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Assessing Pavement Friction Need for Safe Integration of
Autonomous Vehicles into Current Road System
Guangyuan Zhao, Ph.D.1; Liyuan Liu2; Shuo Li, Ph.D., P.E.3; and Susan Tighe, Ph.D., P.E.4
Abstract: Safe integration of autonomous vehicles (AVs) into the current public road system may imply potential improvements to roadway
infrastructure. However, the current research effort is lacking in one of the important infrastructure to vehicle (I2V) areas, that is, roadway
conditions, especially pavement friction. Motivated by the fact that pavement friction plays a critical role in safe driving for conventional
vehicles and the fact that rear-end crashes are the most common type of crashes involving autonomous vehicles, this paper presents a first-of-
its-kind effort to evaluate the driving safety of AVs with respect to pavement friction. An explicit relation was derived between pavement
friction and traffic safety in terms of the stopping sight distance. The statistical characteristics of pavement network friction were determined
from field friction measurements. A typical scenario was created to define rear-end crashes involving self-driving vehicles. The probabilities
of rear-end crashes were estimated using the Monte Carlo method, and their implications were discussed. It was found that there is no urgent
need to increase pavement friction requirements with respect to rear-end crashes involving self-driving vehicles. The findings may also be
used to improve the extent of AVoperational domains (ODs) and facilitate highway agencies to assess the readiness of road infrastructure in
the form of roadway condition to support autonomous driving. DOI: 10.1061/(ASCE)IS.1943-555X.0000615.© 2021 American Society of
Civil Engineers.
Author keywords: Road infrastructure; Autonomous vehicle (AV); Pavement friction; Skid number; Rear-end crash; Stopping sight
distance; Reaction time.
Introduction
Autonomous vehicle (AV) technologies are advancing rapidly due
to the push from political, economic, and technological sectors and
could be accelerated more rapidly after the coronavirus disease
2019 (COVID-19) pandemic. However, safe integration of AVs
into existing roads may imply potential improvements or changes
to the current road system. The focus of the immediate improve-
ments is on infrastructure to vehicle (I2V) communication such as
pavement markings, signage, and signals (Kockelman et al. 2017;
Kortum and Norman 2018). This is probably because most ad-
vanced passenger cars today have at least one advanced driver as-
sistance feature, especially lane departure warning (LDW) or lane
keeping assistance (LKA) that uses cameras to detect lane markings
for determining the lateral position of the vehicle. Line-of-sight has
been identified as another emerging need because forward collision
warning (FCW) systems commonly use LiDAR, radar, or ultrasonic
sensors to detect other roadway users and obstacles (Harrington et al.
2018;Pape and Habtemichael 2018). These sensors may become
ineffective in certain driving environments. Recognizing the possible
far-reaching impacts on roadway infrastructure and the great poten-
tial to improve traffic safety, the Federal Highway Administration
(FHWA), in partnership with their key stakeholders, is conducting
research to ensure the quality and uniformity of road markings,
signage, and other traffic control devices to support safe and effi-
cient driving by both human drivers and AVs (USDOT 2018).
Nevertheless, the current research effort is lacking in one of the
important infrastructure areas with respect to the physical condition
of roadway surface, especially pavement friction. It has been well
recognized that pavement friction plays a critical role in ensuring
safe driving of conventional vehicles. Research by the FHWA in-
dicates that 70% of wet pavement crashes can be prevented or mini-
mized by improved pavement friction (FHWA 2016). Good friction
is a necessity to provide sufficient skid resistance at the tire–
pavement interface for safe lane changing, emergency braking, and
maneuvering through curves and can be achieved through sound
pavement friction management such as testing and preventative
maintenance treatments (NAS 2009;McGovern et al. 2011;Merritt
et al. 2015). In the authors’opinion, pavement friction is also one of
the critical factors for the driving safety of both autonomous and
connected vehicles. In reality, two studies show that rear-end
crashes are the most common crash involving self-driving vehicles,
and the majority of the rear-end crashes involved self-driving ve-
hicles rear-ended by conventional vehicles (Schoettle and Sivak
2015;Blanco et al. 2016). Rear-end crashes may arise due to fac-
tors such as sight distance, driver behavior, and vehicle, in addition
to pavement friction. Insufficient sight distance can lead to rear-end
crashes because motorists may be unable to see and react to ap-
proaching vehicles (Fambro et al. 1997;Herbel et al. 2010;McGee
2018). Driver behavior such as distraction and speeding may affect
1Postdoctoral Research Associate, Centre for Pavement and Transpor-
tation Technology (CPATT), Dept. of Civil and Environmental Engineer-
ing, Univ. of Waterloo, Waterloo, ON, Canada N2L 3G1. ORCID: https://
orcid.org/0000-0002-4654-9408. Email: luke.zhao@uwaterloo.ca
2Ph.D. Candidate, Key Laboratory of Road and Traffic Engineering of
Ministry of Education, Tongji Univ., Shanghai 201804, China; Research
Engineer, International Cooperation Research Center, Univ. of Waterloo
and Shanxi Transportation Research Institute, Taiyuan, Shanxi 030024,
China. Email: lly901124@163.com
3Research Engineer, Research Div., Indiana Dept. of Transportation,
West Lafayette, IN 47906 (corresponding author). ORCID: https://orcid
.org/0000-0003-1070-9155. Email: sli@indot.in.gov
4Professor, Dept. of Civil and Environmental Engineering, Univ. of
Waterloo, Waterloo, ON, Canada N2L 3G1. Email: sltighe@uwaterloo.ca
Note. This manuscript was submitted on May 14, 2020; approved on
December 22, 2020; published online on March 19, 2021. Discussion per-
iod open until August 19, 2021; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Infrastructure Sys-
tems, © ASCE, ISSN 1076-0342.
© ASCE 04021007-1 J. Infrastruct. Syst.
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the ability to see and time to react to changes on the road forward.
Efforts have been made in the past to determine the factors that
affect driver’s reaction time (Johansson and Rumar 1971;Lee et al.
2007;Campbell et al. 2012;Wood and Zhang 2017). It was found
that a brake reaction time of 2.5 s is well established for deriving
sight distance requirements but should not be viewed as a fixed
human attribute because it is influenced by many factors, including
age, visibility, object size, complexity, and distraction. It was also
found that the majority of drivers were not necessarily following
too closely at the onset of lead-vehicle braking, and the majority of
rear-end crashes were collisions with a stopped lead vehicle.
Autonomous driving sensors provide sensing accuracy and
range beyond human capabilities, leading to enhanced collision
warning, quicker reaction times, and, therefore, reduction in vehicle
crashes. However, it is anticipated that a traffic mix of autonomous
and conventional vehicles will be operating on public roads for an
extended period of time, and the importance of pavement friction
can never be overestimated. Very little information is currently
available for roadway practitioners to understand how human driv-
ers interact with autonomous vehicles and how pavement friction is
considered in the operational domains (ODs) of AVs now or in the
future. This paper presents a first-of-its-kind effort made to evaluate
the driving safety of AVs by considering the combined effect of
pavement friction and driver behavior based on the fundamentals
of roadway safety design. An explicit relation between pavement
friction and safety was derived in terms of the stopping sight dis-
tance, one of the critical safety features in roadway geometric de-
sign. The statistical characteristics of pavement network friction
were determined from multiyear friction measurements in the real-
world pavement network. A scenario defining rear-end crashes
involving AVs was created, and the relevant crash probabilities
were assessed at different combinations of pavement friction, reac-
tion time, headway, and speed using the Monte Carlo method. In
the authors’opinion, the stochastic characteristics of pavement fric-
tion presented in this paper may be used to improve the extent of
AV OD for enhancing safety, particularly in rainy weather. The pro-
posed algorithm can be used to better understand how conventional
vehicles respond to AVs. The findings will also be useful for high-
way agencies to address the needs in terms of pavement friction
management. It is also anticipated that this paper may provide food
for thought for roadway practitioners to realistically evaluate the
readiness of road infrastructure for safely integrating AVs into
the existing roadway system and to narrow the knowledge gap be-
tween AV and roadway communities.
Fundamental Relation between Safe Stopping Sight
Distance and Pavement Friction
Safe Stopping Sight Distance
Determining stopping sight distance (SSD) is one of the critical
safety aspects in roadway geometric design. A safe SSD is the length
of the roadway ahead, which is visible to the driver so that a complete
stop can be enabled before the vehicle reaches a stationary object in
its path. According to the design policy by the AASHTO, “APolicy
on Geometric Design of Highways and Streets”(AASHTO 2018), a
safe SSD is the sum of two distances travelled during braking: the
distance traveled during perception-reaction time and the distance to
fully stop the vehicle. For level and straight roads, SSD is computed
as follows:
SSD ¼0.278Vt þ0.0039 V2
a=gð1Þ
where SSD = stopping sight distance, m; V= design speed, km=h;
t= reaction time, s; a= deceleration rate, m=s2;andg= gravitational
acceleration constant, 9.81 m=s2.
In the AASHTO design policy mentioned earlier, a brake reac-
tion time of 2.5 s is recommended as the design criterion. This de-
sign criterion is considered adequate for conditions that are more
complex than the simple conditions used in laboratory and road
tests. It encompasses the capabilities of most drivers, including
those of older drivers, and exceeds the 90th percentile of reaction
time for all drivers. In addition, the policy indicates that approxi-
mately 90% of all drivers decelerate at rates greater than 3.4m=s2.
Such decelerations are within the driver’s capability to stay within
his or her lane and maintain steering control during the braking
maneuver on wet surfaces and are comfortable for most drivers.
Therefore, 3.4m=s2is recommended as the deceleration threshold
for determining the safe SSD. This implies that the friction avail-
able on most wet roadway surfaces and the capabilities of most
vehicle braking systems should provide braking friction that ex-
ceeds this deceleration rate.
Minimum Requirement for Pavement Friction
For a vehicle traveling on a straight, level pavement at a constant
speed of V, the vehicle that is braking can be modeled as an object
with mass msliding on a level surface, as shown in Fig. 1. Given
that the vehicle is braking at a constant deceleration rate of a, the
forces acting on the vehicle include the force of gravity mg and the
friction force Fμ, occurring at the interface of vehicle (tire) and
pavement surface. In analysis of vehicle braking, it is assumed that
the deceleration of the vehicle is solely caused by the friction force.
Applying Newton’s second law to the horizontal movement gives
the following equation:
Fμ¼ma ð2Þ
where Fμ= friction force; m= mass of vehicle; and a= deceler-
ation rate.
The friction force Fμcan be approximated from Coulomb’s law
of friction as follows:
Fμ¼μðmgÞð3Þ
where μ= coefficient of friction of pavement; and all other vari-
ables are as defined earlier.
Substituting Eq. (3) into Eq. (2) yields the relation between the
deceleration rate and the coefficient of friction
Fig. 1. Forces acting on braking vehicle.
© ASCE 04021007-2 J. Infrastruct. Syst.
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μ¼a
gð4Þ
where all variables are as defined earlier.
As shown in Eq. (4), the requirement for pavement friction; that
is, μ, is readily defined by the design criterion of deceleration rate
a. Accordingly, a deceleration threshold of 3.4m=s2as recom-
mended in the AASHTO design policy implies a minimum friction
coefficient of 0.35 (=3.4/9.81) that applies for most wet pavement
surfaces. In the United States, ASTM E274, “Standard Test Method
for Skid Resistance of Paved Surfaces Using a Full-Scale Tire
(ASTM 2015c),”has long been used to guide pavement friction
testing by state DOTs. This test measures the steady-state friction
force on a locked test wheel as it is dragged over a wetted pavement
surface under constant load and at a constant speed. The resulting
friction force is computed as follows:
SN ¼F
W
×100 ð5Þ
where SN = skid number; F= tractive force, that is, horizontal force
applied to the test tire at the tire-pavement contact patch; and W=
dynamic vertical load on test wheel.
Coincidentally, the study by Kummer and Meyer (1967) recom-
mends a SN of 37 measured at 64 km=h (40 mi/h) as the tentative
minimum requirement for pavement friction on main rural high-
ways. Friction number (FN) is often used interchangeably with SN
in the literature to represent the measured friction force. A SN of 37
can be converted into a friction coefficient of 0.37 that is remark-
ably close to the minimum friction coefficient of 0.35 implied in the
AASHTO policy. Currently, the ASTM E274 test can be performed
with either a standard rib (ASTM 2015a) or smooth tire (ASTM
2015b). The study by Henry (2000) indicates that the standard
smooth tire was developed in 1975 and given equal status in 1990.
This suggests that the minimum SN recommended by Kummer and
Myer was based on the standard rib tire. For the standard smooth
tire, the study by Li et al. (2005a) shows that the minimum SN is
approximately 20–30 at 64 km=h (40 mi/h).
Statistical Modeling of Pavement Network Friction
Variations of Pavement Friction
The literature (Li et al. 2004,2005b) provides detailed information
about a typical pavement network friction inventory test program
by the Indiana Department of Transportation (INDOT). The current
best practice in pavement friction management in the United States
can be found elsewhere (Henry 2000;NAS 2009). INDOT con-
ducts network inventory friction testing annually for interstate
highways and in a 3-year cycle for conventional highways. Field
pavement friction is measured in the driving lane at an interval of
one test per mile with the standard smooth tire using the ASTM
E274 locked wheel skid tester (LWST) and reported as SN at
64 km=h (40 mi/h). Pavement friction commonly decreases as the
test speed increases. Therefore, pavement friction measurements
made at other speeds should be adjusted according to the standard
speed. It should be further pointed out that in many Asian and
European countries, side-force coefficient (SFC) measured in
accordance with the method such as BS 7941-1, “Methods for
Measuring the Skid Resistance of Pavement Surfaces-Part 1:
Sideway-Force Coefficient Routine Investigation Machine”(BSI
2006), is widely used to measure the performance of pavement
friction.
Pavement friction varies from road to road, direction to direc-
tion, lane to lane, and location to location, due to the separate and
combined effects of pavement traffic application, type of pave-
ment, aging, and maintenance. The graph in the top left of Fig. 2
shows the friction measurements on three different roads, includ-
ing I-65, SR-3, and US-31. I-65 is an interstate highway. SR-3 and
US-30 are both conventional roads. The majority of the friction
numbers fall in the range of 20–70 for these three roads. The
graph in the top right of Fig. 2presents the average friction num-
bers measured in both directions, respectively, on seven roads.
The largest difference is 6.8% on US-30. On average, the friction
of hot mix asphalt (HMA) pavements is 29% greater than that of
portland cement concrete (PCC) pavements (see the graph in the
bottom left of Fig. 2). Overall, the pavement network friction per-
formance has not changed significantly over the last 10 years (see
the graph in the bottom right of Fig. 2). The average friction num-
bers varied approximately between 40 and 50 regardless of
road class.
Approximation of Pavement Network Friction
Distributions
To integrate the information on pavement friction into I2V technol-
ogies, it is of importance to understand the underlying distribution
of pavement network friction. Presented at the top of Fig. 3are
histograms of friction measurements made on I-65 and SR-1, re-
spectively. There are a total of 664 friction measurements on I-65
and 194 friction measurements on SR-1. It is shown that both histo-
grams are roughly bell-shaped. Chi-squared tests were conducted to
test whether the friction measurements follow a normal distribu-
tion. To accomplish this, the friction data set was first arbitrarily
divided into five subsets: (−∞, 30), (30, 40), (40, 50), (50, 60),
and (60, ∞). The computed χ2statistics are 2.08 and 3.30 for
I-65 and SR-1, respectively. Using the significance level of 0.05,
the critical value of χ2with 2 degrees of freedom, χ2
0.05;2, is 5.99
from the table of critical χ2(Devore 2000). Because the computed
χ2statistics for both I-65 and SR-1 are less than the critical χ2,it
can be concluded that a normal distribution provides a good
approximation of the distribution of pavement friction on I-65 and
SR-1, respectively.
If the ASTM E670-09 test method (ASTM 2015d) is used to
provide continuous measurement of pavement such as SFC, a large
amount of friction data can be generated on a single road. Shown in
the graph in the bottom right of Fig. 3are the distributions of SFC
measurements on three roads, including Huohou expressway, Pin-
gyang freeway, and Yangji freeway in the province of Shanxi,
China. There are a total of 9,000–12,800 SFC measurements on
each of these three roads. The distribution of SFC on Huohou ex-
pressway is slightly right skewed, and the distributions of SFC are
slightly left skewed on both Pingyang and Yangji freeways. Due to
the extremely large sample size at the network level, it becomes
tricky and difficult to use normality tests such as the chi-squared
and Shapiro–Wilk tests to determine whether the data follow a nor-
mal distribution. However, a roadway network is composed of indi-
vidual roads. It can be inferred from the central limit theorem
(Devore 2000) that the normal distribution is an appropriate
approximation for the average of the friction measurements on
all individual roads in the network. Displayed in the graph in
the bottom left of Fig. 3are the distributions of the pavement net-
work inventory friction measurements made in 2016, 2017, and
2018, respectively. The 5th, 25th, 50th, and 75th percentile friction
numbers, respectively, are approximately 22, 34, 43, and 55, with a
coefficient of variation of 30% at the network level.
© ASCE 04021007-3 J. Infrastruct. Syst.
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Algorithm for Predicting Friction Dependent
Rear-End Crash
Friction-Dependent Car-Following Model
A friction-dependent car-following model is proposed in the cur-
rent paper to predict the likelihood involving AVs by the present
authors. Like the traditional models documented in the literature
(Gazis et al. 1959;Levin and Boyles 2016;Hyden 1987), safety
in the proposed friction-dependent-car following model is gov-
erned by the safe following distance that is computed according
to the law of kinematics. Unlike traditional models, the proposed
friction-dependent car-following model is simplified by consider-
ing only a vehicle pair. This is extremely helpful in understanding
how conventional vehicles respond to AVs and allows the friction
car flowing model to predict vehicle crashes involving AVs, in par-
ticular rear-end crashes during emergency braking. In the proposed
friction-dependent car-following model, the safe following distance
between two consecutive vehicles is computed as the safe SSD by
replacing the acceleration of vehicle, that is, a=gin Eq. (1), with the
pavement coefficient of friction, that is, μin Eq. (4), as follows:
SSD ¼0.278Vt þ0.0039 V2
μð6Þ
where all variables are as defined earlier.
Consequently, it becomes possible to explicitly assess the sen-
sitivity of rear-end crash to pavement friction. Presented in Fig. 4is
a graphical illustration of the friction-dependent car-following
model, where the black car represents the leading (i.e., front) car,
and the grey car represents the following car. The leading car travels
at speed V1with a reaction time t1. The following car travels at
speed V2with a distance gap hbehind the leading car and a reaction
time t2. Consider the following case: the leading car perceives a
critical situation and then applies the brake to a safe stop to avoid
a crash. Assume that the following car starts to respond at the time
the leading car starts to apply the brake, and therefore, a lag time t1
exists until the following car starts to respond. When the two con-
secutive cars are fully stopped, the distance traveled by the leading
car SSD1, the distance traveled by the following car SSD2, and the
gap between these two cars ΔD, respectively, can be computed as
follows:
SSD1¼0.278V1t1þ0.0039 V2
1
μð7Þ
SSD2¼0.278V2ðt1þt2Þþ0.0039 V2
2
μð8Þ
ΔD¼SSD2−ð0.278thV2þSSD1Þ
¼0.278V2ðt2−thÞþ0.278t1ðV2−V1Þþ0.0039 V2
2−V2
1
μ
ð9Þ
where th= time gap, s; and all other variables are as defined earlier.
0 25 50 75 100 125 150 175 200 225 250
0
10
20
30
40
50
60
70
80
90
100
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
30
32
34
36
38
40
42
44
46
48
50
47.8
36.7
45.9 44.5
37.4
42.2 43.5
49.2
38.9
42.9 44.6
37.5
44.2 45.5
49.4 47.3 48.1
37 38.1 37.3
SR-3 US-31 I-65
Skid Number (SN)
Mile Marker
SR-3 SR-62 US-30 US-31 I-465 I-65 I-80
0
10
20
30
40
50
60
Skid Number (SN)
Road
Northbound/Eastbound Southbound/Westbound
Interstate Conventional All Roads
0
10
20
30
40
50
60
Skid Number (SN)
Pavement Type
HMA PCC
Average Skid Number (SN)
Year of Test
Interstate Conventional All Roads
(a) (b)
(c) (d)
Fig. 2. Variations of pavement friction: (a) along road; (b) in direction; (c) by pavement type; and (d) over time.
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Assessing Probability of a Rear-End Crash
A rear-end crash occurs if ΔD>0, which is adopted as the criterion
in the current paper to predict rear-end crashesusing the Monte Carlo
method. Specifically, when the behavior of leading car is indepen-
dent of the following car and the only evasive action by the following
car is applying the brake, the iteration process becomes fairly
straightforward and consists of the following steps integrated to as-
sess the probability of an event, that is, a rear-end crash:
1. Generate random numbers uniformly distributed over the continu-
ous range (0, 1) for the input variables included in Eqs. (7)–(9).
2. Transform random numbers to random input values based on the
probabilistic distributions of the input variables, respectively,
using the inverse transformation methods.
3. Perform a computation trial that yields SSD1, SSD2, and ΔDby
substituting the random input values into Eqs. (7)–(9), respec-
tively; and
4. Repeat the previous steps and estimate the likelihood of crash as
follows:
pc¼nc
Nð10Þ
where pc= probability of rear-end crash; N= total number of
iterations (or trials); and nc= number of iterations that have
ΔD>0.
As noted earlier, an AV followed by a conventional vehicle
is one of the most useful cases for understanding how conven-
tional vehicles respond to AVs and assessing the effects of rel-
evant driving behavior and interaction characteristics on driving
safety during emergency braking. To accomplish this goal, a
vehicle pair comprising a leading self-driving vehicle and a fol-
lowing conventional vehicle is considered as the basic scenario
that allows for further assessment of the effect of pavement fric-
tion on the driving safety involving AVs. A study indicates that
the average reaction time is 0.83–0.84 s for self-driving vehicles
(Dixitetal.2016). Human drivers’reaction times have been
well studied over the last decades (AASHTO 1028;Johansson
and Rumar 1971). The statistics of vehicle speeds and time gaps
can be found elsewhere (Jiang et al. 2006). The skid numbers
at the 5th, 25th, 50th, and 75th percentiles can be approximated
from Fig. 3(d).Table1shows the summary statistics of the
random variables used as iteration inputs in the following
sections.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0
400
800
1200
1600
2000
2400
2800
3200
0 102030405060708090100110
0
200
400
600
800
1000
1200
1400
1600
1800
0
13
97
171
202
128
19 28
6
02
14
54
62
42
12
53
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
0
40
80
120
160
200
240
Frequency
Skid Number (SN)
0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
0
10
20
30
40
50
60
70
Frequency
Skid Number (SN)
Frequency
Sideway Force Coefficient (SFC)
Huohou Expressway
PingYang Freeway
YangYi Freeway
Frequency
Skid Number (SN)
2016
2017
2018
(a) (b)
(c) (d)
Fig. 3. Distributions of friction measurements: (a) interstate; (b) state road; (c) expressway or freeway; and (d) pavement network.
v
2
, t
2
SSD1
SSD2
h
v
1
, t
1
∆D
Fig. 4. Graphical illustration of friction-dependent car-following
model.
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Results and Their Implications
Effects of Driving Behavior Characteristics
Plotted in Fig. 5are the results by the iteration process as presented
earlier for all 1,152 possible combinations of inputs from Table 1.
In each iteration, the speeds of the two vehicles follow the same
distribution but are generated separately. Also, the coefficient of
friction was adjusted for each vehicle according to their speeds.
There are three typical trends associated with the variations of crash
probabilities with vehicle speed, depending on both the time gap
and the conventional vehicle’s reaction time (CVRT). When CVRT
is equal to time gap, the crash probabilities remain essentially
around 50%, and the effects of the self-driving vehicle’s reaction
time (SVRT), the speeds of both vehicles, and pavement friction
may be neglected. When CVRT is less than time gap, the crash
probability increases as speed increases. However, the crash prob-
ability decreases as speed increases when CVRT is greater than
time gap. One possible reason is that the stopping sight distance
is defined by the combined effect of vehicle’s reaction time and
pavement friction. If Eq. (9) is rearranged, ΔDhas a term, that is,
0.278V2(t1–th). Depending on if (t1–th) is positive or negative,
the speed will have opposite effect on ΔD. As shown in Eq. (6), the
stopping distance increases as CVRT increases and pavement fric-
tion decreases. Pavement friction is speed dependent. A higher
speed will result in a decrease in pavement friction and therefore
an additional increase in the braking distance. Consequently, the
rate of increase in the conventional vehicle’s stopping sight distance
becomes much lower when CVRT is greater than time gap than
when CVRT is less than time gap. However, the self-driving
vehicle’s stopping sight distance remains essentially unchanged.
The self-driving-vehicle’s reaction time, that is, SVRT, does af-
fect the crash probability. Nevertheless, the degree of effect can be
neglected. As an illustration, the crash probability increases from
16.5% to 19.7% when SVRT increases from 0.2 to 1.0 s at a time
gap of 1.5 s and CVRT of 0.66 s. This may not apply to other types
of vehicle crashes, such as single-vehicle crashes. Both CVRT and
time gap affect crash probability significantly. Given a speed of
50 km=h, time gap of 1.5 s, SVRT of 0.6 s, and FN of 43 (50th
percentile), for example, the crash probability approximately in-
creases from 49% to 75% when CVRT increases from 1.5 to
2.5 s and decreases from 75% to 49% when the time gap increases
Table 1. Summary statistics of input random variables as iteration inputs
Variable Mean/standard deviationa
Self-driving reaction time, s 0.2=0.1,0.6=0.3,1.0=0.5
Human reaction time, s 0.66=0.26,1.5=0.6,2.0=0.8,2.5=1.0
Time gap, s 1.5=0.3,2.0=0.4,2.5=0.5
Vehicle speed, km=h50=7.5,60=9,70=10.5,80=12,90=13.5,
100=15,110=16.5,120=18
Skid number (SN)22=6.6,34=10,43=13,53=16
aThe numbers above and below the slash line denote the mean and standard
deviation, respectively.
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5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.2 s, Gap = 1.5 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.2 s, Gap = 2.0 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.2 s, Gap = 2.5 s
Crash Probability (%)
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.6 s, Gap = 1.5 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.6 s, Gap = 2.0 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 0.6 s, Gap = 2.5 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 1.0 s, Gap = 1.5 s
Vehicle Speed (km/h)
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 1.0 s, Gap = 2.0 s
5th 25th 50th 75th
CVRT = 2.5 s
CVRT = 2.0 s
CVRT = 1.5 s
CVRT = 0.66 s
SVRT = 1.0 s, Gap = 2.5 s
Fig. 5. Probabilities of rear-end crashes estimated in terms of conventional vehicle reaction time (CVRT), self-driving vehicle reaction time (SVRT),
time gap, speed, and pavement friction.
© ASCE 04021007-6 J. Infrastruct. Syst.
J. Infrastruct. Syst., 2021, 27(2): 04021007
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from 1.5 to 2.5 s. The previous observations can be extended to
imply that pavement friction does not affect rear-end crashes inde-
pendently. Rear-end crashes involving self-driving vehicles rely
primarily on how the following conventional vehicle responds to
the leading self-driving vehicle such as time gap, CVRT, or both.
Potential Effects of Pavement Friction
A more careful inspection of those curves presented in Fig. 5shows
that pavement friction can have widely different effects on crash
probability, which also depends on the time gap and CVRT. When
CVRT is equal to the time gap, the effect of pavement friction is
negligible. When CVRT is less than the time gap, the crash prob-
ability increases as pavement friction decreases. When CVRT is
greater than the time gap, the crash probability decreases as pave-
ment friction increases. As pointed out earlier, the stopping sight
distance decreases as pavement friction increases. However, the
rate of increase is much lower when CVRT is less the than time
gap than when CVRT is greater than time gap. Consequently, the
crash probability may increase or decrease as pavement friction in-
creases. It is shown that the curves vary more greatly when CVRT is
less than time gap than when CVRT is greater than time gap. This
indicates that pavement friction affects the crash probability more
significantly when CVRT is less than time gap than when CVRT
is greater than time gap. Nevertheless, all the curves with CVRT
greater than time gap demonstrate a clear convergence, regardless
of pavement friction. As speed increases, the crash probability ap-
proaches a limit that is always less than 50%. The greater the
CVRT, the greater the limit.
At the 50th percentile (median) pavement friction, the crash
probabilities vary between 5% and 75%. As shown in Fig. 5, over-
all, the probabilities of rear-end crashes range between 2% and
76%. Further examination of those curves with CVRT less than
time gap shows that increasing pavement friction number from
43 (50th percentile) to 53 (75th percentile) may result in an absolute
decrease of 5% or less in crash probability. On average, increasing
vehicle speed from 50 to 120 km=h may yield an absolute increase
of 19% in crash probability at the 5th percentile pavement friction
and 18.9% at the 75th percentile pavement friction. Obviously, the
potential differences are negligible. The previous observations in-
dicate again that pavement friction does not affect rear-end crashes
independently. Therefore, it may be concluded that there is no ur-
gent need to increase current pavement friction requirements with
respect to rear-end crashes. From the safety standpoint, increasing
pavement friction will ultimately reduce vehicle crashes, particu-
larly single-vehicle crashes. However, it may not be cost effective
to increase to the current friction requirements to reduce rear-end
crashes involving autonomous vehicles.
The previous analysis focuses on rear-end crashes during emer-
gency braking under adverse conditions. It is well known that dur-
ing normal traffic, the speeds of two consecutive vehicles may be
closely correlated. To further assess the possible effects of pave-
ment friction on rear-end crashes when the two speeds are closely
correlated, two example scenarios may be considered, as follows:
(1) V1¼V2, and (2) V1and V2are closely correlated; that is, V2¼
2.20 þ0.97V1(Burghout and Koutsopoulos 2009). Presented in
Fig. 6are the variations of crash probabilities with pavement fric-
tion for these two scenarios. In Scenario 1, the probabilities ≈10%
(i.e., constant). This is because when V1¼V2, the third term con-
taining pavement friction on the right-hand side of Eq. (9) will be
cancelled, and the crash probability depends fully on the following
vehicle. In Scenario 2, where V1and V2are closely correlated, the
crash probability increases slightly from 6.3% to 8.7% as the level
of pavement friction increases from 0.22 (i.e., very low) to 0.70
(i.e., very high). The previous examples imply that when the speeds
of two consecutive vehicles are closely correlated, the effect of
pavement friction on the probability of a rear-end crash may be
neglected.
Conclusions
To further facilitate industries to improve the extent of AV OD and
highway agencies to assess the readiness of road infrastructure in
the form of road surface condition, this paper assessed the probabil-
ities of vehicle crashes involving AVs based on the actual pavement
network friction performance. The main findings are summarized
subsequently.
The actual friction measurements show that the majority of
existing pavements maintained by INDOT can provide a friction
number of 23 or higher that is sufficient to allow most drivers
to decelerate at rates greater than 3.4m=s2. The variations of pave-
ment network friction can be modeled using a normal distribution.
The typical mean friction number is around 44 with a standard
deviation of around 15 across the entire pavement network.
A typical scenario consisting of a vehicle pair, particularly a
leading self-driving vehicle and a following conventional vehicle,
can be used to assess the probability of a rear-end crash according
to the stopping distances calculated from randomly assigned speed,
reaction time, gap, and pavement friction. Rear-end crashes involv-
ing self-driving vehicles rely primarily on how the following con-
ventional vehicle responds to the leading self-driving vehicle such
as time gap and conventional vehicle’s reaction time, in particular
the combined effect of both.
Pavement friction can have widely different effects on crash
probability but does not affect rear-end crashes independently.
As pavement friction varies with vehicle speed, its effect on
rear-end crashes also varies with speed, time gap, and reaction time.
When the consecutive vehicle speeds are closely correlated, the ef-
fect of pavement friction on the probability of a rear-end crash
should be neglected. The calculated results indicate that there is
no urgent need for increase friction requirements with respect to
rear-end crashes. A sound pavement network friction test program
can enhance road infrastructure readiness to support autonomous
driving.
Data Availability Statement
All data, models, and code generated or used during the study
appear in the published article.
0
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12
0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75
Crash Probability (%)
Coefficient of Friction
Scenario 1 Scenario 2
Fig. 6. Probabilities of rear-end crashes estimated with closely corre-
lated speeds.
© ASCE 04021007-7 J. Infrastruct. Syst.
J. Infrastruct. Syst., 2021, 27(2): 04021007
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Acknowledgments
This paper is made possible through the support from many people.
Especially, the authors would like to thank Tim Wells and Karen
Zhu of Indiana Department of Transportation, Ruey (Kelvin) Cheu
of The University of Texas at El Paso, and Bin Yu of Tongji Uni-
versity for their unconditional help and useful discussions.
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