types of collisions. Table 1 shows general contributory factors of RTCs in the literature.

Many studies show that minor road width is associated with an increase in approach speed and collision frequency both globally (i.e. Harnen et al., 2003; Vieira Gomes, 2013) and in the UK (i.e. Summersgill et al., 2001). However, these studies could not explain the wider minor road width, radii and visibility connections.

Vehicle speed is the most commonly recognised contributory factor for collisions. Ziolkowski (2016) examined the effect of geometric variables and road features on vehicle speeds in urban areas and found that an increase in road width was associated with an increase in speed. Salifu (2004) observed that the major arm's standard deviation of the approach speed was significantly and positively correlated with collision frequency. However, the speed effect may also be contradictory for specific types of collisions, such as right-turning and left-turning movement collisions from minor roads. A microsimulation study of three-arm priority intersections by Zhang et al. (2017) found that the number of collisions for turning vehicles from minor roads decreased with increased speed on the major road. The authors thought psychological factors could explain why drivers turning from the minor road may drive cautiously when traffic speed on the major arm is relatively high.

Researchers have paid considerable attention to the relationship between traffic collisions and traffic flow (i.e. Salifu, 2004; Vieira Gomes, 2013; Bonneson and McCoy, 1993; Hauer et al., 1988; Kulmala, 1996; Golias, 1991). The common sense of traffic safety concludes that collisions cannot occur with zero traffic flow (Turner et al., 2003) and

Table 1 General contributory factors of road traffic collisions at priority intersection.

Feature Reference
The number of arms/approach lanes
in junction		 Vieira Gomes (2013), Wang et al. (2015)
Channelisation (Ghost Island, Left Summersgill et al. (1996), Abdel-Aty and
Turning Line, Right Turning Line) Haleem (2011), Salifu (2004)
The distance to the nearest other
intersection		 Haleem and Abdel-Aty (2010)
Visibility York et al. (2007), TMS Consultancy (2010),
Summersgill et al., (2001), Pickering et al.
(1986)
Road Width Ziolkowski (2016), Greibe (2003), Salifu
(2004), Harnen et al. (2003), Vieira Gomes
(2013), Ahmed et al. (2014)
Road surface conditions Akin and Akbas (2010), Wang et al. (2015),
Hassan and Al-Faleh (2013)
Speed (Mean, St. deviation, 85th
percentage, speed limit)		 Charlton (2003), Haleem and Abdel-Aty
(2010), Sarkar et al. (2012), Salifu (2004),
Wang et al. (2015)
Day or Night Wang et al. (2015), Hassan and Al-Faleh
(2013)
Road Lighting Salifu (2004), Hassan and Al-Faleh (2013)
Weather Condition Akin and Akbas (2010), Wang et al. (2015)
Traffic Volume Salifu (2004), Vieira Gomes (2013),
Bonneson and McCoy (1993), Hauer et al.
(1988), Kulmala (1996), Golias (1991),
Abdel-Aty and Haleem (2011)
Car Parking Sarkar et al. (2012)
Guard, Pedestrian Crossing, Cycle
Lane		 Salifu (2004), Summersgill et al. (1996)
Day of the Week, Time of Day Hassan and Al-Faleh (2013)

Annual Average Daily Traffic (AADT) flow is a significant predictor of collisions (Kim et al., 2007).

The study of Salifu (2004) at priority T intersections revealed that the absence of street lighting, right turn storage on major arms (left-hand drive perspective), the standard deviation of approach speed on the major arm and wider road width of the minor road were all significantly and positively correlated with the frequency of collisions (Salifu, 2004).

2.2. Human factors

The studies in section 2.1 considered factors associated with the intersection. However, research has shown that factors associated with the driver are the most common cause of road traffic collisions, such as speeding, careless driving, distraction due to the use of handheld devices, driving under the influence of alcohol or drugs and other risktaking behaviours. The characteristics of the driver are shown to relate to some of these behaviours, with young men being particularly prone to aggressive driving and higher risk-taking behaviours, which is believed to be the main reason why younger men are more likely to be involved in road traffic collisions than their female counterparts (Stanton and Salmon, 2009; Massie et al., 1995; Holland et al., 2010). Amin (2020) examined the effect of contributory factors on male and female older drivers in the West Midlands of the United Kingdom. Complex intersection geometry, extreme weather conditions and time of day were significant factors for older driver collisions.

Human errors have the highest collision contributions depending on research outcomes, between 75 % and 95 % (Stanton and Salmon, 2009; Kostelec, 2020).

Whilst it can be seen from these two datasets that road conditions (including here road geometries) feature little in terms of the causes, it is highly plausible that many of the driver behaviours listed as causes are themselves influenced by the geometric design of intersections, particularly the level of care drivers show at an intersection, risk-taking behaviours and speed, which are some of the most critical factors in road traffic collisions.

2.3. Visibility issues at three-arm priority intersections

Some researchers have used microsimulation studies to explore the causes of road traffic collisions (i.e. Darzentas et al., 1980; Zhang et al., 2017). Microsimulation approaches depend on gap acceptance and other driver characteristics specified within the simulation. Hence, they may not be appropriate when investigating such behaviours. Moreover, some microsimulation models also assume junction visibilities (Darzentas et al., 1980) rather than investigating their effect.

Most studies in the literature into the causes of collisions are observational rather than based on simulations. Pickering et al. (1986) observed frequencies and characteristics of collisions at priority T intersections in rural areas where the speed limit was 50mph and examined the effect of some features of T intersections, such as ghost islands (major arm to minor arm turning areas demarked with road markings only rather than physical barriers/kerbs) which were found to be associated with a reduction in collisions. The wider road width on the major arm had similar beneficial effects on collisions. The collision rate of turning right movements from the minor road was 40 % lower at intersections without merging and diverging lanes. Pickering et al. (1986) stated that there is no explanation for this but suggested this might be related to visibilities from the minor road. He used the reciprocal and identity forms of visibility variables to test this and found that their inclusion was significant for rear shunt collisions on minor arms only. Longer right-hand visibilities, 9 m back, were associated with higher numbers of minor rear shunt collisions.

Pickering et al. (1986) and the Cost Benefit Analysis of collisions (COBA) procedure requires at least a knowledge of traffic inflow to estimate traffic collisions (Highways Agency, 2022).

Arndt and Troutbeck (2001) concluded that the approaching visibilities at minor arms were not associated with collision rates. However, this study did not examine the causality of traffic collisions regarding visibility.

Methodologically similar to Pickering's study (1986), Summersgill et al. (1996) considered the visibility of intersections by measuring these from 2, 4.5 and 9 m back from the give-way line and the association with collisions. However, they did not assess collision types such as rear shunts, right-turn major arm movements. Layfield et al. (1996) considered staggered intersections in the UK, highlighting that the inverse of visibility from minor roads can predict collisions instead of using the mean speed of major road vehicles. Another study by Summersgill et al. (2001) compared the operational forms of one-way and two-way priority intersections in urban areas. They found that visibility was associated with speed, so these variables may affect collisions by modifying speed. However, the authors could not demonstrate the mechanism by which this might happen. York et al. (2007) and TMS Consultancy (2010) undertook research on visibilities at priority intersections to support the development of the MfS. The results showed that shorter visibility could lower vehicle speeds in line with Summersgill et al. (2001). York et al. (2007) concluded that geometries could reduce both the likelihood and severity of collisions. Visibilities of just 40 m can be safe. However, caution was expressed that visibilities less than 20 m may not be safe as speeds may not be reduced sufficiently to offset the shorter visibility. TMS Consultancy concluded that visibility y distance on the major arms could not be seen as a single deterministic factor for road collisions in high-risk urban areas.

The developing body of research into the negative impacts of excessive visibilities at intersections on collisions led to the guidance in the MfS. In contrast with earlier design guidance and standards (Design and Layout of Roads in Built-up Areas, 1946; Design Manual for Roads and Bridges, 1992), MfS promoted shorter visibilities and geometries in order to reduce vehicle speeds and therefore reduce the likelihood and severity of collisions. MfS requires stopping sight distances to the left and right to be provided from only 2.4 m back from the give-way intersection. This 2.4 m x-distance relates to the distance between the front bumper of a large car and the driver's eye position. In doing so, MfS intersections require the driver on the minor arm to stop at the give-way line, as it is only at this point that they have sufficient visibility to determine if there are gaps in the traffic they can turn into. This is a fundamental difference from earlier design standards that allowed drivers to make such judgements from 9 m back, meaning that they did not necessarily need to stop or slow down considerably at the give-way line as two measurements were illustrated in Fig. 1.

TMS Consultancy (2010), York et al. (2007), and others provide evidence as to the association between visibilities and collisions and an indication that the effect may be through moderation of vehicle speeds, but there remain unanswered questions as to the relationships between geometries, speeds, speed limits and visibilities at intersections in the UK. Their analysis of these associations is problematic. They do not account for the nature of rare collision data, which may not be normally distributed with respect to visibilities. The simple linear regression of a count response variable may not present meaningful results. Generalised Linear Modelling (GLM) approaches taking account of the discrete nature of responses would be more logical. Such approaches have been applied in the UK (Maher and Summersgill, 1996; Pickering et al., 1986) and overseas (i.e. Bonneson and McCoy, 1993; Hauer et al., 1988; Kulmala, 1996; Poch and Mannering, 1996; Salifu, 2004; Sawalha and Sayed, 2006; Sayed and Rodriguez, 1999). However, GLM may not be able to represent the complex inter-relationships, and feedback loops between speeds, visibilities, speed limits and collisions posited in this paper. Moreover, the generalizability of previous research to the context of very low-speed limit areas, such as the Portsmouth 20mph city-wide scheme, is questionable. Recent changes to the Highway Code (DVSA, 2022), changes brought about by new in-vehicle technologies, driving styles and the change in design standards mean that new empirical research may uncover different associations and relationships to those presented in the current literature.

This study, therefore, seeks to understand the complex interrelationships between visibilities, speeds, speed limits, geometries and different types of road traffic collisions in the context of low-speed (20mph) intersections through an analysis of data from Portsmouth, UK.

3. Method and data

This section describes the study area, sampling strategy, data collection approach, and the analytic methods adopted.

While an experimental approach may be beneficial in determining causality (from a statistical perspective), this has significant ethical issues. Changes in the visibilities at intersections to observe whether collision increases would not pass most ethical tests. Also, collisions are rare events, so the data collection for an experimental design may take several years. Microsimulation, which is beneficial if no collision data exists, can be used, but these require gap acceptance and other driver behaviours to be specified for the model to be run. These behaviours are not interesting to this study; hence, this approach was rejected. The overarching methodological approach deemed most appropriate was observational and quantitative due to the convenience, timescales and ethical considerations. The Department publishes detailed secondary datasets on collisions in the UK (STATS19) for Transport (DfT) which enables such observational studies possible across a large population of intersections (Department for Transport UK, 2022).

3.1. Study area

The City of Portsmouth was the first city in the UK to adopt a 20mph speed limit on all residential streets in 2007 (Bunce, 2009). The city is the most densely populated in the UK, with much of the city developed during the industrial Victorian period around the Royal Navy base. Large residential areas are typified by high-density terraced housing with minimal or no setback from the footway and low visibility priority junctions linking these roads to local distributor roads. Mid-century areas adhered to the design standards of the time, which promoted

Fig. 1. Illustration of how visibility distances can be drawn for different x-distances.

high visibility on minor arms of priority intersections to aid traffic capacity. Most recently, the city has adopted the UK's Manual for Streets as the design standard for all new priority intersections in low-speed residential areas.

3.2. Sampling strategy of low visibility three-arm intersections

A stratified sampling strategy was used rather than random sampling to efficiently secure the diversity of variables required. Stratification of priority three-arm intersections was based on minor and major road speed limits: 20mph or 30mph, and the visibility of the intersection: low or high, as shown in Table 2.

A standard way of identifying whether intersections had relatively low or high visibility is to compare the visibility of intersections and the corresponding Stopping Sight Distance (SSD). If the visibility of an intersection is more than the SSD of that intersection, it means that the minimum safety requirement related to visibility was met. Equation (1) shows the basic SSD formula. 'v' is speed (m/s), 't' is the reaction time (s) of drivers to recognise a hazardous situation, and 'd' represents deceleration of vehicles (m/s2 ). Stopping sight distances (SSD) were calculated with 1.5 s reaction time and 4.41 m/s2 deceleration coefficients provided by MfS for light vehicles. A spot speed camera measured the speed of vehicles going through the major roads and approaching the intersections. These speeds were used to calculate the SSD rather than speed limits. Intersection visibilities to the right or left, from 4.5 m back that were equal to or less than 1.1*SSD, were considered low visibility intersections.

$$SSD = v^*t + \frac{v^2}{2^*d}$$ (1)

3.3. Data collection

More than 150 three-arm intersection locations in Portsmouth were reviewed between September 2020 and August 2021 of which 120

Table 2 Sample Stratification.

Speed Limit on
Main Road		 Speed Limit on
Minor Road		 Low
Visibility		 High
Visibility		 Total
20mph 20mph 20 20 40
30mph 20mph 20 20 40
30mph 30mph 20 20 40
Total 60 60 120

priority three-arm intersections met the criteria set out in section 3.2 to be included in this study (Ekmekci et al., 2023). Primary data (Speed & Classified Manual Traffic Counts) were collected from these 120 locations in Portsmouth and Gosport, as shown in Fig. 2. Speed data for approaching vehicles at 360 intersection arms were measured by using an SL700 spot speed camera. Classified 15-minute traffic counts were undertaken in the am, pm or both peak periods. These were converted to AADT using the standard conversion factors suggested by the Chartered Institution of Highways and Transportation (CIHT, 1997). Secondary response variable data in this study was obtained from the STATS19 database downloaded from "data.gov.uk". The dataset includes separately documented collision, casualty and vehicle files for the base years between 2008 and 2020.

Visibilities to the left and the right were measured in two ways. MfS requires visibilities to the left and the right to be measured to the nearside kerb from 2.4 m back from the give-way line. This is because vehicles approaching from the left may be overtaking vehicles or cars parked and hence be on the "wrong" side of the road. Additionally, in this study, visibilities were measured to the centre line of the major arm, as shown in Fig. 3 and also considered obstructions caused by parked vehicles. This study focuses on right-turning vehicles. These involve gaps being accepted to the left and right, hence visibilities to the left and the right. Both sets of visibility measurements were tested in the modelling described later.

3.4. Piecewise structural equation modelling (pSEM)

Piecewise Structural Equations Modelling (pSEM) was developed by Shipley's studies in the 2000 s (Shipley, 2009). The relationships between variables in the traditional SEM are simultaneously estimated in a single variance–covariance matrix (Stein et al., 2012). However, in piecewise SEM (pSEM), each set of relationships are estimated locally (or, in other words, independently) (Shipley, 2009). The traditional SEM uses chi-square tests to compare observed and predicted covariance matrices, while the goodness-of-fit of a pSEM is measured as a "test of directed separation" (Lefcheck, 2016). Shipley (2009) highlighted that this test does not depend on asymptotic methods, so it can be used with smaller sample sizes. Secondly, many problems involving non-normality and non-linearity can be overcome. Another aspect of the "test of directed separation" is that it does not conflict with some problems of covariance matrices involving a maximised loss function. Finally, it allows each piece of the local causal model to determine the extent to which it contributes to the lack of fit (Shipley, 2009). Therefore, pSEM seems to be a robust technique, and the work presented here is believed

Fig. 2. Locations for 120 three-arm priority intersections in Portsmouth data collection.

Fig. 3. Used variables in the initial causal path.

to be the first study that models traffic collisions with pSEM.

R Studio was selected as the analytical package, as it is an opensource programming language supported by various academic environments, with three extensions to run SEMs, including "piecewiseSEM" integrated with Generalized Linear Modelling (GLM) techniques (RC Team, 2020; Lefcheck et al., 2023).

As collisions are rare events, the frequencies will not follow normal distributions. One sample Kolmogorov-Smirnov test was used to check whether they followed Poisson distributions. The results show no significant evidence (Asymp. 2-tailed significance is 0.149) to reject the null hypothesis that "H0: The frequency of the sample significantly differs from a Poisson distribution." Therefore, it is assumed that the collisions follow Poisson distributions, and modelling the data with Poisson regression is appropriate.

The associations between speed variables (mean) and other factors

were modelled with pSEM through multiple linear regression, as speeds are dependent variables. Kolmogorov-Smirnov tests were used to check the normal distribution assumptions. As per the results in Table 3, the variables are assumed to be normally distributed.

Fig. 4 below shows the path diagram of the pSEM model. Response variables are the mean of minor road speed, major road speeds (from right arms to the left and left arms to the right) and traffic collisions.

Table 3 Test of Normality.

Kolmogorov-Smirnova
Statistic df Sig.
Mean of Minor Road Speed 0.075 120 0.094
Mean of Major Road Right to Left Speed 0.071 120 0.200*
Mean of Major Right Left to Right Speed 0.047 120 0.200*

Fig. 4. Initial pSEM causal path.

(2)

(5)

Predictors are traffic flow, the combination of minor road width and corner radii, visibilities, speed limit and major road width, the mean of minor road speed, and major road speeds (from right arms to the left and left arms to the right).

The hypothesized model's equations can be written as follows:

$$\begin{split} AvrSpeedMinor &= [TF.\beta_1 + Int.\beta_2 + VisR24.\beta_3 + VisR9.\beta_4 + VisL9.\beta_6 + SpeedLimit.\beta_7 + AvrSpeedMajRtoL.\beta_8 \ &+ AvrSpeedMajLtoR.\beta_9 + \beta_0] \end{split}$$

AvrSpeedMajRtoL = TF*.β10 + SpeedLimit.β11 + WidthMaj.*β12 + β13

$$AvrSpeedMajLtoR = [TF.\beta{14} + SpeedLimit.\beta{15} + WidthMaj.\beta{16} + \beta{17}]$$ (4)

$$\begin{split} E &= Exp(TF.\beta{18} + Int.\beta{19} + VisR24.\beta{20} + VisR9.\beta{21} + VisL24.\beta{22} + VisL9.\beta{23} \ &+ SpeedLimit.\beta_{24} + AvrSpeedMinor.\mu_1 + AvrSpeedMajRtoL.\mu_2 \ &+ AvrSpeedMajLtoR.\mu3 + \beta{25}) \end{split}$$

Where,

βi and μi : Estimated coefficients.

TF: Traffic Flow (vehicle/hour). Int: Interaction of minor road width and corner radii (metres2 ). VisR24: Right-hand visibility at 2.4 m back from give-way lines projected to the near side kerb of the major road (metres). VisR9: Right-hand visibility at 9 m back from give-way lines projected to the near side kerb of the major road (metres). VisL24: Left-hand visibility at 2.4 m back from give-way lines projected to the centre line of the major road (metres). VisL9: Left-hand visibility at 9 m back from give-way lines projected to the centre line of the major road (metres). SpeedLimit: Speed limit (variable is 1 if 20mph is applied; 0 if not). WidthMinor: Minor road width measured at 9 m back from give-way lines (metres). WidthMaj: Major road width (metres). AvrSpeedMinor: Average speed of vehicles approaching on the minor arms (mph). Avr-SpeedMajRtoL: Average speed of vehicles traveling from the major road's right arm to its left arm (mph). AvrSpeedMajLtoR: Average speed of vehicles traveling from the major road's left arm to its right arm (mph). E: Expected frequency of collisions predicted by the model (collision/year). Exp (): Exponential function of the natural number (e).

4. Results and discussions

The connections in the initial model shown in Fig. 4 were step by step removed from the model using a backward elimination method. The final form of the pSEM path diagram is shown in Fig. 5. Traffic flow, minor road width, visibility to the right (R 2.4 m), and visibility to the left (L 2.4 m) have a statistically significant impact on the number of the turn right from minor motorised veh-veh collisions at the 95 % confidence level (P-value of 0.05).

The parameters estimated and P-values for the latest form of the pSEM model are summarised in Table 4, and estimates of model fit are shown in Table 5. The variables included in the final model were able to predict circa 60 % of the variation in the numbers of right-turn motorised veh-veh collisions. This compares to 37 % for the flow-based model and 50 % for the geometry-flow-based model by Salifu et al. (2004), and two models (multivariate adaptive regression splines (MARS) and negative binomial (NB)) produced by Abdel-Aty and Haleem (2011) with 39 % and 19 %, respectively.

These results reinforce the findings in the literature that vehicle flows relate to the number of collisions at priority intersections (Hauer et al., 1988; Golias, 1991; Kulmala, 1996; Bonneson and McCoy, 1993; Salifu, 2004; Bonneson and McCoy, 1993; Hauer et al., 1988; Kulmala, 1996; Golias, 1991; Salifu, 2004; Vieira Gomes, 2013). This study has also confirmed that these findings remain true in the context of lowspeed limit (20mph) areas.

Speed limit and a combination of approach width and corner radii on the left (geometries) affect approach speed. In low-speed limit areas, the effect of speed limits and geometries on vehicle speeds negates any apparent effects of visibilities on speeds on the minor approach. The lower visibilities are not slowing vehicles down further than the speed limits, and geometry has already slowed vehicles. This may suggest that there is a role for lower speed limits, even at intersections where visibilities are already low. However, visibilities do appear to have a direct relationship with the number of collisions rather than an indirect one through vehicle speeds. Visibility distances at 2.4 m back from the giveway line were directly associated with the number of collisions for rightturning vehicles. All else being equal, the greater the left-hand visibility at 2.4 m back, the better the safety, while greater right-hand visibility had a counter effect on safety. This is contrary to the literature (York et al., 2007; TMS Consultancy, 2010; Summersgill et al., 2001) and to the design standards (Department for Transport, 2007; CHIT, 2010;

Fig. 5. The latest form of pSEM after implementing the backward elimination method.

Table 4 Results of pSEM Parameters estimate and P-value for the final pSEM model.

Response Predictor Estimate P.
Value
Mean of Major Road Right to
Left Speed		 Traffic Flow 0.0005 0.0000
Mean of Major Road Right to
Left Speed		 Speed Limit 3.9902 0.0000
Mean of Major Road Left to
Right Speed		 Traffic Flow 0.0005 0.0000
Mean of Major Road Left to
Right Speed		 Speed Limit 3.1690 0.0000
Mean of Minor Road Speed Speed Limit 2.3575 0.0000
Mean of Minor Road Speed Corner Radii: Minor
Road Width		 0.0221 0.0028
Right Turn from Minor Veh
Veh Collisions		 Vis. Right 2.4 0.0026 0.0364
Right Turn from Minor Veh
Veh Collisions		 Vis. Left 2.4 − 0.0035 0.0293
Right Turn from Minor Veh
Veh Collisions		 Traffic Flow 0.0002 0.0000
Right Turn from Minor Veh
Veh Collisions		 Corner Radii: Minor
Road Width		 0.0113 0.0003

Table 5 R-square values of response variables.

Response R-squared of pSEM
Mean of Major Road Right to Left Speed 0.34
Mean of Major Road Left to Right Speed 0.34
Mean of Minor Road Speed (MMRS) 0.26
Right Turn from Minor Veh-Veh collisions 0.60

Highways Agency, 1994) that do not distinguish between left-hand and right-hand visibilities. The reasons behind this counterintuitive finding are not yet known. It may be the case that for right-turning vehicles, drivers first look for a gap to the right before looking for a gap to the left. When visibility to the right is good, this may encourage drivers to pull out into the intersection when a clear gap to the left is not yet apparent. Further work to investigate this phenomenon is required.

Major road mean speeds are not significant predictors of turning

movement collisions from the minor road. This result is not surprising. A microsimulation study of three-arm priority intersections by Zhang et al. (2017) found that the number of conflicts for turning vehicles from minor roads decreased with increased speed on the major road. The authors thought that psychological factors could explain this situation that drivers turning from the minor road may drive cautiously when traffic speed on the major arm is relatively high.

The results confirm the effects of speed limits and vehicle flows on the approach speeds as expected. On the other hand, Table 6. shows the effect of a + 1 standard deviation change in input variables on traffic collision frequency. The direct effect of traffic flow seems to be more potent than others. + 1 standard deviation change in the visibility (105.4 m) to the left, from the minor arm, was associated with a 31 % reduction of collisions over the observed period. To the contrary, the + 1 standard deviation change in the visibility (91.1 m) to the right was associated with an increase in the number of collisions by 27 %. Additionally, wider approaches and larger radii are associated with higher approach speeds on minor arms. + 1 standard deviation change in this combination caused by 45 % increase in the collision frequency. From a statistical perspective, Fig. 6 provides insight into why the interaction effect of corner radii and minor road width is significant. It is suggested here that this might be due to the fact that at wider minor arms, two cars can be at the give-way line together. Where the corner radii for the leftturning vehicle is small (Fig. 6A), the left-turning vehicle is likely to be

Table 6 The effects of 1 SD change in independent variables on collision frequency.

Variable Mean Standard
Deviation (SD)		 Coefficient Effect on
Collision (%)
Vis. Right 2.4 80.5 91.1 0.0026 EXP (91.1x
0.0026) − 1 =
+27
Vis. Left 2.4 104.8 105.4 − 0.0035 EXP (105.4x
− 0.0035) − 1 =
-31
Traffic Flow 3790.5 3295.6 0.0002 EXP (3295.6x
0.0002) − 1 =
+93
Corner Radii *
Minor Road
Width		 33.5 32.7 0.0113 EXP (32.7x
0.0113) − 1 =
+45

Fig. 6. The effect of the interaction of minor road width and turning radii.

relatively perpendicular to the give-way line. In such an orientation, the driver of the right-turning vehicle sat at the same give-way line is clear as it passes over the bonnet of the left-turning vehicle. Where the corner radii for the left-turning vehicle is wider (Fig. 6B); due to the orientation of the left-turning vehicle, the vision of the right-turning vehicle is obstructed by the cabin space of the left-turning vehicle. See the diagram below.

5. Conclusion and future studies

The purpose of this study was to explain the complex interplay between approach width, radii, speed and visibility in the context of lowspeed limit priority intersections. This paper has provided a deeper insight and given novel evidence into visibility and traffic collision interactions. A novel pSEM approach was adopted to explore these complex interactions. The initial model's connections were refined using a backward elimination procedure to develop the final model. Results of the final pSEM model show that:

  • As expected, flows were found to be important, even in the context of low-speed limit areas.
  • Approach speed is affected by the speed limit and the combination of approach width and left corner radii.

  • On the minor approach, the effect of speed limits and geometry on vehicle speeds negates any apparent benefits of visibilities on speeds in low-speed limit locations. The lower visibility does not slow vehicles any more than the speed limits and geometry already do. This could imply that lower speed limits have a role to play, especially at intersections where visibility is already low. On the other hand,

  • visibilities appear to have a direct relationship with collision frequency rather than an indirect one via vehicle speeds.

  • Major road mean speeds are not significant predictors of the minor road turning movement collisions.

  • Visibilities did not moderate the effect of approaching vehicles' speed at low-speed intersections, while minor road width and turning radii are significant predictors of minor road speed.

  • The direct effect of traffic flow appears to be stronger than others.

  • Collisions are also related to the width and radius of the nearside kerb on minor arms at three-arm priority junctions.

  • Furthermore, wider minor road width and larger radii are related to faster minor arm approach speeds.

  • It is highly plausible that wider road width and corner radii allow a second vehicle wishing to turn left to be at the give-way line blocking the left-hand visibility.

MfS promotes single-lane minor arm intersections and smaller turning radii (MfS section 9.4). However, this study found that the combination of these two factors appears to be significant rather than either factor on its own.

The number of collisions for right-turning vehicles was directly related to visibility distances at 2.4 m back from the give-way line. All else being equal, higher left-hand visibility at 2.4 m increased safety, while greater right-hand visibility decreased safety. This contradicts the literature (York et al., 2007; TMS Consultancy, 2010; Summersgill et al., 2001) and design standards (Department for Transport, 2007; CHIT, 2010; Highways Agency, 1994) that do not differentiate between leftand right-hand visibilities. The causes for this unexpected discovery are unknown. Drivers of right-turning vehicles may check for a gap to the

right before looking for a gap to the left. When visibility to the right is good, drivers may be tempted to pull out from the intersection due to a clear gap to the left is not yet visible. More research into this phenomenon is needed.

Major and minor road speeds cannot be seen as a determining factor of right-turning from minor with major road motor vehicle collisions, even if it is a crucial aspect for another type of collision not included in this paper.

As explanatory variables, visibilities at 9 m to the left and right did not significantly affect the type of collision presented in this paper. However, other types of collisions, such as motor vehicle-bicycle, should be analysed to understand the effect of visibilities at 9 m.

While the study primarily focuses on driving behaviours in the United Kingdom where vehicles are driven on the left side of the road, it is essential to acknowledge the potential applicability of the findings to other high-income countries with right-hand driving practices such as United States. Despite the natural differences in traffic regulations and cultural norms between left and right-hand driving nations, there may be similarities in certain driving behaviours and decision-making processes. However, it is crucial to recognize that direct transferability may be limited due to contextual variations, such as infrastructure differences, road design, and socio-economic factors. Future research should explore how the findings can be estimated for diverse driving environments, thereby contributing to a more comprehensive understanding of global road safety dynamics.

CRediT authorship contribution statement

Mustafa Ekmekci: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. Lee Woods: Conceptualization, Investigation, Methodology, Project administration, Supervision, Writing – review & editing. Nima Dadashzadeh: Conceptualization, Methodology, Supervision, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The data that has been used is confidential.

Acknowledgements

This work is a part of first author's PhD thesis which is fully funded by the Republic of Turkey Ministry of National Education, Çanakkale Onsekiz Mart University: Study Abroad Program.

References