# Improved Driveway Design for Superblocks to Reduce the Crash Risk

Authors: Xi Zhuo; Panos D. Prevedouros; Yongqiang Zhang; Changtai Lu; Yuxin Xiao; Weifan Zheng
Journal: Journal of Advanced Transportation
 (2022)

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## Abstract

The superblock has become a typical land use in China and many growing Asian cities. Superblock access points generate traffic congestion and many conflicts among all road users. Driveway design is a critical process and has a major impact on traffic conditions around superblocks. There are various guidelines for the two key factors for driveway design, driveway width and curb radius, but they provide reference values corresponding to traffic volume and speed; these are not sufficient for managing the complex traffic environment around superblocks. To improve driveway design, we develop detailed access point design models that account for conflicts between turning and through motorized vehicles, conflicts between motorized and nonmotorized traffic, speed differential larger than 10 km/h, and lane encroachments of entering and exiting vehicles. The crash risk models evaluate and optimize the combination of driveway width and curb radius with respect to three traffic safety indexes: traffic conflict, lane encroachment, and speed differential. A case study evaluation shows that the updated driveway design models produce a lower crash risk; seven of the ten driveways improved by 16.14% or more. The updated driveway design for superblocks would be beneficial for analyzing, permitting, and managing traffic operations at superblocks and oversized development with many and complex driveways.


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## Body

## 1. Introduction

Superblock is an urban area of several acres, usually closed to through traffic, having a mix of land uses including residential, commercial, social, and recreational facilities [1]. A typical block in Manhattan in New York City is about 80 m × 275 m (260 ft by 900 ft), and in Chicago, Illinois, and Minneapolis, Minnesota, a typical city block is 100 m × 200 m (330 ft by 660 ft). A superblock is much larger than a typical city block. For example, in New York City, the Stuyvesant Town private market and residential superblock take up about 18 city blocks. In China, the superblock measures about 300 m × 500 m [2]. The superblock has played an important role in the urban growth of China and other major cities in Asia. A superblock is characterized by dense land use that includes housing, businesses, and entertainment venues. Superblocks tend to generate heavy traffic on the adjacent streets; they tend to be congested and the traffic safety risk is elevated due to the multitude of users and maneuvers. Additionally, Ewing et al. have found that the more connected street networks have significantly lower congestion levels, but they do not have measurably lower (or higher) crash rates, presumably due to the prevalence of four-way intersections [3]. Consequently, it is meaningful for us to investigate the relationship between traffic safety and superblock design which plays an important role in street connectivity.Access management strategies can help alleviate traffic problems at superblocks. Access management is the coordinated planning, regulation, and design of access between roadways and land development [4]. Many states in the US have developed access management guidelines, for example, Access Management Guidebook for Texas [5], Access Management Guidebook for Michigan [6], and Access Management Regulations for Virginia [7]. They are focused on providing efficient and safe access for vehicles and pedestrians. They pay more attention to certain traffic management techniques, which are divided into two main parts. One part addresses access spacing, zoning, setbacks, and so on, and the other part addresses frontage roads, medians, turning control, access location, and driveway design [8].The American Association of State Highway and Transportation Officials (AASHTO) provided a fundamental guidance for access management, which is applicable to superblock traffic management, but had limitations [9]. In response to these limitations, in 2019, the National Cooperative Highway Research Program (NCHRP) planned to award a contract for a study and report on “Public Liabilities Relating to Driveway Permits” [10]. Across the USA, there are approximately 2,000 driveway-related crashes per day with about 600 injuries. Therefore, in terms of driveway permits, there is a debate about balancing public interests (safety, efficiency) and private interests (profitability, convenience, and market value). Chakraborty and Gates analyzed safety impacts of driveways of various land utilization and found that commercial driveways possess a stronger effect on crash occurrence than other driveways of land use types, including residential and industrial driveways [11]. A more detailed and logical driveway design method which adapts more closely to the traffic environment of various land use would make the design and review of driveways easier, given that the stage of driveway permitting is critical to the approval and success of a superblock development. The superblock design presented herein also applies to extra-large urban block development and for theme parks, stadiums, and other large developments with multiple driveways.Driveway design is mainly composed of methods to design length, width, median, cross slope, intersection angle, horizontal alignment, grade, and auxiliary lanes of driveways [12]. Compared with urban streets, driveway design has its distinct geometry, road environment, and traffic operations. The basic design parameters are shown in Figure 1; the driveway width provides adequate space for vehicles entering and leaving the superblock. The width of a driveway should reflect the needs of both motorized and nonmotorized traffic [12]. Various guidelines provide reference values for the driveway width based on traffic volume, design vehicles, design speed, and so on. However, for complex driveways such as those at superblocks and other large venues, it is meaningful to develop a model for driveway width, which is adaptive to a complex access environment, instead of a design that only satisfies a few fixed standards.Figure 1
Width and curb radius of the driveway.In Figure1, the curb radius should assist right-turning vehicles with more smooth trajectories. A small radius causes a tight turn and may lead to encroachments of the curb or other lanes on the driveway or the main road [13]. To provide easier entry and exit movements for vehicles, guides give reference values of the curb radius, depending on the volume and speed of vehicles.Driveway width and curb radius are interrelated. If the curb radius is short, the vehicle needs a longer width to complete the entry movement, as shown in Figure2 [4]. NCHRP Report 659 provides reference values of combination of driveway width and curb radius, corresponding to a driveway entry speed [12]. The recommended values may not suit the whole range of access management and superblock access in particular. A quantitative model for the joint estimation of driveway width and curb radius is needed. Zou et al. applied the Bayesian Model Averaging for analyzing freeway traffic incident clearance time for emergency management, which can be used for predicting traffic incident clearance time when model uncertainty is considered [14]. The method provides the theory basis for optimizing the combination of driveway width and curb radius to reduce the crash risk.Figure 2
Turning trajectory of entry maneuver.The remainder of this paper is organized as follows. In Section2, we present past studies related to our research, including studies about superblock traffic management, the relationship between the driveway width and curb radius, and evaluation methods for driveway design. In Section 3, we present driveway width models based on conflicts between turning and through vehicles and those between motorized and nonmotorized traffic. In Section 4, we propose curb radius models, which consider entering and exiting turns, aiming at reducing the phenomenon of larger speed differential between turning and through vehicles, and lane encroachment. In Section 5, we present crash risk models to evaluate and optimize the combination of driveway width and curb radius by analyzing number of traffic conflicts. In Section 6, we conduct a case study on a superblock in China to evaluate the developed models. In Section 7, we discuss the pros, cons, and use value of the models. In Section 8, we present the conclusions of our study.


## 2. Past Research and Guidance

The superblock concept establishes a hierarchy of surrounding streets by separating through roads and roads serving local traffic [15]. The driveway is the connection between the Superblock Collector Street adjacent to the superblock and internal roads of the superblock. Throughout this paper, we use SCS for Superblock Collector Street to represent the roadway adjacent to the superblock. These connections often become bottlenecks due to the large number of turning movements and interference with pedestrians and nonmotorized traffic. Therefore, the design of driveways is a critical component of a superblock.AASHTO’s Green Book includes driveway width guidelines, which provide reference values of driveway width and number of lanes based on driveway usage [9]. NCHRP Report 659 indicates that design vehicle and design speed are fundamental factors affecting the driveway width design, and the width of a driveway is a function of the number of driveway lanes, the width of those lanes, and the presence and width of the median, if applicable [12].Levinson et al. state that the elements of driveway entry width (throat width), entry geometry (curved radius or straight taper), and entry shape dimensions must be considered together [16]. NCHRP Report 659 points out that the driveway width and the curb radius can perform in concert, so to some degree one can increase as the other decreases, which means that if the entry speed is constant, then there is an inverse relationship between entry radius and entry lane width [12]. An FHWA synthesis shows the relationships between driveway width, curb radius, and vehicle speed [17]. The Access Management Manual suggests that a designer could choose from a number of combinations of driveway width and curb radius, taking the design speed and driveway use intensity into account, and it is possible that the choice of minimum and maximum radii from one table and the minimum and maximum driveway widths from another table may cause conflicts in design [4]. Stover and Koepke found that a better practice is to use a specific combination of radius and throat width to accommodate a selected design condition [18], and NCHRP Report 15–35 indicates that certain collision types on the driveway, such as rear-end, right-angle, and head-on angle, are caused by the maneuvers of entering and exiting vehicles, which yields the fundamental safety or conflict points to optimize the combination of width and radius [19]. It is interesting that some researchers found that increasing the driveway width increases the crash frequency, but increasing the number of driveway entry lanes from 1 to 2 decreases the crash rate [20].Sultana et al. used a generalized negative binomial model to identify the impact of access parameters on truck-related crashes [21]. Their study demonstrated that significant factors in crash frequency prediction include standard deviation of commercial driveway throat width, flared commercial driveway throat width and its standard deviation, proportion of divided commercial driveways, signal density, and shoulder width. Chowdhury et al. evaluated different kinds of driveway design; each of the access management alternatives was evaluated in terms of travel time, number of stops, delay, and stopped delay using microscopic traffic simulation [22]. They found that the effectiveness of access management strategies is site-specific, but the driveway consolidation strategy yields a consistent improvement on almost all study corridors in terms of travel time. Richards studied the effects of driveway width, curb radius, and offset taper approach treatments on the speed and path of driveway users; his study found that average entry speed decreased as available width and/or curb radius decreased, and if the curb radius is large, then the path of vehicles turning right into the driveway tended to parallel the entry curb line [23].The aforementioned literature suggests that driveway design is important for access. The various guides focus mostly on reference values and qualitative guidelines of driveway width and curb radius. Our proposed driveway model includes width and curb radius, is based on spatiotemporal vehicle paths on the driveway and the adjacent street, and facilitates analysis with simulation and regression methods.


## 3. Driveway Width Models

To reduce conflicts, we propose models of driveway width and then combine them to find a better estimate for width. There are two types of typical entering movements, that is, 2 and 3 in Figure3, and two types of typical exiting movements, that is, 1 and 4 in Figure 3. Driveway width influences the possibility of exiting vehicles to use the gap in the through traffic flow, while it does not affect entering turns directly. Therefore, our research focuses on exiting movements 1 and 4 in Figure 3.Figure 3
Typical movements between SCS and driveway.For exiting movements, there are two types of crossing conflict areas. One is the conflict area of the motorized traffic; the other is the conflict area between the motorized and nonmotorized traffic.


### 3.1. Conflicts between Left-Turning and through Vehicles

Normally, the SCS is a two-way street. If there is no median on the SCS, left-turning vehicles would cross the through traffic flow, as shown in Figure4.Figure 4
Left-turning on two-way SCS. (a) Right-side left-turning. (b) Left-side left-turning.
(a)(b)Sometimes, the SCS is a one-way street, so an exiting vehicle should turn left to merge into the traffic flow, as shown in Figure5.Figure 5
Left-turning on one-way SCS. (a) Right-side left-turning. (b) Left-side left-turning.
(a)(b)Figures4 and 5 have similar traffic features, so we consider them together. There is a crossing conflict between left-turning vehicle 2 on the exit lane and through vehicle 1 on the SCS (see Figure 5). In this study, we make the following assumptions:(1)
Vehicle 1 is on the lane nearest to the superblock access.(2)
Trajectory of turning vehicle 2 is a circular arc.(3)
Vehicle 2 keeps the same turning radius for the whole turn.(4)
PointM, the starting point of turning trajectory, is in the middle of the exit lane on the driveway.(5)
PointA is the position of the front of vehicle 2 at the boundary of conflict area. When vehicle 2 turns left, A is on the extended centerline or the edge line of the driveway. Point B is the point of intersection between line OM and vertical line through point A. Point O is the center of turning circle. ΔABO is a right-angled triangle, which implies that OM is perpendicular to the driveway centerline or edge line.(6)
The widths of entrance and exit lanes are the same.The minimum gap that all drivers in the minor stream are assumed to accept at all similar locations is the critical gaptc (s) [24]. So tcl (s) is the minimum gap for left-turning vehicle 2 to leave the driveway and pass over the conflict area, shown in the following equation:(1)te+t2≥tcl,where te is the travel time for vehicle 2 to enter the boundary of the conflict area(s); t2 is the time for vehicle 2 to pass through the conflict area(s).In Figure5, by analyzing the geometrical relationship in this crossing conflict, we find that te could be calculated by the following formula:(2)te=3.6arccosRl−W/4RlRlVae,where Rl is the radius of left-turning trajectory (m); W is the width of driveway (m); Vae is the average travel speed of vehicle 2 (km/h).Then as the adequate driveway width is beneficial for vehicle 2 to cross the conflict area formed by the conflict between vehicle 1 and 2, we have the equations below.t2 can be calculated by the following equation:(3)t2=3.6WvehVae,where Wveh is the width of vehicle (m).Combining equations (1)–(3), we can calculate W by using the following equation:(4)W≤4Rl−4RlcosVaetcl−3.6Wveh3.6Rl.


### 3.2. Conflicts between Right-Turning and through Vehicles

When vehicle 2 turns right from the driveway to the SCS, vehicle 2 should merge into the traffic flow of the lane nearest to the superblock on the SCS (see Figure6). In addition to the assumptions above, we also assume that when vehicle 2 turns right, A is on the centerline of the lane nearest to the superblock on the SCS.Figure 6
Conflict between right-turning and through vehicles.We also get the following formula to present the relationship between travel time and gap:(5)te+t3≥tcr,where t3 is the time for vehicle 2 to turn right into the through traffic flow(s); tcr (s) is the minimum gap for right-turning vehicle 2 to leave the driveway and merge into the through traffic flow.In Figure6, point K is the point of intersection between line BM and the edge line of driveway. Further, according to the law of cosines, we derive the following formula for the angle at the center of arc AM⌢, that is, γ (rad):(6)γ=arccosKO2+AO2−AK22KO×AO=arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4Rr,where KO is the distance of line KO (m); AO is the distance of line AO (m); AK is the distance of line AK (m); Rr is the radius of right-turning trajectory (m); Wcro is the width of crosswalk (m); Wnv is the width of nonmotorized vehicle lane (m); Wlu is the width of the lane nearest to the superblock on the SCS (m); δ is the included angle between line AK and line BK (rad).Therefore, with equation (6), we find that te can be calculated as follows:(7)te=3.6γRrVae=3.6arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4RrRrVae.t3 is(8)t3=3.6WvehVae.Combining equations (5), (7), and (8), we calculate W as follows:(9)3.6arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4RrRrVae+3.6WvehVae≥tcr.


### 3.3. Conflicts between Motorized and Nonmotorized Traffic

When the vehicle turns left or right, the motorized and nonmotorized traffic have to share the same space on the crosswalk, as there are normally no pedestrian signals at the driveway.The nonmotorized traffic is able to safely traverse the driveway, only if the time gap between arrivals of the motorized and nonmotorized traffic is greater than the threshold for the crossing decision of the nonmotorized vehicletmn (s) or the decision standard of pedestrian tvp (s) [25], as shown in Figure 7.Figure 7
Crossing decision process.(1)
Considering the conflict area between motorized and nonmotorized vehicles, we propose the following equation:(10)3.6lmVae−3.6lnmVnm≥tmn,wherelm is the distance from the head of the exiting vehicle to the collision point between motorized and nonmotorized vehicles (m); lnm is the distance from the location of a nonmotorized vehicle beginnig to move to the edge of conflict area(m); Vnm is the velocity of nonmotorized vehicle (km/h).Considering the safety distance between motorized and nonmotorized vehicles, we assume thatlnm is equal to the half of the driveway width W. Therefore, based on equation (10), W can be calculated as follows:(11)W≤2lmVnmVae−tmnVnm1.8.Stopping sight distance is needed to check the road visibility, so that drivers can identify the dangerous object and control the vehicle to stop safely in front of it. When the vehicle exits, the driver requires adequate time to identify and deal with the possible collision point, so the distance from the head of the exiting vehicle to the collision point between motorized and nonmotorized vehicleslm must be long enough to ensure that the driver can see, understand, and react to the collision point in the crosswalk and then stop the car. Consequently, the distance lm longer than stopping sight distance may be meaningful. Therefore, we assume that the minimum value of lm is the sum of the stopping sight distance [26] and the width of crosswalk.(12)lm,min=Vddtpr3.6+Vdd2254φ+i′+l0+Wcro,wherelm,min is the minimum value of lm (m); Vdd is the design speed of driveway (km/h); tpr is the perception-reaction time (s); φ is the longitudinal friction coefficient between the vehicle and the pavement; i′ is the driveway slope; l0 is the safety space headway (m).Superblock has very limited land resources, which are compact and valuable. If the driveway width is too large, there would be less land for development in superblocks. Therefore, we think that, on the basis of meeting the requirement of traffic safety, the smaller driveway width means the better land use efficiency for superblocks. Furtherly, according to equation (11), smaller value of lm would lead to smaller W alternative values, which can still meet the demand of traffic safety. Therefore, with equation (11), we use lm,min to obtain the possible W alternative values, which has both advantages of avoiding conflicts between motorized and nonmotorized vehicles and promoting efficient use of land resources for superblocks as follows:(13)W≤2lm,minVnmVae−tmnVnm1.8.Combining equations (12) and (13), we find the following model:(14)W≤2Vddtpr3.6+Vdd2254φ+i′+l0+WcroVnmVae−tmnVnm1.8.(2)
For the conflict area between vehicles and pedestrians, there is the following equation [25]:(15)3.6lmpVae−3.6lpVp≥tvp,where lmp is the distance from exiting vehicle head to the position that vehicle rear is at the edge of crosswalk (m); lp is the distance from the location of a pedestrian to the edge of conflict area (m); Vp is the velocity of a pedestrian (km/h).We assume thatlp is equal to one half of the driveway width. Based on equation (15), W can be calculated as follows:(16)W≤2lmpVpVae−tvpVp1.8.Similarly as mentioned above, we assume that the minimum value oflmp is the stopping sight distance [26], and then, according to equation (16), W is calculated as follows:(17)W≤2Vddtpr3.6+Vdd2254φ+i′+l0VpVae−Vptvp1.8.


## 3.1. Conflicts between Left-Turning and through Vehicles

Normally, the SCS is a two-way street. If there is no median on the SCS, left-turning vehicles would cross the through traffic flow, as shown in Figure4.Figure 4
Left-turning on two-way SCS. (a) Right-side left-turning. (b) Left-side left-turning.
(a)(b)Sometimes, the SCS is a one-way street, so an exiting vehicle should turn left to merge into the traffic flow, as shown in Figure5.Figure 5
Left-turning on one-way SCS. (a) Right-side left-turning. (b) Left-side left-turning.
(a)(b)Figures4 and 5 have similar traffic features, so we consider them together. There is a crossing conflict between left-turning vehicle 2 on the exit lane and through vehicle 1 on the SCS (see Figure 5). In this study, we make the following assumptions:(1)
Vehicle 1 is on the lane nearest to the superblock access.(2)
Trajectory of turning vehicle 2 is a circular arc.(3)
Vehicle 2 keeps the same turning radius for the whole turn.(4)
PointM, the starting point of turning trajectory, is in the middle of the exit lane on the driveway.(5)
PointA is the position of the front of vehicle 2 at the boundary of conflict area. When vehicle 2 turns left, A is on the extended centerline or the edge line of the driveway. Point B is the point of intersection between line OM and vertical line through point A. Point O is the center of turning circle. ΔABO is a right-angled triangle, which implies that OM is perpendicular to the driveway centerline or edge line.(6)
The widths of entrance and exit lanes are the same.The minimum gap that all drivers in the minor stream are assumed to accept at all similar locations is the critical gaptc (s) [24]. So tcl (s) is the minimum gap for left-turning vehicle 2 to leave the driveway and pass over the conflict area, shown in the following equation:(1)te+t2≥tcl,where te is the travel time for vehicle 2 to enter the boundary of the conflict area(s); t2 is the time for vehicle 2 to pass through the conflict area(s).In Figure5, by analyzing the geometrical relationship in this crossing conflict, we find that te could be calculated by the following formula:(2)te=3.6arccosRl−W/4RlRlVae,where Rl is the radius of left-turning trajectory (m); W is the width of driveway (m); Vae is the average travel speed of vehicle 2 (km/h).Then as the adequate driveway width is beneficial for vehicle 2 to cross the conflict area formed by the conflict between vehicle 1 and 2, we have the equations below.t2 can be calculated by the following equation:(3)t2=3.6WvehVae,where Wveh is the width of vehicle (m).Combining equations (1)–(3), we can calculate W by using the following equation:(4)W≤4Rl−4RlcosVaetcl−3.6Wveh3.6Rl.


## 3.2. Conflicts between Right-Turning and through Vehicles

When vehicle 2 turns right from the driveway to the SCS, vehicle 2 should merge into the traffic flow of the lane nearest to the superblock on the SCS (see Figure6). In addition to the assumptions above, we also assume that when vehicle 2 turns right, A is on the centerline of the lane nearest to the superblock on the SCS.Figure 6
Conflict between right-turning and through vehicles.We also get the following formula to present the relationship between travel time and gap:(5)te+t3≥tcr,where t3 is the time for vehicle 2 to turn right into the through traffic flow(s); tcr (s) is the minimum gap for right-turning vehicle 2 to leave the driveway and merge into the through traffic flow.In Figure6, point K is the point of intersection between line BM and the edge line of driveway. Further, according to the law of cosines, we derive the following formula for the angle at the center of arc AM⌢, that is, γ (rad):(6)γ=arccosKO2+AO2−AK22KO×AO=arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4Rr,where KO is the distance of line KO (m); AO is the distance of line AO (m); AK is the distance of line AK (m); Rr is the radius of right-turning trajectory (m); Wcro is the width of crosswalk (m); Wnv is the width of nonmotorized vehicle lane (m); Wlu is the width of the lane nearest to the superblock on the SCS (m); δ is the included angle between line AK and line BK (rad).Therefore, with equation (6), we find that te can be calculated as follows:(7)te=3.6γRrVae=3.6arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4RrRrVae.t3 is(8)t3=3.6WvehVae.Combining equations (5), (7), and (8), we calculate W as follows:(9)3.6arccosRr−W/42+Rr2−Wcro+Wnv+Wlu/22/sin2δ2Rr−W/4RrRrVae+3.6WvehVae≥tcr.


## 3.3. Conflicts between Motorized and Nonmotorized Traffic

When the vehicle turns left or right, the motorized and nonmotorized traffic have to share the same space on the crosswalk, as there are normally no pedestrian signals at the driveway.The nonmotorized traffic is able to safely traverse the driveway, only if the time gap between arrivals of the motorized and nonmotorized traffic is greater than the threshold for the crossing decision of the nonmotorized vehicletmn (s) or the decision standard of pedestrian tvp (s) [25], as shown in Figure 7.Figure 7
Crossing decision process.(1)
Considering the conflict area between motorized and nonmotorized vehicles, we propose the following equation:(10)3.6lmVae−3.6lnmVnm≥tmn,wherelm is the distance from the head of the exiting vehicle to the collision point between motorized and nonmotorized vehicles (m); lnm is the distance from the location of a nonmotorized vehicle beginnig to move to the edge of conflict area(m); Vnm is the velocity of nonmotorized vehicle (km/h).Considering the safety distance between motorized and nonmotorized vehicles, we assume thatlnm is equal to the half of the driveway width W. Therefore, based on equation (10), W can be calculated as follows:(11)W≤2lmVnmVae−tmnVnm1.8.Stopping sight distance is needed to check the road visibility, so that drivers can identify the dangerous object and control the vehicle to stop safely in front of it. When the vehicle exits, the driver requires adequate time to identify and deal with the possible collision point, so the distance from the head of the exiting vehicle to the collision point between motorized and nonmotorized vehicleslm must be long enough to ensure that the driver can see, understand, and react to the collision point in the crosswalk and then stop the car. Consequently, the distance lm longer than stopping sight distance may be meaningful. Therefore, we assume that the minimum value of lm is the sum of the stopping sight distance [26] and the width of crosswalk.(12)lm,min=Vddtpr3.6+Vdd2254φ+i′+l0+Wcro,wherelm,min is the minimum value of lm (m); Vdd is the design speed of driveway (km/h); tpr is the perception-reaction time (s); φ is the longitudinal friction coefficient between the vehicle and the pavement; i′ is the driveway slope; l0 is the safety space headway (m).Superblock has very limited land resources, which are compact and valuable. If the driveway width is too large, there would be less land for development in superblocks. Therefore, we think that, on the basis of meeting the requirement of traffic safety, the smaller driveway width means the better land use efficiency for superblocks. Furtherly, according to equation (11), smaller value of lm would lead to smaller W alternative values, which can still meet the demand of traffic safety. Therefore, with equation (11), we use lm,min to obtain the possible W alternative values, which has both advantages of avoiding conflicts between motorized and nonmotorized vehicles and promoting efficient use of land resources for superblocks as follows:(13)W≤2lm,minVnmVae−tmnVnm1.8.Combining equations (12) and (13), we find the following model:(14)W≤2Vddtpr3.6+Vdd2254φ+i′+l0+WcroVnmVae−tmnVnm1.8.(2)
For the conflict area between vehicles and pedestrians, there is the following equation [25]:(15)3.6lmpVae−3.6lpVp≥tvp,where lmp is the distance from exiting vehicle head to the position that vehicle rear is at the edge of crosswalk (m); lp is the distance from the location of a pedestrian to the edge of conflict area (m); Vp is the velocity of a pedestrian (km/h).We assume thatlp is equal to one half of the driveway width. Based on equation (15), W can be calculated as follows:(16)W≤2lmpVpVae−tvpVp1.8.Similarly as mentioned above, we assume that the minimum value oflmp is the stopping sight distance [26], and then, according to equation (16), W is calculated as follows:(17)W≤2Vddtpr3.6+Vdd2254φ+i′+l0VpVae−Vptvp1.8.


## 4. Curb Radius Models

Adequate curb radius would help a turning vehicle travel faster, reducing the speed differential between the turning and through vehicles, and would keep it from encroaching the adjacent lane. To achieve these two goals, we propose models of curb radius.For right turns, there are four possible combinations of turning movements, as shown in Figure8.Figure 8
Combinations of right-turning movements. (a) Entering and exiting turns at the near side of the curb. (b) Entering and exiting turns at the far side of the curb. (c) Entering turns at the near and far side of the curb. (d) Exiting turns at the near and far side of the curb.
(a)(b)(c)(d)For left turns, there are also four turning combinations, as shown in Figure9.Figure 9
Combinations of left-turning movements. (a) Entering and exiting turns at the near side of the curb. (b) Entering and exiting turns at the far side of the curb. (c) Entering turns at the near and far side of the curb. (d) Exiting turns at the near and far side of the curb.
(a)(b)(c)(d)From Figures8 and 9, we observe that trajectories of turning movements 1 and 2 are at the near side of the curb, so curb radius affects and guides the movements. However, as turning movements 3 and 4 are at the far side of the curb, the curb radius cannot affect them directly. It can be found that, for a small curb radius, movement 1 or 2 may affect movement 4 or 3, as shown in Figure 10. In other words, the impact of curb radius on movement 1 or 2 is a critical factor for curb radius models.Figure 10
Interaction of turning movements. (a) Interaction of entering right turns. (b) Interaction of exiting right turns. (c) Interaction of entering left turns. (d) Interaction of exiting left turns.
(a)(b)(c)(d)Our research focuses on movements 1 and 2 in Figures8 and 9, with the following assumptions:(1)
The starting point of travel trajectory of turning vehicle is at the edge of the curb(2)
The trajectory of turning vehicle is a curve, defined by a composite function (e.g., equation (18) or (32) [27])(3)
Turning vehicles travel between the lane nearest to the superblock on the SCS and the drivewayAs the entering and exiting turning trajectories have different traffic impacts, the curb radius models are different.


### 4.1. Radius Based on Entering Turns

We analyze the entering right-turn trajectories, with respect to different types of radius, as shown in Figure11.Figure 11
Right turns on the driveway. (a) Driveway without entering radius. (b) Driveway with small entering radius. (c) Driveway with large entering radius.
(a)(b)(c)Vehicles turn left from the one-way SCS into the superblock, as shown in Figure12.Figure 12
Left turns on the driveway. (a) Driveway without entering radius. (b) Driveway with small entering radius. (c) Driveway with large entering radius.
(a)(b)(c)As Figures11 and 12 have similar traffic features, we consider them together. For the turning trajectory, a coordinate system is put forward, where vertical line through the starting point of turning trajectory is the x-axis, and the edge line of the lane nearest to the superblock on the SCS is the y-axis. We assume that, in this coordinate system, the turning vehicle decelerates slowly from point C, the starting point of vehicle trajectory, to point D, the effective starting point of turning movement, and then turns to point H, the effective end point of turning movement, and accelerates to point E, the end point of vehicle trajectory. Point G is the point of intersection between driveway edge line and perpendicular line through point E, and point F is the point of intersection between perpendicular line through point D and line EG. CD and HE are straight lines, and DH is a curve of equation (18) [27].Qu et al. gave models for indicating the right-turning vehicle trajectories at the signalized intersection [27]. When entering turns are hindered by the crossing nonmotorized traffic, which is exactly the problem depicted in Figures 11 and 12, their models [27] can be used as follows:(18)y=a+blnx+cV3.62+dV3.6,(19)a=20.453−0.699RcN−5.131l+2.24Rc2+1.314l2,(20)b=58.789−0.3472RcN−11.04l+0.127Rc2−10.599θ2,(21)c=0.0721+0.039Rc−0.417lN+0.023Rc2,(22)d=153.9−1.623Rc−208.2θ−1.325Rc2+59.98θ2+3.985Rcθ,where y is the value of y-axis (m); x is the value of x-axis (m); a, b, c, and d are coefficients; V is the speed of turning vehicle (km/h); Rc is the curb radius (m); N is the number of traffic conflicts between turning vehicles and nonmotorized vehicles in the peak hour (h−1); l is the distance between the centerline of the exit lane and the curb edge (m); θ is the angle of corner (rad).It is the fact that driveways are normally perpendicular to SCS; that is,θ=π/2. Considering the definition, l should be one quarter of driveway width W. Then, based on the models above, we propose a revised method for calculating the curb radius as follows:(1)
Lane encroachment: The objective of the method is to ensure that the turning vehicle would not encroach onto the adjacent lane, shown in the following equation:(23)EG−l+Wveh2=W4,whereEG is the distance between points E and G (m).By analyzing the geometrical relationship and using equation (18), the following can be deduced:(24)EG=EF−FG=yE−yF−Rc=yE−yD−Rc=blnxE+cVE23.62+dVE3.6−blnxD+cVD23.62+dVD3.6−Rc,whereEF is the distance between points E and F (m); FG is the distance between points F and G (m); yE is the value of y-axis at point E (m); yF is the value of y-axis at point F (m); yD is the value of y-axis at point D (m); xE is the value of x-axis at point E (m); VE is the speed of turning vehicle at point E (km/h); xD is the value of x-axis at point D (m); VD is the speed of turning vehicle at point D (km/h).(2)
Speed differential: According to the People's Republic of China Industry Standard, that is, “Specifications for Highway Safety Audit” [28], the speed differential between neighboring road sections should be no more than 10 km/h:(25)VD≥VC−10,whereVC is the speed of turning vehicle at point C (km/h).Meanwhile, we assume thatVC is the same as the design speed of SCS Vdu (km/h), and VE is the same as the design speed of driveway Vdd (km/h).(3)
Location analysis: From Figures11 and 12, we observe that xD is one half of the width of the lane nearest to the superblock on the SCS Wlu. Additionally, by analyzing the geometrical relationship, xE can be calculated as follows:(26)xE=xH+HE=Rc+Wlu+Wnv+HE,where xH is the value of x-axis at point H (m); HE is the distance between points H and E (m).Qu et al. found that, during the right-turning process, the velocity of vehicles normally decreases and then increases [27]. So we assume that vehicle movement from point H to point E is as follows:(27)HE=VE2−VH22×3.62aEH,where VH is the speed of turning vehicle at point H (km/h); aEH is the acceleration rate on the line between points E and H (m/s2).In accordance with assumption and analysis above, combining equations (18) to (27), we obtain the following formulas for Rc:(28)W2−Wveh2≤blnRc+Wlu+Wnv+Vdd2−VH22×3.62aEH+cVdd23.62+dVdd3.6−blnWlu2+cVdu−1023.62+dVdu−103.6−Rc,(29)b=32.637−0.3472RcN−2.76W+0.127Rc2,(30)c=0.0721+0.039Rc−0.1043WN+0.023Rc2,(31)d=4.637Rc−1.325Rc2−25.145.


### 4.2. Radius Based on Exiting Turns

We analyze the exiting right-turn trajectories, with respect to different types of radius, as shown in Figure13.Figure 13
Right turns on the driveway. (a) Driveway without exiting radius. (b) Driveway with small exiting radius. (c) Driveway with large exiting radius.
(a)(b)(c)Vehicles turn left from the superblock onto the one-way SCS, as shown in Figure14.Figure 14
Left turns on the driveway. (a) Driveway without exiting radius. (b) Driveway with small exiting radius. (c) Driveway with large exiting radius.
(a)(b)(c)As Figures13 and 14 have similar traffic features, we consider them together. When exiting turns are also hindered by the crossing nonmotorized traffic in Figures 13 and 14, other models given by Qu et al. [27] can be used for these turning trajectories as follows:(32)y=a′+b′lnx+c′V3.62+d′V3.6,(33)a′=19.986−0.892RcN−6.141l+2.27Rc2+1.213l2,(34)b′=61.134−0.3997RcN−11.431l+0.1354Rc2−11.58θ2,(35)c′=0.0923+0.086Rc−0.412lN+0.012Rc2,(36)d′=123.5−1.785Rc−195.2θ−1.123Rc2+52.34θ2+2.546Rcθ,where a′, b′, c′, and d′ are coefficients.From Figures13 and 14, we assume that VC is the same as Vdd, VE is the same as Vdu, and xD is one quarter of W, and then we obtain the following formulas:(37)l=Wlu2+Wnv,(38)EG−l+Wveh2=Wlu2,(39)EG=b′lnxE+c′VE23.62+d′VE3.6−b′lnxD+c′VD23.62+d′VD3.6−Rc,(40)xE=Rc+W2+VE2−VH22×3.62aEH.Combining equations (25) and (32) to (40), we obtain the following formulas for Rc:(41)Wlu−Wveh2+Wnv≤b′lnRc+W2+Vdu2−VH22×3.62aEH+c′Vdu23.62+d′Vdu3.6−b′lnW4+c′Vdd−1023.62+d′Vdd−103.6−Rc,(42)b′=−0.3997RcN−11.431Wlu2+Wnv+0.1354Rc2+32.5615,(43)c′=0.0923+0.086Rc−0.412Wlu2+WnvN+0.012Rc2,(44)d′=2.214Rc−1.123Rc2−53.976.


## 4.1. Radius Based on Entering Turns

We analyze the entering right-turn trajectories, with respect to different types of radius, as shown in Figure11.Figure 11
Right turns on the driveway. (a) Driveway without entering radius. (b) Driveway with small entering radius. (c) Driveway with large entering radius.
(a)(b)(c)Vehicles turn left from the one-way SCS into the superblock, as shown in Figure12.Figure 12
Left turns on the driveway. (a) Driveway without entering radius. (b) Driveway with small entering radius. (c) Driveway with large entering radius.
(a)(b)(c)As Figures11 and 12 have similar traffic features, we consider them together. For the turning trajectory, a coordinate system is put forward, where vertical line through the starting point of turning trajectory is the x-axis, and the edge line of the lane nearest to the superblock on the SCS is the y-axis. We assume that, in this coordinate system, the turning vehicle decelerates slowly from point C, the starting point of vehicle trajectory, to point D, the effective starting point of turning movement, and then turns to point H, the effective end point of turning movement, and accelerates to point E, the end point of vehicle trajectory. Point G is the point of intersection between driveway edge line and perpendicular line through point E, and point F is the point of intersection between perpendicular line through point D and line EG. CD and HE are straight lines, and DH is a curve of equation (18) [27].Qu et al. gave models for indicating the right-turning vehicle trajectories at the signalized intersection [27]. When entering turns are hindered by the crossing nonmotorized traffic, which is exactly the problem depicted in Figures 11 and 12, their models [27] can be used as follows:(18)y=a+blnx+cV3.62+dV3.6,(19)a=20.453−0.699RcN−5.131l+2.24Rc2+1.314l2,(20)b=58.789−0.3472RcN−11.04l+0.127Rc2−10.599θ2,(21)c=0.0721+0.039Rc−0.417lN+0.023Rc2,(22)d=153.9−1.623Rc−208.2θ−1.325Rc2+59.98θ2+3.985Rcθ,where y is the value of y-axis (m); x is the value of x-axis (m); a, b, c, and d are coefficients; V is the speed of turning vehicle (km/h); Rc is the curb radius (m); N is the number of traffic conflicts between turning vehicles and nonmotorized vehicles in the peak hour (h−1); l is the distance between the centerline of the exit lane and the curb edge (m); θ is the angle of corner (rad).It is the fact that driveways are normally perpendicular to SCS; that is,θ=π/2. Considering the definition, l should be one quarter of driveway width W. Then, based on the models above, we propose a revised method for calculating the curb radius as follows:(1)
Lane encroachment: The objective of the method is to ensure that the turning vehicle would not encroach onto the adjacent lane, shown in the following equation:(23)EG−l+Wveh2=W4,whereEG is the distance between points E and G (m).By analyzing the geometrical relationship and using equation (18), the following can be deduced:(24)EG=EF−FG=yE−yF−Rc=yE−yD−Rc=blnxE+cVE23.62+dVE3.6−blnxD+cVD23.62+dVD3.6−Rc,whereEF is the distance between points E and F (m); FG is the distance between points F and G (m); yE is the value of y-axis at point E (m); yF is the value of y-axis at point F (m); yD is the value of y-axis at point D (m); xE is the value of x-axis at point E (m); VE is the speed of turning vehicle at point E (km/h); xD is the value of x-axis at point D (m); VD is the speed of turning vehicle at point D (km/h).(2)
Speed differential: According to the People's Republic of China Industry Standard, that is, “Specifications for Highway Safety Audit” [28], the speed differential between neighboring road sections should be no more than 10 km/h:(25)VD≥VC−10,whereVC is the speed of turning vehicle at point C (km/h).Meanwhile, we assume thatVC is the same as the design speed of SCS Vdu (km/h), and VE is the same as the design speed of driveway Vdd (km/h).(3)
Location analysis: From Figures11 and 12, we observe that xD is one half of the width of the lane nearest to the superblock on the SCS Wlu. Additionally, by analyzing the geometrical relationship, xE can be calculated as follows:(26)xE=xH+HE=Rc+Wlu+Wnv+HE,where xH is the value of x-axis at point H (m); HE is the distance between points H and E (m).Qu et al. found that, during the right-turning process, the velocity of vehicles normally decreases and then increases [27]. So we assume that vehicle movement from point H to point E is as follows:(27)HE=VE2−VH22×3.62aEH,where VH is the speed of turning vehicle at point H (km/h); aEH is the acceleration rate on the line between points E and H (m/s2).In accordance with assumption and analysis above, combining equations (18) to (27), we obtain the following formulas for Rc:(28)W2−Wveh2≤blnRc+Wlu+Wnv+Vdd2−VH22×3.62aEH+cVdd23.62+dVdd3.6−blnWlu2+cVdu−1023.62+dVdu−103.6−Rc,(29)b=32.637−0.3472RcN−2.76W+0.127Rc2,(30)c=0.0721+0.039Rc−0.1043WN+0.023Rc2,(31)d=4.637Rc−1.325Rc2−25.145.


## 4.2. Radius Based on Exiting Turns

We analyze the exiting right-turn trajectories, with respect to different types of radius, as shown in Figure13.Figure 13
Right turns on the driveway. (a) Driveway without exiting radius. (b) Driveway with small exiting radius. (c) Driveway with large exiting radius.
(a)(b)(c)Vehicles turn left from the superblock onto the one-way SCS, as shown in Figure14.Figure 14
Left turns on the driveway. (a) Driveway without exiting radius. (b) Driveway with small exiting radius. (c) Driveway with large exiting radius.
(a)(b)(c)As Figures13 and 14 have similar traffic features, we consider them together. When exiting turns are also hindered by the crossing nonmotorized traffic in Figures 13 and 14, other models given by Qu et al. [27] can be used for these turning trajectories as follows:(32)y=a′+b′lnx+c′V3.62+d′V3.6,(33)a′=19.986−0.892RcN−6.141l+2.27Rc2+1.213l2,(34)b′=61.134−0.3997RcN−11.431l+0.1354Rc2−11.58θ2,(35)c′=0.0923+0.086Rc−0.412lN+0.012Rc2,(36)d′=123.5−1.785Rc−195.2θ−1.123Rc2+52.34θ2+2.546Rcθ,where a′, b′, c′, and d′ are coefficients.From Figures13 and 14, we assume that VC is the same as Vdd, VE is the same as Vdu, and xD is one quarter of W, and then we obtain the following formulas:(37)l=Wlu2+Wnv,(38)EG−l+Wveh2=Wlu2,(39)EG=b′lnxE+c′VE23.62+d′VE3.6−b′lnxD+c′VD23.62+d′VD3.6−Rc,(40)xE=Rc+W2+VE2−VH22×3.62aEH.Combining equations (25) and (32) to (40), we obtain the following formulas for Rc:(41)Wlu−Wveh2+Wnv≤b′lnRc+W2+Vdu2−VH22×3.62aEH+c′Vdu23.62+d′Vdu3.6−b′lnW4+c′Vdd−1023.62+d′Vdd−103.6−Rc,(42)b′=−0.3997RcN−11.431Wlu2+Wnv+0.1354Rc2+32.5615,(43)c′=0.0923+0.086Rc−0.412Wlu2+WnvN+0.012Rc2,(44)d′=2.214Rc−1.123Rc2−53.976.


## 5. Design Evaluation and Optimization

With equations (4), (9), (13), (17), (28) to (31), and (41) to (44), we can calculate alternative ranges of driveway width and curb radius, and then, by considering the requirement of the guide [29], we can adjust the alternative ranges to get better ranges for field conditions.Models of driveway width and curb radius are from the perspective of crash risk. The purpose of driveway width models is reducing the crash risk caused by conflicts between left-turning and through vehicles, conflicts between right-turning and through vehicles, and conflicts between motorized and nonmotorized traffic. Meanwhile, the purpose of curb radius models is reducing the crash risk caused by lane encroachment and speed differential. Consequently, to verify the traffic safety effects of the design models, we establish a model for optimizing the combination of driveway width and curb radius in alternative ranges, with respect to traffic safety indexes, such as traffic conflicts, lane encroachment, and speed differential, as follows:(45)PWR=Pvv+Pmn+Psd+Ple,where PWR is the crash risk with one combination of driveway width and curb radius (%); Pvv is the crash risk from conflicts between motorized vehicles (%); Pmn is the crash risk from conflicts between motorized and nonmotorized traffic (%); Psd is the crash risk due to speed differential larger than 10 km/h (%); Ple is the crash risk from lane encroachment of entering and exiting vehicles (%).


### 5.1. Definitions

Pvv is estimated as follows [26]:(46)Pvv=NtcNpcu,where Ntc is the number of motorized traffic conflicts in the peak hour; Npcu is the Passenger Car Equivalent values of motorized traffic in the peak hour.Similarly, we definePmn, Psd, and Ple as follows:(47)Pmn=NtcnNpcu+Nnt,where Ntcn is the number of traffic conflicts between motorized and non-motorized traffic; Nnt is the number of nonmotorized traffic in the peak hour; and(48)Psd=NsdNpcu,where Nsd is the number of speed differentials larger than 10 km/h in the peak hour; and(49)Ple=NleNpcu,where Nle is the number of lane encroachments in the peak hour.Ntc, Npcu, Ntcn, Nnt, Nsd, and Nle are calculated in functional areas of the driveway, comprised of four parts, upstream and downstream functional areas of SCS and upstream and downstream functional areas of driveway, as shown in Figure 15.Figure 15
Functional area of the driveway.Then we can utilize the VISSIM microscopic traffic analysis software to develop statistics for functional areas of driveways. In VISSIM [31], we use function “Vehicle Inputs” to obtain Npcu and Nnt, function “Speed Difference” to get Nsd, and function “Lane Change” to obtain Nle.A traffic conflict is a traffic event involving the interaction of two or more road users, where one or both drivers take evasive action such as braking or swerving to avoid a collision [32]. Therefore, we can identify traffic conflicts by analyzing the interaction status of two or more road users. In VISSIM, function “Vehicle Record” outputs attribute values for each vehicle as raw data in one row per time step, which provides the moving status of individual vehicle. Then we can recognize the traffic conflicts by counting data from function “Vehicle Record.” First of all, we use subfunction “interaction state” in “Vehicle Record,” which can demonstrate the interaction of vehicles. If the value of “interaction state” is Brake BX, Brake AX, Close up, Brake ZX, Brake SPW, Brake COOP, or Pass [31], the vehicle is influenced by others, so we can judge that the raw data of the row from “Vehicle Record” file shows the traffic conflict has happened. Secondly, based on vehicle interactions, we use subfunctions “Acceleration,” “Number of Stops,” and “Lane Change” which provide values of evasive actions, such as acceleration, stop number, and lane change, to reconfirm that those row data are phenomenon of traffic conflicts. Thirdly, we count the number of those rows, that is, the number of traffic conflicts in the peak hour. Finally, with subfunctions “Lane” (number of lanes on which the vehicle is used) and “Position” (distance on the link from the beginning of the link or connector), which present locations where traffic conflicts happen, we can divide the number of traffic conflicts into the number of motorized traffic conflicts Ntc and the number of traffic conflicts between motorized and nonmotorized traffic Ntcn.For example, we may obtain sample attribute values from the ∗.fzp file of “Vehicle Record,” as shown in Table1.According to the discussion above, from Table1, we can see that the 1st, 2nd, 3rd, 5th, 7th, 8th, 9th, and 10th rows are phenomenon of traffic conflicts, so the number of traffic conflicts is 8. Then as the crosswalk for nonmotorized traffic is 63.320 m from the beginning of the link, 7th and 10th rows present traffic conflicts happening at the edge of crosswalk, which are conflicts between motorized and nonmotorized traffic. Consequently, Ntc is 6 and Ntcn is 2 in this example.Table 1
Sample attribute values for each vehicle from “Vehicle Record.”
Simulation second (s)Number of the vehiclesInteraction stateAcceleration (m/s2)Number of stopsLane changeLanePosition (m)1982.601240Brake BX−0.020None1–148.2691982.601241Close up−2.170None1–119.2591982.601242Brake AX−0.020None1–157.5981982.601243Free0.190None1–194.5691982.701230Pass−2.311Left1–132.9261982.701236Free0.130None2–134.6581982.801232Close up−1.370None2–162.3201982.701237Close up−1.931None2–115.4251982.701238Brake ZX−6.650Right1–146.7201982.801239Close up−0.450None2–162.320


### 5.2. Regression Models and Programming

In VISSIM, we design different combinations of driveway width and curb radius for various traffic volumes on the SCS and the driveway, to investigate the relationship among the crash risk, driveway width, and curb radius. We use a range of values of driveway width and curb radius based on driveway guide [29], as shown in Table 2.Table 2
Alternative values of driveway width and curb radius.
Driveway lane widthWlane (m)33.253.53.7544.254.54.7555.255.5Driveway widthW (m)66.577.588.599.51010.511Curb radiusRc (m)1015202530354045505560Note: we assume that the driveway has only two lanes.From Table2, we can see that there are 121 pairs of driveway width and curb radius. Based on simulation results, each pair of driveway width and curb radius corresponds to different values of Pvv, Pmn, Psd, and Ple. Consequently, we can derive regression models to describe the relationship of crash risk and design factors. The regression models show that Pvv=f1W,Rc, Pmn=f2W,Rc, Psd=f3Rc,W, and Ple=f4Rc,W, meaning that these four types of crash risk are functions of driveway width and curb radius.Consequently, we first obtain the alternative ranges ofW and Rc by using Matlab to program equations (4), (9), (13), (17), (28) to (31), and (41) to (44) and then use equation (45) for PWR, which combines these regression models, to verify the alternative ranges of W and Rc, and find the optimal pair.


## 5.1. Definitions

Pvv is estimated as follows [26]:(46)Pvv=NtcNpcu,where Ntc is the number of motorized traffic conflicts in the peak hour; Npcu is the Passenger Car Equivalent values of motorized traffic in the peak hour.Similarly, we definePmn, Psd, and Ple as follows:(47)Pmn=NtcnNpcu+Nnt,where Ntcn is the number of traffic conflicts between motorized and non-motorized traffic; Nnt is the number of nonmotorized traffic in the peak hour; and(48)Psd=NsdNpcu,where Nsd is the number of speed differentials larger than 10 km/h in the peak hour; and(49)Ple=NleNpcu,where Nle is the number of lane encroachments in the peak hour.Ntc, Npcu, Ntcn, Nnt, Nsd, and Nle are calculated in functional areas of the driveway, comprised of four parts, upstream and downstream functional areas of SCS and upstream and downstream functional areas of driveway, as shown in Figure 15.Figure 15
Functional area of the driveway.Then we can utilize the VISSIM microscopic traffic analysis software to develop statistics for functional areas of driveways. In VISSIM [31], we use function “Vehicle Inputs” to obtain Npcu and Nnt, function “Speed Difference” to get Nsd, and function “Lane Change” to obtain Nle.A traffic conflict is a traffic event involving the interaction of two or more road users, where one or both drivers take evasive action such as braking or swerving to avoid a collision [32]. Therefore, we can identify traffic conflicts by analyzing the interaction status of two or more road users. In VISSIM, function “Vehicle Record” outputs attribute values for each vehicle as raw data in one row per time step, which provides the moving status of individual vehicle. Then we can recognize the traffic conflicts by counting data from function “Vehicle Record.” First of all, we use subfunction “interaction state” in “Vehicle Record,” which can demonstrate the interaction of vehicles. If the value of “interaction state” is Brake BX, Brake AX, Close up, Brake ZX, Brake SPW, Brake COOP, or Pass [31], the vehicle is influenced by others, so we can judge that the raw data of the row from “Vehicle Record” file shows the traffic conflict has happened. Secondly, based on vehicle interactions, we use subfunctions “Acceleration,” “Number of Stops,” and “Lane Change” which provide values of evasive actions, such as acceleration, stop number, and lane change, to reconfirm that those row data are phenomenon of traffic conflicts. Thirdly, we count the number of those rows, that is, the number of traffic conflicts in the peak hour. Finally, with subfunctions “Lane” (number of lanes on which the vehicle is used) and “Position” (distance on the link from the beginning of the link or connector), which present locations where traffic conflicts happen, we can divide the number of traffic conflicts into the number of motorized traffic conflicts Ntc and the number of traffic conflicts between motorized and nonmotorized traffic Ntcn.For example, we may obtain sample attribute values from the ∗.fzp file of “Vehicle Record,” as shown in Table1.According to the discussion above, from Table1, we can see that the 1st, 2nd, 3rd, 5th, 7th, 8th, 9th, and 10th rows are phenomenon of traffic conflicts, so the number of traffic conflicts is 8. Then as the crosswalk for nonmotorized traffic is 63.320 m from the beginning of the link, 7th and 10th rows present traffic conflicts happening at the edge of crosswalk, which are conflicts between motorized and nonmotorized traffic. Consequently, Ntc is 6 and Ntcn is 2 in this example.Table 1
Sample attribute values for each vehicle from “Vehicle Record.”
Simulation second (s)Number of the vehiclesInteraction stateAcceleration (m/s2)Number of stopsLane changeLanePosition (m)1982.601240Brake BX−0.020None1–148.2691982.601241Close up−2.170None1–119.2591982.601242Brake AX−0.020None1–157.5981982.601243Free0.190None1–194.5691982.701230Pass−2.311Left1–132.9261982.701236Free0.130None2–134.6581982.801232Close up−1.370None2–162.3201982.701237Close up−1.931None2–115.4251982.701238Brake ZX−6.650Right1–146.7201982.801239Close up−0.450None2–162.320


## 5.2. Regression Models and Programming

In VISSIM, we design different combinations of driveway width and curb radius for various traffic volumes on the SCS and the driveway, to investigate the relationship among the crash risk, driveway width, and curb radius. We use a range of values of driveway width and curb radius based on driveway guide [29], as shown in Table 2.Table 2
Alternative values of driveway width and curb radius.
Driveway lane widthWlane (m)33.253.53.7544.254.54.7555.255.5Driveway widthW (m)66.577.588.599.51010.511Curb radiusRc (m)1015202530354045505560Note: we assume that the driveway has only two lanes.From Table2, we can see that there are 121 pairs of driveway width and curb radius. Based on simulation results, each pair of driveway width and curb radius corresponds to different values of Pvv, Pmn, Psd, and Ple. Consequently, we can derive regression models to describe the relationship of crash risk and design factors. The regression models show that Pvv=f1W,Rc, Pmn=f2W,Rc, Psd=f3Rc,W, and Ple=f4Rc,W, meaning that these four types of crash risk are functions of driveway width and curb radius.Consequently, we first obtain the alternative ranges ofW and Rc by using Matlab to program equations (4), (9), (13), (17), (28) to (31), and (41) to (44) and then use equation (45) for PWR, which combines these regression models, to verify the alternative ranges of W and Rc, and find the optimal pair.


## 6. Case Study Evaluation

Field survey and sample data were collected from 6:00 pm to 7:00 pm on June 29, 2019, at Wanda Plaza, Cangshan District, Fuzhou City, China. Wanda Plaza is a type of superblock called city complex with dimensions of approximately 290m × 580m. There are business centers, pedestrian streets, high end hotels, office buildings, and residential apartments as well as retail, catering, cultural, and entertainment venues.(1)
There are many pedestrians and nonmotorized vehicles crossing the driveways, which contribute to traffic congestion and elevated traffic safety risk(2)
A basic design of driveways yields adverse impacts in the efficiency of turning movements of vehiclesThe driveway and adjacent road system of Wanda Plaza are shown in Figure16. Features of these driveways are shown in Table 3 and Figure 17. Driveways 9 and 10 are toward different destinations, so we separate them into two driveways, as illustrated in Figure 17(i).Figure 16
Driveway system of Wanda Plaza.Table 3
Current design of driveways.
Driveway numberNumber of lanesLane directionControl measureWidthW (m)Curb radiusRc (m)12Entrance lanesNo control8022One entrance lane and one exit laneNo control81832One entrance lane and one exit laneBarrier control62542One entrance lane and one exit laneBarrier control7052Exit lanesNo control4.52062Exit lanesBarrier control61572One entrance lane and one exit laneBarrier control6082Entrance lanesBarrier control7.51592Entrance lanesNo control720102Entrance lanesNo control720Figure 17
Wanda Plaza driveways. (a) Driveway 1. (b) Driveway 2. (c) Driveway 3. (d) Driveway 4. (e) Driveway 5. (f) Driveway 6. (g) Driveway 7. (h) Driveway 8. (i) Driveways 9 and 10.
(a)(b)(c)(d)(e)(f)(g)(h)(i)The driveway width and curb radius models need some basic traffic data. According to these design models, we list the data source in Tables4–6. For traffic volume data, we collect and count the number of different kinds of traffic and then obtain the traffic volume, as shown in Table 4. For other driveway traffic data, we found the design drawings and took video pictures of traffic flow in real field. Then we acquired the driveway slope, longitudinal friction coefficient, and lane width from design drawings and obtained radii of turning trajectories, number of traffic conflicts, included angle of trajectories, and required velocities by analyzing the video pictures taken from the real field, as shown in Table 5. For assumed data, we list the assumed values and their data source in Table 6.Table 4
Traffic volume from 6:00 pm to 7:00 pm on June 29, 2019
Driveway number12345678910Crossing pedestrians (ped/h)29226832841612096180216531415Crossing nonmotorized vehicles (veh/h)36422423616888132244324279281Motorized vehicles on the adjacent urban lane (pcu/h)58062828820029464332474692692Motorized vehicles on the driveway (pcu/h)38040088521688444156254362Table 5
Other collected driveway traffic data.
Driveway number12345678910i′0000000———N (h−1)1518——8911162521Rl (m)——1718141816———Rr (m)812————————Vae (km/h)6.727.688.057.527.328.216.43———Vdd (km/h)20252525252520202020Vdu (km/h)50503030304040406060VH (km/h) (SCS)3536——212829———VH (km/h) (driveway)—17————15151813Vnm (km/h)12151513222013———Vp (km/h)4.914.125.014.823.415.354.70———Wcro (m)3344435———Wlu (m)3.53.5——3.53.53.53.53.53.5Wnv (m)2.52.533333333Wveh (m)1.81.81.81.81.81.81.81.81.81.8δ (rad)0.69811.0472————————φ0.60.60.60.60.60.60.6———Table 6
Assumed values for driveway traffic analysis.
Driveway numberSource12345678910aEH (m/s2)[33]1.51.5——1.51.51.51.51.51.5l0 (m)[26]3333333———tcl (s)[34]——5.775.775.775.775.77———tcr (s)[34]2.942.94————————tmn (s)∗3.53.53.53.53.53.53.5———tpr (s)[26]1.21.21.21.21.21.21.21.21.21.2tvp (s)[35]4.44.44.44.44.44.44.4———Note: “∗” denotes assumed value; “—” denotes that parameter is not needed.Based on the applicable conditions at Wanda Plaza superblock, we combine equations to optimize the driveways as shown in Table7.Table 7
Relationship between driveways and design models.
Driveway numberWidth optimization modelsCurb radius optimization models1Equations (9), (13), and (17)Equations (41) to (44)2Equations (9), (13), and (17)Equations (28) to (31) and (41) to (44)3Equations (4), (13), and (17)—4Equations (4), (13), and (17)—5Equations (4), (13), and (17)Equations (41) to (44)6Equations (4), (13), and (17)Equations (41) to (44)7Equations (4), (13), and (17)Equations (28) to (31) and (41) to (44)8—Equations (28) to (31)9—Equations (28) to (31)10—Equations (28) to (31)Note: “—” indicates currently no model available for movements on this type of driveway. For driveways 3 and 4, there is no movement 1 or 2 in Figures9 and 10, so no curb radius model can be used for them. For driveways 8 to 10, there are no exiting movements in Figure 3, so no driveway width model is fit for them.Let us take driveway 1 as an example. As Table7 indicates, we program equations (9), (13), (17), and (41) to (44) in Matlab and input data from Tables 5 and 6. Then combining the output of Matlab program above and alternative design values from Table 2, the following design range for driveway 1 is produced. Following the same process, we calculate separate design ranges for the driveways, as shown in Table 8.Table 8
Alternative driveway design range.
Driveway numberRange of driveway widthW (m)Range of curb radiusRc (m)16≤W≤810≤Rc≤5026≤W≤8.515≤Rc≤5536≤W≤92546≤W≤10056≤W≤815≤Rc≤6066≤W≤910≤Rc≤4576≤W≤8.510≤Rc≤5087.520≤Rc≤559715≤Rc≤6010720≤Rc≤60We use VISSIM to simulate the different combinations of driveway width and curb radius for various traffic volumes on the SCS and the driveway, so as to obtain conflict results, that is, values of crash risk, for polynomial regression models. Some relevant parameters are set in accordance with the driving characteristics of local drivers in VISSIM simulator, for example, various speed, and others are set from references, for example, acceleration rate, minimum gap, and perception-reaction time.To verify the validity of simulation, we add one comparison of the simulation results with the actual observed results. Firstly, we choose driveway 1 of Fuzhou Wanda Plaza as an example and then count traffic conflicts by personal judgment on video pictures of real field. Secondly, we simulate the current situation of driveway 1 and then recognize traffic conflicts in VISSIM simulation. Finally, we compare the traffic conflict results from simulation and actual observation of driveway 1, as shown in Table9.From Table9, we find that the difference rate of simulation and actual observation of driveway 1, is less than 5%. By using the same method, we compare the results of simulation and actual observation of driveway 2 to 10 and get the same result that difference rates are less than 5%. So we can draw a conclusion that simulation results are acceptable. Therefore, by using traffic volumes from Table 4 and driveway width and curb radii from Table 2, we perform simulation in VISSIM. Taking driveway 1 as an example, we obtain values for variables in the crash risk models. Then, by using formulas (46) to (49), we calculate Pvv, Pmn, Psd, and Ple and deduce polynomial regression models for driveway 1 as follows:(50)Pvv=1.66−6.10e−1W−3.90e−3Rc+7.63e−2W2+3.64e−4WRc+4.86e−5Rc2−3.03e−3W3−2.21e−5W2Rc−3.456e−7WRc2−2.59e−8Rc3,(51)Pmn=2.87e−1−1.13e−1W−8.80e−4Rc+1.46e−2W2+3.01e−4WRc−7.20e−7Rc2−5.80e−4W3−2.55e−5W2Rc+2.23e−6WRc2+3.73e−8Rc3,(52)Psd=8.76e−1−2.92e−1W−3.00e−3Rc+3.54e−2W2+2.86e−4WRc+3.33e−6Rc2−1.38e−3W3−1.21e−5W2Rc−6.91e−7WRc2+4.74e−7Rc3,(53)Ple=9.38e−1−3.46e−1W+1.62e−3Rc+4.35e−2W2−8.68e−4WRc+5.40e−5Rc2−1.75e−3W3+5.06e−5W2Rc−8.19e−7WRc2−1.16e−7Rc3.Table 9
Comparison of simulation and actual observation of driveway 1.
Conflict resultsNumber of motorized traffic conflicts in the peak hourNtcNumber of traffic conflicts between motorized and nonmotorized trafficNtcnNumber of speed differentials larger than 10 km/h in the peak hourNsdNumber of lane encroachments in the peak hourNleActual observation1824411355Simulation1894210857Difference rate3.85%−4.55%−4.42%3.64%And we also analyze the goodness of fit of these curve fitting equations, indicating that they are suitable for scatter fitting, as shown in Table10.Table 10
Goodness of fit of equations.
Indices of goodness of fitSum of squared errors (SSE)R2Root mean squared error (RMSE)Equation (50)0.0023680.95440.004619Equation (51)0.00059330.97610.002312Equation (52)0.0032960.91790.005449Equation (53)0.0034850.91060.005013For driveway 1, we combine equations (50) to (53) to obtain the optimization function, based on equation (45), as follows:(54)PWR=3.76−1.36W−6.16e−3Rc+1.70e−1W2+8.31e−5WRc+1.05e−4Rc2−6.74e−3W3−9.11e−6W2Rc+3.71e−7WRc2+3.69e−7Rc3.The diagram of the relationship amongPWR, W, and Rc is shown in Figure 18.Figure 18
Curve of relationship amongPWR, W, and Rc for driveway 1.By using a similar process, we estimate polynomial regression models for driveways 2 to 10, which are shown in Figure19.Figure 19
Curves of relationship amongPWR, W, and Rc for driveways. (a) Driveway 2. (b) Driveways 3 and 4. (c) Driveway 5. (d) Driveway 6. (e) Driveway 7. (f) Driveways 8, 9, and 10.
(a)(b)(c)(d)(e)(f)The outcomes shown in Figures18 and 19 suggest the following key findings for driveway radius and width:(1)
Optimization forW and Rc: for driveways 1, 2, 5, 6, and 7, the value of PWR decreases at first and then increases, with an increase of Rc. However, for driveways 1 and 2, the value of PWR increases at first and then decreases, with an increase of W, while for driveways 5, 6, and 7, the value of PWR decreases at first and then increases, with an increase of W. Consequently, we can see that a certain range of curb radius and driveway width would lead to lower crash risk. The reason for it is that, for driveways 1 and 2, traffic volume of either nonmotorized vehicles or motorized vehicles is relatively high, so that Pvv and Pmn have a large impact on PWR, which means that a smaller driveway width and larger curb radius would be better, but for driveways 5, 6, and 7, the traffic volume is relatively low, so Pvv and Pmn have a small impact on PWR, which means that a larger driveway width and curb radius work better. However, when the curb radius or driveway width is too large, there will be a longer pedestrian crossing area, leading to more crash risk.(2)
Optimization forW: for driveways 3 and 4, while Rc is the fixed value, the value of PWR decreases at first and then increases, with an increase of W, meaning that a certain range of driveway width would lead to lower crash risk. The reason for it is that the traffic volume of either nonmotorized or motorized vehicles in functional areas of these driveways, as shown in Table 4, is relatively low, so that Pvv and Pmn have a small impact on PWR, but Psd and Ple have large influence on PWR, which means that a larger driveway width would be better. However, same as above, when the driveway width is too large, there is more crash risk among vehicles and pedestrians.(3)
Optimization forRc: for driveways 8, 9, and 10, while W is the fixed value, the value of PWR decreases at first and then increases, with an increase of Rc, meaning that a certain range of curb radius would lead to lower crash risk. The reason for it is that the traffic volume of either nonmotorized or motorized vehicles is relatively high, so that the values of Psd and Ple are large, which means that a larger curb radius would be better. However, same as above, when the curb radius is too large, there is more crash risk among vehicles and pedestrians.(4)
Traffic volumes are closely related to the value ofPWR. Higher traffic volumes normally yield more crash risk.Based on Table8, we find the optimal driveway design for driveways, as shown in Table 11, by using the regression models for PWR.Table 11
Optimal driveway design.
Driveway numberDriveway widthW (m)Curb radiusRc (m)16.530264537.52548056.54567.530773087.535973510740Compared with the current design, the updated design will reduce crash risk by 4.32% to 52.61%, with 7 out of 10 driveways improving by 16.14% or more, as shown in Table12. As the effectiveness of access management strategies is location-specific, indicated by Chowdhury et al. [22], there are large differences among improvements of driveways.Table 12
Crash riskPWR comparison.
Driveway numberCurrent driveway designOptimal driveway designImprovement (%)10.30910.178042.41%20.30980.196536.57%30.17970.150716.14%40.13880.13284.32%50.18360.087052.61%60.10310.059941.90%70.20870.140332.77%80.22220.179619.17%90.38020.325714.33%100.35600.308313.40%


## 7. Discussion and Limitations

In this research, we put forward driveway width models, based on conflicts between left-turning and through vehicles, conflicts between right-turning and through vehicles, and conflicts between motorized and nonmotorized traffic. The width values calculated by the models would help turning vehicles and nonmotorized traffic make full use of the gap, so as to reduce the crash risk from conflicts between motorized vehiclesPvv, and the crash risk from conflicts between motorized and nonmotorized traffic Pmn. The models can be used for acquiring the range of driveway width of superblocks. At the same time, we propose curb radius models, aiming to reduce the speed differential and avoid lane encroachment. The curb radius values calculated by the models are beneficial for reducing the crash risk due to speed differential larger than 10 km/h Psd and the crash risk from lane encroachment of entering and exiting vehicles Ple. The models can be used for acquiring the range of curb radius of superblocks.The models of driveway width and curb radius optimize the driveway width and curb radius from the perspective of crash risk based on traffic safety indexes. However, the models should not neglect the capacity demand of SCS and driveway, which is the basis for improving traffic efficiency. Therefore, future research will focus on the driveway width and curb radius models based on traditional models corresponding to traffic volume and speed, for example, traffic arrival models based on the traffic wave theory [36], to heighten the level of both safety and efficiency. Meanwhile, the models assume that the starting position and traffic trajectories are fixed, but the starting position may be flexible, and shapes of traffic trajectories in real situation are variable and more complicated. Further research is needed to investigate the impact of different positions and trajectories on the driveway width and curb radius. Additionally, driveway width models for avoiding conflicts between motorized and nonmotorized traffic give consideration to both traffic safety and land resources, but the consideration is qualitative and hypothetical. In the future, we will pay more attention to the quantitative analysis of relationship of land use efficiency and traffic safety.We also provide the crash risk models, which can be used for evaluating the alternative ranges of driveway width and curb radius, and find the optimal pair. The models will give the safety effect of different design schemes and provide the safest design. However, these evaluation models have not considered the capacity effects yet, which should be studied in the future research.We measured and obtained the data from one superblock from 6:00 pm to 7:00 pm on June 29, 2019. As the data size is small, we used the data directly for design models and did not preprocess data and check the accuracy of the data in advance. In the future research, we should obtain adequate data size in more superblocks and then preprocess the data and check the accuracy of the data, so as to ensure the validity of the design models.


## 8. Conclusions

Current guidelines for driveway design and traffic safety provide reference values and qualitative guidance. Superblock driveways generate a busy and complex traffic environment, which requires detailed quantitative models for design, evaluation, and permitting. Driveway width and curb radius are key factors of driveway design. Recent research indicates that these two design factors are closely connected. This paper investigates and develops models of driveway width and curb radius and proposes crash risk models for design evaluation and optimization.Driveway width models are based on conflicts between exiting turns and through flow, the interaction between motorized and nonmotorized traffic, and the competition for available and acceptable gaps. The developed models can calculate a range of driveway widths, given their turning movements. The updated driveway width estimates can reduce traffic conflicts between exiting turn and through vehicles and decrease the number of conflicts between exiting vehicles and crossing nonmotorized traffic.Curb radius models account for turning paths, speed differential, and lane encroachment. The updated models connect the driveway width and curb radius, and they can produce a range of curb radius estimates for driveways with entering and exiting movements. Also, the updated curb radius can decrease the number of speed differences larger than 10 km/h and lane encroachments.The crash risk models account for traffic conflicts, speed differential, and lane encroachment. The relationships among crash risk, driveway width, and curb radius are represented with polynomial regression models. The results indicate that (i) larger curb radius and smaller driveway width would lead to lower crash risk, when traffic volumes are high; (ii) larger curb radius and driveway width would lead to lower crash risk, when traffic volumes are low; (iii) when curb radius or driveway width is too large, a higher crash risk is possible; and (iv) higher traffic volumes increase crash risk.Finally, we find that design ranges by using the proposed models are reasonable and effective; compared with the current design, the updated design reduces crash risk. Although the steps of analysis and formulas for driveway design and evaluation are complex, the method can be automated by computer programming and the required inputs for solving the problem are modest, as shown by the data in Tables4, 5, and 6.



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*Source: 8964170-2022-03-18.xml*