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infrastructures
Article
Geometric and Operational Features of Horizontal
Curves with Specific Regard to Skidding Proneness
Paolo Intini *, Nicola Berloco, Vittorio Ranieri and Pasquale Colonna
Department of Civil, Environmental, Land, Building Engineering, and Chemistry, Polytechnic University of Bari,
4 via Orabona, 70125 Bari, Italy; nicola.berloco@poliba.it (N.B.); vittorio.ranieri@poliba.it (V.R.);
pasquale.colonna@poliba.it (P.C.)
*Correspondence: paolo.intini@poliba.it; Tel.: +39-080-5963390
Received: 29 November 2019; Accepted: 20 December 2019; Published: 28 December 2019
Abstract:
(1) Run-off-road (ROR) crashes are a crucial issue worldwide, resulting in a disproportionate
number of traffic deaths. In safety research, macro-level analysis on large datasets is usually conducted
by linking explanatory variables to ROR crash frequency/severity. Micro-analysis approaches, like the
one used in this study, are instead less frequent. (2) A comprehensive Italian Fatal +Injury (FI) crash
dataset was filtered to identify two-way two-lane rural road curves on the national road network on
which more than one ROR FI crash (i.e., at least two crashes) in the observation period of four years
had occurred. The typical features of the ROR FI crashes and the recurrent geometric (characteristics
of tangents and curves) and operational features (inferred speeds, acceleration/decelerations) of
the crash sites were reconstructed. (3) The main contributory factors in ROR FI crashes are: wet
pavements, speeding, and distraction. Sites with a relevant history of ROR FI crashes present recurrent
safety issues such as inadequate horizontal curve coordination, an insufficient tangent length for
decelerating, and inferred operating speeds comparable/higher than the inferred design speeds.
(4) Based on findings, some practical suggestions for road safety management and maintenance are
proposed through specific indicators and countermeasures (speed, perception, and friction related).
Keywords: rural two-lane roads; run-offcrashes; road geometric design; road friction
1. Introduction
Among all the crash types, run-off-road (ROR) crashes are a major concern worldwide, given the
considerable number of fatalities and serious injuries related to them (see [
1
–
3
]). These are typically
single-vehicle accidents with few interactions with other drivers. In Europe, overall, single vehicle
collisions result in about one third of all deaths on roads [
4
], with most of them occurring in rural
environments. The problem is even worse in the United States, particularly for ROR crashes, since
fatalities resulting from them account for about half of all traffic fatalities [3].
Clearly, a remarkable number of single-vehicle rural run-off-road crashes (henceforth referred
to as ROR crashes) may occur at curves, which involves design aspects that should be highlighted
while conducting safety analyses on existing roads [
5
]. For example, a study by SWOV (Institute
for Road Safety Research) [
6
] (as reported in [
4
]) highlighted that in a vast majority of ROR crashes
at curves (about 90%), the curve radius was inappropriate for the posted speed limit. Moreover,
considering detailed statistics from Italy (2014–2017 [
7
]), ROR crashes at curves with at least one
injured person involved accounted for about 3% of all fatal +injury recorded crashes. However, the
percentage of fatalities from curve ROR crashes among all fatal crashes is more than double at about
7%. Specifically focusing on undivided two-way rural roads, the disproportion between single-vehicle
ROR fatal and fatal +injury crashes increases, about 4% and 1% among the total fatal and fatal +injury
crashes, respectively.
Infrastructures 2020,5, 3; doi:10.3390/infrastructures5010003 www.mdpi.com/journal/infrastructures
Infrastructures 2020,5, 3 2 of 25
Among the main causes of ROR crashes, speed, distraction, and fatigue play an important role
(see [
4
]). Moreover, when specifically focusing on curves, the occurrence of ROR crashes may be
influenced, among the other factors, by these road design aspects:
•Geometric curve design, in particular a sharp radius of curvature (see [6,8]);
•Tire-road friction, particularly the side friction available in different conditions [9,10]; and
•Road design consistency, which is intrinsically related to the drivers’ expectations.
In detail, while the first two factors are essentially physically-based and interact between them
(design speeds, side friction, and the radii of curvature are typically related), the third factor is more
complex. In recent research [
11
,
12
], it was shown how crash rates at curves may be influenced by the
design characteristics of nearby road elements. For example, drivers, especially if unfamiliar with the
road [
13
], may not expect a sharp curve after a very long tangent. The occurrence of the latter was
actually found to be a recurrent safety problem, especially for two-way two-lane rural roads [5].
Research in this field usually includes these above-mentioned factors while investigating ROR
crashes. In particular, statistical techniques (e.g., [
1
,
14
,
15
]) are used to capture the most relevant
factors that may influence both the occurrence and severity of ROR crashes. However, as previously
explained, the most relevant factors may be inter-dependent, both design- and human-related, and
may be site-specific. For this reason, in this study, the analysis of ROR crashes was conducted from a
“micro” perspective, which has rarely been performed in the literature. In detail, the analysis focused
on specific sites with a previous remarkable history of ROR crashes through in depth study of the
accident contributory factors and the geometric and operational characteristics of the selected road
sites (see [
16
–
18
]). In this way, specific patterns may be revealed, which are difficult to find with the
usual macro-level modeling strategies.
In detail, the study aimed at answering the following research questions:
•
What are the typical features of ROR crashes occurring at curves on rural roads, in particular
two-way two-lane rural segments?
•
What are the recurrent road geometric and operational characteristics of segments including the
highlighted curves with a relevant history of ROR crashes?
•
Which of the previously highlighted aspects can be useful, and in which way, from a road safety
management perspective?
To answer these research questions, two-way two-lane rural road sites seriously affected by ROR
crashes at curves belonging to the main Italian national road network were analyzed. In particular, the
micro-analysis approach used in this study is presented in Section 2. Thereafter, the results obtained are
described and discussed in Section 3. Finally, in Section 4, our conclusions are drawn by focusing on
the findings that can be useful for road safety management/maintenance practice (i.e., in the network
screening stage by road agencies [
19
,
20
], with the aim of reducing the specific ROR crash type through
safety-based maintenance (see [3]).
2. Materials and Methods
The materials and methods used in this study are described as follows. First, the road sites to be
analyzed in detail were identified based on their recent history of ROR crashes, according to data from
the Italian National Institute of Statistics (ISTAT) [
7
]. Hence, the crash dataset was presented and the
criteria used for selecting road sites defined. Next, the criteria used for analyzing the crashes at these
road sites and their geometric and operational characteristics were defined.
2.1. Selection of Road Sites Based on Their Run-Off-Road Crash History
The crash dataset used in this study is publicly available on the website of the Italian National
Institute of Statistics (ISTAT) [
7
]. It includes all crashes recorded in Italy with at least one vehicle
involved and at least one injured person (i.e., Fatal +Injury (FI) crashes). The time span considered
Infrastructures 2020,5, 3 3 of 25
was set according the most complete and recent data available, which was a 4-year observation period
from 2014 to 2017.
During this period, a total number of 702,227 FI crashes were recorded (175,557 FI crashes per
year on average). Out of this total, 21,608 crashes were ROR crashes at curves. About half of the ROR
crashes at curves (9749 FI crashes, of which 518 were fatal (F) crashes) occurred at two-way two-lane
rural road segments. It should be noted that, while the number of ROR crashes at curves on these
roads have decreased on average over the years, following the general national trend, fatal crashes of
this specific type are slightly increasing (or not decreasing) over time.
Based on the information reported in the dataset, it is possible to locate them on the road network
(the name of the road and the exact kilometer are generally included in the dataset). Two-way two-lane
rural roads can either be main, secondary, or local roads. For the sake of analyzing segments belonging
to the same road type, typically carrying comparable traffic volumes, only the main state-level two-way
two-lane rural roads were analyzed, for which the localization of crashes was made easier by the
presence of evident road milestones. This led to a further narrowing of the number of ROR crashes at
curves to 1650 FI crashes over the four year period (412.5 FI crashes/year).
Among those crashes, based on the exact localization (e.g., road has a given ID, at the specific
section from the beginning of the road at km X +YYY: kilometer X, YYY meters), the road curves at
which more than one crash occurred in the considered 4 year period were selected. In some instances,
the road ID and/or the exact localization (km X +YYY) was not provided and so they were excluded
from the analysis. Typically, the precision of localization is in the order of 100 m (e.g., km 1 +100 or
km 1 +200). Hence, two (or more) crashes that occurred at a distance of less than 100 m and both
classified as crashes on curve sections were preliminary assigned to the same road curve.
This selection stage led to the identification of 80 curved two-way two-lane rural road sites at
which more than one crash occurred in the four year period. These sites were visually inspected by
means of on-line sources (i.e., mainly Google Earth
®
and Street View
®
). The visual inspection aimed
to check if the characteristics specified in the dataset actually matched the real conditions, and if there
were surrounding elements that may act as confounding factors for the analysis. In fact, ROR crashes
at curves may also be influenced by the characteristics of other nearby elements [
11
–
13
]. At the end of
this process, 17 sites were discharged because it was not possible to precisely localize the crash in the
case of very close subsequent curves; five due to road works; 12 due to main intersections or significant
cross-sectional modifications; nine were partially or entirely placed in sub-urban/urban environments;
five were actually not two-lane rural road curves; one was a hairpin turn; and one was close to a tunnel.
At the end of the verification process, 30 two-way two-lane uninterrupted rural road segments
belonging to the Italian national road network including the curved ROR crash sites (more than one
ROR FI crash in the period 2014–2017) were so selected.
2.2. Geometric Characteristics of the Selected Road Sites
Once road segments including the curved ROR crash sites were identified, their geometric
characteristics were collected. This operation was manually conducted by means of on-line sources (i.e.,
mainly Google Earth
®
and Street View
®
, see [
21
,
22
]) given the unavailability of consistent datasets of
road geometric information (such as those used in [13]).
The following geometric features of road segments were inferred (see Figure 1):
•Radius (“R,c”) of the curve (“C”) at which more than one ROR FI crash has occurred;
•Length of the above defined curve (“L,c”)
•Radius (“R,c+1”) and length (“L,c+1”) of the curve (“C+1”) following the curve “C”;
•Radius (“R,c-1”) and length (“L,c-1”) of the curve (“C-1”) previous to the curve “C”;
•Length (“L,t1) of the tangent (“T1”) included between the curves “C” and “C-1”; and
•Length (“L,t2”) of the tangent (“T2”) included between the curves “C” and “C+1”.
Infrastructures 2020,5, 3 4 of 25
In addition to these measures, the average road width “W,c” at the curve “C” was collected,
alongside the average slope “i,c” of the curve “C”, which was estimated through the elevation profile
obtained through Google Earth
®
. Note that the attributes “previous” and “following” given to the
curves/tangents were defined as only based on the order in which they were reconstructed, since the
direction of travel of the crashed vehicle was unknown.
Infrastructures 2020, 5, x FOR PEER REVIEW 4 of 25
curves/tangents were defined as only based on the order in which they were reconstructed, since the
direction of travel of the crashed vehicle was unknown.
Figure 1. Main information collected regarding the horizontal alignment of the road site where the
curved ROR site lies (curve “C”) including information about the radii and lengths of the previous
(“C-1”) and following (“C+1”) curves, and the lengths of the included tangents (“T1”, “T2”).
Based on these direct measures, other indirect measures of curvature were computed, namely
the curvature change ratio (CCR) [23] both for curve “C” and the overall segment, as follows:
𝐶𝐶𝑅, 𝑐 = 𝛼,𝑐
𝐿,𝑐 = 63.66
𝑅,𝑐 [𝑘𝑚] (1)
𝐶𝐶𝑅, 𝑡𝑜𝑡 = ∑𝛼
𝐿,𝑡𝑜𝑡= ∑(𝐿
𝑅)
𝐿,𝑡𝑜𝑡 = (𝐿
𝑅), +(𝐿
𝑅), +(𝐿
𝑅),
𝐿, +𝐿, +𝐿, +𝐿, +𝐿, (2)
where
CCR,c = curvature change ratio of the ROR crash curve C [gon/km];
CCR,tot = curvature change ratio of the overall segment [gon/km];
𝛼,𝑐 = angle included between the two tangents preceding and following the curve C [gon];
𝛼,𝑖 = angle included between the two tangents preceding and following a given curve [gon];
L,tot = total segment length [km].
R,
c
, R,
c-1
, R,
c+1
, L,
c-1
, L,
c
, L,
c+1
, L,
t1
, and L,
t2
are the measures above specified in this paragraph [km].
It should be noted that it is possible to plausibly reconstruct the geometry of curves without
relying on transition curves, and then Equations (1) and (2) do not account for them. Clearly, on one
hand, the reconstructions were limited by the use of on-line sources, but on the other hand, the
transition curves could actually be absent. In fact, in most cases, the road layouts analyzed were very
old and have belonged to the main national network for decades, which could explain the absence of
transition curves.
2.3. Operational Characteristics of the Selected Road Sites
Based on the reconstructed geometric characteristics, it was possible to infer the operational
characteristics of the 30 selected road segments where these characteristics mainly concerned speeds.
2.3.1. Inferred Operating Speeds
Figure 1.
Main information collected regarding the horizontal alignment of the road site where the
curved ROR site lies (curve “C”) including information about the radii and lengths of the previous
(“C-1”) and following (“C+1”) curves, and the lengths of the included tangents (“T1”, “T2”).
Based on these direct measures, other indirect measures of curvature were computed, namely the
curvature change ratio (CCR) [23] both for curve “C” and the overall segment, as follows:
CCR,c=α,c
L,c=63.66
R,c[km](1)
CCR,tot =Piαi
L,tot =PiL
Ri
L,tot =L
R,C−1+L
R,C+L
R,C+1
L,C−1+L,C+L,C+1+L,t1+L,t2
(2)
where
CCR,c=curvature change ratio of the ROR crash curve C [gon/km];
CCR,tot =curvature change ratio of the overall segment [gon/km];
α,c=angle included between the two tangents preceding and following the curve C [gon];
α,i=angle included between the two tangents preceding and following a given curve [gon];
L,tot =total segment length [km].
R,
c
,R,
c-1
,R,
c+1
,L,
c-1
,L,
c
,L,
c+1
,L,
t1
, and L,
t2
are the measures above specified in this paragraph [km].
It should be noted that it is possible to plausibly reconstruct the geometry of curves without
relying on transition curves, and then Equations (1) and (2) do not account for them. Clearly, on
one hand, the reconstructions were limited by the use of on-line sources, but on the other hand, the
transition curves could actually be absent. In fact, in most cases, the road layouts analyzed were very
old and have belonged to the main national network for decades, which could explain the absence of
transition curves.
Infrastructures 2020,5, 3 5 of 25
2.3. Operational Characteristics of the Selected Road Sites
Based on the reconstructed geometric characteristics, it was possible to infer the operational
characteristics of the 30 selected road segments where these characteristics mainly concerned speeds.
2.3.1. Inferred Operating Speeds
Operating speeds can be computed based on the geometric characteristics through appropriate
local models from previous research. The selected road segments belong to the Italian national road
network and so Italian operating speed models were searched. Models retrieved in [
24
,
25
], namely for
two-way two-lane rural road curves and tangents, were selected from the review of operating speed
models included in [26]. These models are reported as follows:
S85,C=a−b RC,i−0.5 (3)
S85,T=S85,Cp +0.081 LT,i0.75 (4)
where
S85,C=85th percentile of the operating speed at the two-way two-lane rural curve C,i [km/h];
S85,T=85th percentile of the operating speed at the two-way two-lane rural tangent T,i [km/h];
S85,Cp =85th percentile of the operating speed at the curve Cpprevious to the tangent T,i [km/h];
RC,i=radius of curvature of the curve C,i [m];
LT,i=length of the tangent T,i [m];
a
=constant [km/h] depending on the CCR computed for the single curve C (see Equation (1)),
namely equal to 124.1 (CCR <30 gon/km), 118.1 (30
≤
CCR <80 gon/km), 111.6 (80
≤
CCR <160 gon/km),
110.8 (CCR ≥160 gon/km);
b
=constant [km*m
0.5
/h] depending on the CCR computed for the single curve C (see Equation (1)),
namely equal to 563.78 (CCR <30 gon/km), 510.56 (30
≤
CCR <80 gon/km), 437.44 (80
≤
CCR <160
gon/km), 346.62 (CCR ≥160 gon/km).
Equations (3) and (4) were used in this study to compute the speeds at tangents and curves of
the investigated road segments, based on their geometric characteristics. Note that the inferred 85
th
operating speed was deemed more informative than the posted speed limits since: (a) the maximum
speed limit on this Italian specific road category is 90 km/h, but the geometric characteristics may
compel drivers to lower speeds; (b) no fixed speed control enforcement systems were noted on the
segments, mainly located in sparsely populated rural areas; and (c) in several cases, it was not possible
to associate a specific posted speed limit to the road sections analyzed.
2.3.2. Inferred Design Speeds
Operating speeds (measured through their 85
th
percentiles, as in Equations (3) and (4) may suggest
the actual speed that is not exceeded by 85% of drivers at a given curve or tangent, based on their
geometric characteristics. If the operating speeds are much higher than the design speeds for each
road element, this may result in a safety issue [
5
,
20
,
27
]. This is particularly relevant for curves, for
which high speeds may result in not meeting equilibrium conditions. For this reason, in this study, the
difference between curve operating and design speeds was investigated.
The theoretical curve design speeds can be inferred from standard equilibrium considerations:
RC=SD,Ci2
127 ∗(q(RC,i)+ft(SD,Ci)) (5)
where
SD,Ci =inferred design speed for the curve C,i [km/h];
RC,i=radius of curvature of the curve C,i [m];
q(RC,i)=cross slope (superelevation) of the curve C,i, usually set as a function of RC,i[-];
Infrastructures 2020,5, 3 6 of 25
ft(SD,Ci)
=side tire-pavement friction coefficient at the curve C,i, which depends on several
variables and is usually assumed as varying with vehicle speed SD,Ci at curve C,i [-].
The inferred design speed obtained by inverting Equation (5) is equal to the maximum speed
allowed for a given radius under given friction coefficients and cross slopes. Hence, for existing roads
(see [
5
,
27
]), if operating speeds are higher than the design speeds inferred based on their geometric
characteristics, a safety issue can be highlighted. In this study, this comparison was conducted for
both ROR crash curves and adjacent non-ROR crash curves, to reveal potential differences. Since the
direction of travel of the crashed vehicle is not known from the dataset, differences were searched
between the crash curves and the adjacent (previous/following) curves through averages.
It should be pointed out that Equation (5) is internationally used in the practice of road design.
However, both relationships
q=q(RC)
and
ft=ft(SD,C)
actually vary between countries (see [
28
]) as
well as the maximum values for cross slopes (e.g., 0.07 for Italy [
29
], 0.08 for the United States [
30
],
and 0.10 in local Australian guidelines [
31
]). Since the curves on Italian two-way two-lane national
road network were analyzed in this study, those relationships were developed according to the Italian
standards [29] for the relevant road type, and are reported as follows:
Infrastructures 2020, 5, x FOR PEER REVIEW 6 of 25
direction of travel of the crashed vehicle is not known from the dataset, differences were searched
between the crash curves and the adjacent (previous/following) curves through averages.
It should be pointed out that Equation (5) is internationally used in the practice of road design.
However, both relationships 𝑞= 𝑞(𝑅) and 𝑓=𝑓
𝑆, actually vary between countries (see [28])
as well as the maximum values for cross slopes (e.g., 0.07 for Italy [29], 0.08 for the United States [30],
and 0.10 in local Australian guidelines [31]). Since the curves on Italian two-way two-lane national
road network were analyzed in this study, those relationships were developed according to the
Italian standards [29] for the relevant road type, and are reported as follows:
𝑖𝑓 𝑅, ≤ 𝑅, → 𝑞 = 𝑞 =0.070 (6)
𝑞𝑅, 𝑖𝑓 𝑅, <𝑅, < 𝑅, → 𝑞 = 𝑞 (𝑅
𝑅,)(
/,
,) (7)
𝑖𝑓 𝑅, ≥ 𝑅, → 𝑞 = 𝑞 =0.025 (8)
𝑓
(𝑆,)=𝑘 𝑆,−𝑘 𝑆, +𝑘 (9)
where
𝑅,,𝑞𝑅,,𝑆, has been previously defined with the inferred 𝑆, computed according to
Equation (5). Note that for new projects, the design speed of all of the road layout elements should
be included between 60 km/h and 100 km/h, according to the reference Italian standards [29], but this
was not considered since design speeds were here inferred for existing roads;
𝑅, = minimum radius for which the minimum cross slope 𝑞 is implemented;
𝑅, = maximum radius for which the maximum cross slope 𝑞 is implemented;
𝑘,𝑘,𝑘 = coefficients of the regression curve obtained based on the values suggested: (a) in the
Italian standards in case of wet pavements, (b) in [27,32] in the case of dry pavements. (c) In the case
of icy pavements, 𝑓 was assumed to be constant in the range of possible values: 𝑘 = 𝑘 = 0, 𝑘 =
0.10 (see e.g., [33]). Note that dry and icy coefficients are not mentioned in the Italian standards [29]
and so they were otherwise determined.
The application of Equations from (6) to (9) to Equation (5) provides the following Equation (10):
𝑆,1
127𝑅, −𝑘+𝑘 𝑆, −𝑞𝑅,+ 𝑘=0 (10)
where all the terms have been previously defined. The solution of Equation (10) provides the inferred
design speed 𝑆, for a given radius of curvature according to the values imput for the triad of
coefficients 𝑘,𝑘,𝑘, previously defined for dry, wet, and icy conditions, respectively. The crash
dataset analyzed included information on the pavement conditions at the moment of the crash (i.e.,
dry, wet, or icy). Hence, it was possible to compute a design speed value for each pavement condition
at each crash site where relevant (e.g., using wet coefficients in case of crashes on wet pavements at
a given site).
2.3.3. Acceleration Rates
The inferred operating speeds were also used to compute acceleration/deceleration rates in
approaching/departing from curves for the curves at which ROR FI crashes occurred. Instead of
relying on single constant values, acceleration/deceleration rates were computed based on local
acceleration models such as in the case of operating speeds. In this case, experimental models
retrieved in [24] were selected from the review of acceleration models included in [26], which relate
the acceleration/deceleration rates [m/s2] (namely AR and DR) to the radius of curvature 𝑅, [m]:
𝐴
𝑅,𝑖=1.328−0.159ln𝑅, (11)
𝐷𝑅,𝑖=1.757−0.222ln𝑅, (12)
ft(SD,C)=k1SD,C2−k2SD,C+k3(9)
where
RC,i
,
q(RC,i)
,
SD,Ci
has been previously defined with the inferred
SD,Ci
computed according to
Equation (5). Note that for new projects, the design speed of all of the road layout elements should be
included between 60 km/h and 100 km/h, according to the reference Italian standards [
29
], but this was
not considered since design speeds were here inferred for existing roads;
Rq,min =minimum radius for which the minimum cross slope qmin is implemented;
Rq,max =maximum radius for which the maximum cross slope qmax is implemented;
k1
,
k2
,
k3
=coefficients of the regression curve obtained based on the values suggested: (a) in the
Italian standards in case of wet pavements, (b) in [
27
,
32
] in the case of dry pavements. (c) In the case of
icy pavements,
ft
was assumed to be constant in the range of possible values:
k1
=
k2
=0,
k3
=0.10 (see
e.g., [
33
]). Note that dry and icy coefficients are not mentioned in the Italian standards [
29
] and so they
were otherwise determined.
The application of Equations from (6) to (9) to Equation (5) provides the following Equation (10):
SD,Ci2 1
127RC,i
−k1!+k2SD,Ci −(q(RC,i)+k3)=0 (10)
where all the terms have been previously defined. The solution of Equation (10) provides the inferred
design speed
SD,Ci
for a given radius of curvature according to the values imput for the triad of
coefficients
k1
,
k2
,
k3
, previously defined for dry, wet, and icy conditions, respectively. The crash
dataset analyzed included information on the pavement conditions at the moment of the crash (i.e.,
dry, wet, or icy). Hence, it was possible to compute a design speed value for each pavement condition
at each crash site where relevant (e.g., using wet coefficients in case of crashes on wet pavements at a
given site).
Infrastructures 2020,5, 3 7 of 25
2.3.3. Acceleration Rates
The inferred operating speeds were also used to compute acceleration/deceleration rates in
approaching/departing from curves for the curves at which ROR FI crashes occurred. Instead of
relying on single constant values, acceleration/deceleration rates were computed based on local
acceleration models such as in the case of operating speeds. In this case, experimental models
retrieved in [
24
] were selected from the review of acceleration models included in [
26
], which relate
the acceleration/deceleration rates [m/s2] (namely AR and DR) to the radius of curvature RC,i[m]:
AR,i=1.328 −0.159 ln RC,i(11)
DR,i=1.757 −0.222 ln RC,i(12)
Based on the accelerations/decelerations inferred from the above defined equations for each
curve, it is possible to compute the necessary lengths for the acceleration/deceleration to occur, in
other words, for accelerating after the curve (to the following tangent speed based on Equation (4)) or
decelerating before it (starting from the previous tangent speed, Equation (4)). In some cases, it could
also be possible (e.g., in the case of short tangents included between a sharp and a larger radius of
curvature) that the previous tangent speed is lower than the inferred following curve speed. In this
case, an acceleration is likely to occur before the curve, rather than a deceleration.
The acceleration/deceleration lengths can be easily computed as follows:
L,a=0.077 (S2
0−S2
1)
±2a(13)
where
L,a =length of acceleration/deceleration [m];
S0=initial speed [km/h];
S1=final speed [km/h];
a=acceleration (AR, computed from Equation (11)) or deceleration (DR, computed from
Equation (12)) [m/s2], in the case of deceleration, the minus sign is considered.
Based on the computed lengths through Equation (13), three cases can occur (see Figure 2):
1.
The tangent before the crash curve C can include both the previous curve-to-tangent acceleration
length and the tangent-to-curve C acceleration/deceleration length;
2.
The tangent before the curve C is not long enough to include both the previous curve-to-tangent
acceleration length and the tangent-to-curve C acceleration/deceleration length; and
3.
The tangent before the curve C is so short that it cannot even include the tangent-to-curve C
acceleration/deceleration length.
Infrastructures 2020, 5, x FOR PEER REVIEW 7 of 25
Based on the accelerations/decelerations inferred from the above defined equations for each
curve, it is possible to compute the necessary lengths for the acceleration/deceleration to occur, in
other words, for accelerating after the curve (to the following tangent speed based on Equation (4))
or decelerating before it (starting from the previous tangent speed, Equation (4)). In some cases, it
could also be possible (e.g., in the case of short tangents included between a sharp and a larger radius
of curvature) that the previous tangent speed is lower than the inferred following curve speed. In this
case, an acceleration is likely to occur before the curve, rather than a deceleration.
The acceleration/deceleration lengths can be easily computed as follows:
𝐿,𝑎 = 0.077 (𝑆
−𝑆
)
±2 𝑎 (13)
where
L,a = length of acceleration/deceleration [m];
𝑆= initial speed [km/h];
𝑆= final speed [km/h];
a = acceleration (AR, computed from Equation (11)) or deceleration (DR, computed from
Equation (12)) [m/s2], in the case of deceleration, the minus sign is considered.
Based on the computed lengths through Equation (13), three cases can occur (see Figure 2):
1. The tangent before the crash curve C can include both the previous curve-to-tangent acceleration
length and the tangent-to-curve C acceleration/deceleration length;
2. The tangent before the curve C is not long enough to include both the previous curve-to-tangent
acceleration length and the tangent-to-curve C acceleration/deceleration length; and
3. The tangent before the curve C is so short that it cannot even include the tangent-to-curve C
acceleration/deceleration length.
Figure 2. Three cases considered for acceleration/deceleration depending on the road horizontal
alignment and related speed measures.
In both cases 1 and 2, the assumptions about the acceleration/deceleration rates computed
through Equation (11) and (12) are reasonable: there is enough space for the driver to
accelerate/decelerate through these rates. However, in the second case, since there is not enough
space on the included tangent for two acceleration/deceleration phases (from the previous curve to
the tangent, and from the tangent to the curve C), a single acceleration/deceleration phase is
considered, depending on the difference between the subsequent curve speeds (Figure 2). In the case
of curve C with a speed less than the previous curve speed, a single deceleration phase (DR
depending on curve C, Equation (12)) is considered. In the opposite case, a single acceleration phase
is considered (AR depending on curve C-1, Equation (11)).
In the third case instead, assuming the computed AR/DR (Equation (11) and (12)) as a reference
is misleading, since an adequate tangent length is not available (assuming constant speeds in curves).
Only in this case, the corrected actual AR/DR are computed by inverting Equation (13), as follows:
±𝑎 = 0.077 (𝑆
−𝑆
)
2 𝐿 (14)
where all the terms were previously defined (in this case, the initial speed is the previous curve speed,
the final speed is the curve C speed, and the length LT is the tangent length).
Figure 2.
Three cases considered for acceleration/deceleration depending on the road horizontal
alignment and related speed measures.
In both cases 1 and 2, the assumptions about the acceleration/deceleration rates computed through
Equations (11) and (12) are reasonable: there is enough space for the driver to accelerate/decelerate
Infrastructures 2020,5, 3 8 of 25
through these rates. However, in the second case, since there is not enough space on the included
tangent for two acceleration/deceleration phases (from the previous curve to the tangent, and from
the tangent to the curve C), a single acceleration/deceleration phase is considered, depending on the
difference between the subsequent curve speeds (Figure 2). In the case of curve C with a speed less
than the previous curve speed, a single deceleration phase (DR depending on curve C, Equation (12))
is considered. In the opposite case, a single acceleration phase is considered (AR depending on curve
C-1, Equation (11)).
In the third case instead, assuming the computed AR/DR (Equations (11) and (12)) as a reference
is misleading, since an adequate tangent length is not available (assuming constant speeds in curves).
Only in this case, the corrected actual AR/DR are computed by inverting Equation (13), as follows:
±a=0.077 (S2
C−1−S2
C)
2LT
(14)
where all the terms were previously defined (in this case, the initial speed is the previous curve speed,
the final speed is the curve C speed, and the length LTis the tangent length).
Note that the acceleration/deceleration rates and the related relationships are independently
computed for both directions of travel for the sake of obtaining a complete portrait of
acceleration/deceleration behaviors at curves. This means that the three cases depicted in Figure 2
were taken into account for both directions of travel.
2.4. Safety Measures of Selected Road Sites
Finally, safety indicators were computed for the curves included in the selected road sites.
The selected indicators were two crash modification factors (CMFs) for horizontal curves on two-way
two-lane rural roads: the first included in the Highway Safety Manual (HSM) [
19
] (based on [
34
]),
considering the absence of spiral transition curves in Equation (15), and the second provided in [
12
]
(adapted from the original source in Equation (16), considering the presence of curves and the CCR
measure). These can be reported as follows:
CMF,i(HSM)=1+80.2
1.55 ∗RC,i[f t]∗LC,i[mi]=1+25380.9
RC,i[m]∗LC,i[m](15)
CMF,i(Gooch et al. 2016)=exp(0.053 +0.001479 CCR)(16)
where all the terms have been previously defined.
The computation of the CMF for both curves with ROR FI crashes and adjacent curves with no
ROR FI crashes was performed in order to reveal significant differences.
3. Results and Discussion
Results obtained from the analysis are reported and discussed as follows, according to the
main research questions posed in the introduction. The typical features of ROR crashes occurring at
curves of two-way two-lane rural roads segments and the recurrent road geometric and operational
characteristics of these ROR FI highly-prone segments are shown. The way in which these aspects
could be useful from a road safety management perspective will also be discussed.
3.1. Typical Features of Run-Off-Road Fatal+Injury Crashes
On the curved road sites identified, 69 ROR FI crashes occurred during the observation period
(2.3 ROR FI crash/curve, maximum: 5, minimum: 2). Those crashes resulted in 85 injuries (1.23 per
crash, 2.83 per curve), and four deaths (0.06 per crash, 0.13 per curve). Moreover, an additional six
ROR FI crashes recorded at curves adjacent to the crash C curves were included in the study segments.
Infrastructures 2020,5, 3 9 of 25
The typical features of the ROR FI crashes that occurred at the road curves analyzed are reported
in Table 1, with specific regard to the period of the day, the pavement conditions, the vehicle involved
in the crash, the main reported contributory factor reported, and the driver age.
Table 1.
Run-Off-Road Fatal+Injury specific crash features at the selected two-way two-lane rural road
curves with statistics averaged over the total crashes (69) and total curve sites (30).
Crash Features Classes of the Crash Features
Period of the day Morning Afternoon Evening Night
Per crash 21 (0.30) 34 (0.49) 6 (0.09) 8 (0.12)
Per curve site
(most frequent class per site) 13 (0.10) 10 (0.33) 0 (0.00) 3 (0.10)
(most frequent together with others) 214 (0.47) 21 (0.7) 4 (0.13) 5 (0.17)
Pavement conditions Dry Wet Icy
Per crash 29 (0.42) 38 (0.55) 2 (0.03)
Per curve site
(most frequent class per site) 19 (0.30) 12 (0.40) 0 (0.00)
(most frequent together with others) 217 (0.57) 20 (0.67) 2 (0.07)
Vehicle Auto Motorcycle Heavy vehicle
Per crash 47 (0.68) 14 (0.20) 8 (0.12)
Per curve site
(most frequent class per site) 116 (0.53) 4 (0.13) 1 (0.03)
(most frequent together with others) 225 (0.83) 8 (0.27) 6 (0.20)
Contributory factor Speeding Distraction Avoiding strike Missing
Per crash 29 (0.42) 29 (0.42) 5 (0.07) 6 (0.09)
Per curve site
(most frequent class per site) 18 (0.27) 8 (0.27) 2 (0.07) 0 (0.00)
(most frequent together with others) 215 (0.50) 20 (0.67) 3 (0.10) 4 (0.13)
Driver age Young:
18–29
Adult:
30–64 Over 65 Missing
Per crash 15 (0.22) 46 (0.67) 7 (0.10) 1 (0.01)
Per curve site
(most frequent class per site) 12 (0.50) 14 (0.67) 0 (0.10) 0 (0.00)
(most frequent together with others) 210 (0.33) 28 (0.93) 5 (0.17) 1 (0.03)
1
Quantifies in how many curves the specific class of the crash feature was the most frequent by also presenting
the percentage over all curves (e.g., in three sites out of 30 (10% of sites), morning crashes were the most frequent).
2
Quantifies in how many curves the specific class of the crash feature was the most frequent together with the
others (i.e., the most frequent feature shared between two or more classes given the small amount of data) by also
presenting the relative percentage over all curves (e.g., in 14 sites out of 30 (47% of sites), morning crashes were the
most frequent or the most frequent together with other periods such as evening/night).
Some useful indications can be argued from the data in Table 1. In 14 out of 69 ROR FI curve
crashes, the crash occurred during the evenings or nights (21% of all crashes). It is worth noting that at
three sites, night crashes were the most frequent (up to five sites if they are considered the most frequent
together with other periods). At four sites, evening crashes were the most frequent (together with other
periods). This means that at nine sites (30% of all sites), lighting systems could be a serious issue (lack
of visibility has been previously linked to these types of crashes [
35
]), since most evening/night crashes
occur at these curves. The percentage of evening/night crashes (21%) was less than the percentage
(36%) computed for all traffic crashes that occurred in Italy on all roads (i.e., in 2017, as a benchmark
sample). This could be related to the typical features of the investigated segments, which were far
from densely populated urban centers with a likelihood of scarce traffic in the evening/night hours.
As expected, most of the ROR FI crashes analyzed occurred in wet pavement conditions. This
was the most frequent condition (in some cases shared with other conditions) in 20 sites out of 30.
Infrastructures 2020,5, 3 10 of 25
However, this means that several crashes also occurred during dry conditions. The icy pavement
condition was very rare (only two crashes out of 69). The percentage of wet pavement crashes (55%)
was disproportionate with respect to the benchmark dataset for all crashes, where it was only 13%.
This was expected and is coherent with previous research [
35
,
36
], given that loss of friction is more
likely on wet pavements.
A significant number of ROR FI curve crashes involved motorcyclists. Considering that most
of the investigated segments are far from densely populated urban settlements, motorcycle crashes
should be even more highlighted (and is actually a well-known issue, see [
37
]). Moreover, at eight
sites, motorcycle ROR FI crashes were the most frequent (together with other vehicles). However,
the percentage of motorcycle crashes (20%) was not disproportionate with respect to the benchmark
dataset for all crashes (15%). Conversely, there were few crashes with heavy vehicles involved (about
10%), while in other contexts, this was raised as a more urgent problem [38].
Data on contributory factors are considerably important in understanding the crash dynamics,
even if they are essentially based on police reports, and in some cases are subjective and/or may be
biased. Aside from the “speeding” contributory factor, which was overwhelmingly expected (see [
39
]
or [
36
] for fatal crashes), the “distraction” factor was also revealed to be important (42% of crashes, the
same as speeding crashes). Clearly, defining if the driver was distracted immediately before the crash
is a hard task, even based on police reports. However, this is an interesting aspect that is consistent
with previous research [
35
], which will be addressed in more detail. It is paramount that even for
distracted drivers, speed could have been a crucial factor: when the curve is noticed, a low speed
could have helped in the case of very delayed steering maneuvers, while high speeds could have been
detrimental. In this case, it is difficult to make comparisons with the benchmark dataset for all crashes,
since the number and the nature of contributory factors may vary in the official statistics by ISTAT [
7
],
according to the crash type. However, note that the percentages for the “distraction” contributory
factor and the “speeding/not complying with limits” contributory factor accounted for only 10% and
14% in the benchmark dataset for all crashes, respectively.
Concerning the driver age, there are no particular results to highlight being that the “adult”
(30–64 years old) class was the most involved in these crashes. Nevertheless, the number of young
drivers involved was noticeable, with 22% of crashes involving drivers aged 18–30. However, this
percentage is strictly in line with that estimated from the benchmark dataset for all crashes. Moreover,
the small dataset does not allow for investigation into combinations of these factors, but previous
research has shown that the ages of different drivers may also be associated with different risk factors
for ROR crashes [15].
3.2. Typical Features of Road Segments Including Curves with Notable History of ROR FI Crashes
In this section, the results obtained from the investigation of typical features of segments including
curves with a notable history of ROR FI crashes are presented and discussed. The presentation is divided
according to the different characteristics investigated: geometric, operational, and safety-related.
3.2.1. Geometric Characteristics
General results.
The 30 road segments analyzed, which included the ROR FI crash-prone curves,
were on average 562.9 m long (st. dev. =461.3 m, max. =1846.0 m, min. =175.0 m). A synthetic
average measure of their curvature was obtained through the overall CCR (curvature change ratio)
of the segment: 380.1 gon/km (st. dev. =285.9 gon/km, max. =1250.0 gon/km, min. =39.6 gon/km).
These two measures show a high variability within the sample of segments analyzed: on average, they
include three curves in about 600 m, but the standard deviation was not negligible: some segments
were extremely short (down to 175 m), while others were very long (up to about 2 km). This means that
the possible influence of the lengths of tangents included between the curves on speeds (see [
27
]) is
extremely variable within the segments. A very broad variation of the curvature can also be appreciated:
Infrastructures 2020,5, 3 11 of 25
some segments had a negligible curvature compared to their length (down to about 40 gon/km), while
for others, the CCR was noticeable (up to about 1300 gon/km).
Hence, further investigations are needed to highlight some common features, besides those used
in preliminary measures. More detailed information about geometric features are reported in Table 2.
Synthetic measures were computed for the crash curve C (see Figure 1), which included other geometric
information about the analyzed segment (tangents, previous and following curves).
Table 2.
Descriptive statistics of the geometric features of ROR FI curved crash sites (each statistic is
computed over the total number of curve sites: 30).
Crash Curve Geometric Features Descriptive Statistics
Mean St. Dev. Maximum Minimum
Radius of curvature Rc [m] 112.3 86.9 364.0 26.0
Length of the curve Lc [m] 93.7 79.3 302.0 24.0
CCR ratio–curve C [gon/km] 924.6 607.2 2448.5 174.9
Length of adjacent tangent 1[m] 151.7 212.3 1193.0 9.0
Curve road width [m] 7.5 1.2 9.5 4.5
Curve average longitudinal slope [%] 4.0 2.8 12.0 0.0
Mean radius of adjacent curves 1[m] 190.9 160.3 814.0 26.0
Mean length of adjacent curves 1[m] 82.9 63.3 299.0 7.0
CCR ratio—adjacent curves 1[gon/km] 618.5 534.8 2448.5 78.2
1
Statistics for adjacent curves refer to the average between the following and previous curves to curve C (i.e., curves
C-1 and C+1 in Figure 1).
As expected, the average radius of the curvature of the crash curves was sharp (about 110 m on
average) and the related standard deviation was relatively small (with a maximum radius of 364 m).
This means that there were no large curves (e.g., with a radius >400 m) in the analyzed sample of the
ROR FI crash-prone curves. A similar tendency was noted for the crash curve lengths: on average,
curves were only about 100 m long. On the other hand, there was high variability in the average length
of the previous/following tangents of about 150 m long, with a standard deviation greater than the
mean. Note that the minimum average tangent is about 10 m long (practically negligible, i.e., the
tangent could have no effect on speeds, which are mainly governed by the subsequent curves), while
the maximum average tangent is more than 1 km long (high speeds can be reached on tangents before
curves). The crash curve width is in line with standard measures for two-way two-lane rural roads.
However, curve enlargements may be needed for different reasons (i.e., for visibility reasons or to
avoid dangerous encroachments of heavy vehicles). Hence, it seems that in several cases (given an
average curve width of 7.5 m), enlargements were not present. Note that there were also cases of crash
curves on narrow roads (down to 4.5 m). Moreover, it is important to note that most crash curves are
on a notably steep longitudinal slope (average of 4%, up to 12%). This could clearly have affected the
vehicle dynamics while approaching curves (i.e., while braking in downhill sections).
Furthermore, the measures computed by taking into account the geometric features of adjacent
elements provide some additional insights. In detail, the mean radius of adjacent curves was
significantly greater than the crash curve radius (about 190 m, with respect to about 110 m).
The computed average ratio of the crash curve radius to the average previous/following curve
radii was 0.78 (st. dev. =0.56). However, the mean length of adjacent curves (about 80 m) was
comparable with the mean length of the crash curves (about 90 m). The average CCR computed for
the adjacent curves was significantly higher than the average crash curve CCR. Considering both the
above reported comparisons for the curve radii and lengths, this noticeable difference in the CCR
values can be mostly attributed to largely different radii.
In-depth analysis.
The qualitatively identified differences between the radii and lengths of the
crash curves with respect to adjacent curves on which, on the contrary, no ROR FI crashes have occurred
were tested by means of statistical tools. Given that the distributions of both curve radii and lengths do
Infrastructures 2020,5, 3 12 of 25
not evidently follow normal distributions, non-parametric tests were conducted. Moreover, the crash
curve and the adjacent curves (both the populations of previous and following curves) belong to the
same segment. Hence, they were considered as paired measures, thus leading to the selection of the
non-parametric Friedman test. The differences between (a) the radii of curvature, and (b) the lengths
of the three populations of crash curves C, previous curves C-1, and following curves C+1 were tested.
Six adjacent curves to the analyzed crash curves C on which one ROR FI crash had occurred in the
observation period were discharged. In this way, differences between the ROR FI crash-prone curves
(more than two crashes in four years) and the no-ROR FI crash curves can be captured.
As a result of the tests, there was a statistically significant difference at the 5% significance level in
the radius of curvature depending on the curve type (crash/previous/following curve),
χ
2(2) =10.126,
p=0.006 (see boxplots in Figure 3). Post-hoc analysis with the Nemenyi test revealed that, as expected,
the only statistically significant differences were between curves C/C-1 and C/C+1, and not between
curves C-1/C+1. In fact, the boxplots in Figure 3evidently show that the radius of the curvature
of the adjacent curves was higher, on average, than the radius of the curvature of the crash curve.
Instead, there was no statistically significant difference in the curve length depending on the curve
type (crash/previous/following curve), χ2(2) =0.083, p=0.959.
Infrastructures 2020, 5, x FOR PEER REVIEW 12 of 25
radius of the curvature of the road section). Moreover, the homogeneity of the subsequent curve radii
is a recommendation/prescription included in several guidelines/standards worldwide [23]. Hence,
this result shed additional light on the importance of consistency between adjacent road curves. The
opposite trend is also known from previous research: when a curve is included between sharper
adjacent curves, its safety performance improves [11,12]. In this study, the lack of consistency was
specifically linked to the ROR FI crash frequency occurrence (at least two ROR FI crashes in four years
of observation). Hence, it can surely be used as an indicator while conducting a road safety audit or
when planning inspections [20], specifically in case of a dedicated safety campaign (e.g., [41]). On the
other hand, among other characteristics, it seems that the relationship between the length of adjacent
curves and the length of the crash curve is not influential. In practice, the curve minimum length can
be set as a function of its speed (and then its radius) [29], but without specifying the relationship
between subsequent curve lengths. In this case, if the radii are consistently designed, then the lengths
will also be consistently designed as a consequence. Moreover, when checked against Italian
requirements [29] for minimum curve lengths (which can be traveled in at least 2.5 s), only two crash
curves out of 30 did not meet the minimum requirements. Hence, this can be considered as a minor
issue.
Figure 3. Boxplots of the distribution of the radius of curvature values for the three types of curves
(previous C-1, crash C, and following C+1 curves).
Link between geometric and crash features. As previously discussed, the unexpected nature of
the curve (i.e., with a significantly sharper radius) can lead to sudden maneuvers with undesired
outcomes. Clearly, this process can be further hampered if the driver is distracted or in the case of
non-optimal visibility conditions. Given the available data, some further analyses were conducted to
investigate this aspect in detail. In fact, the number of crash sites in which (a) most crashes had
distraction as a main contributory factor, and (b) the most crashes that occurred during evening/night
have been previously defined (see Table 1 for the case of the most frequent together with other
factors). Binary logistic regression was used to establish if the average ratio between the crash curve
and the average adjacent curves radii could predict: (a) the likelihood of being a “distraction” crash
site versus a “non-distraction” crash site, and (b) the likelihood of being a “evening/night” crash site
versus a “morning/afternoon” crash site.
As a result of the binary logistic regression, an increase in the percentage ratio (crash curve to
adjacent curves radius) was associated with a decreased likelihood (odds ratio = 0.983, p = 0.097) at
Figure 3.
Boxplots of the distribution of the radius of curvature values for the three types of curves
(previous C-1, crash C, and following C+1 curves).
Results from the statistical tests suggest that a significantly different radius of the crash curve
with respect to the adjacent curves could have fostered the crash to occur at that specific curve. This
was expected from previous research on road design consistency (see [
40
], with respect to the average
radius of the curvature of the road section). Moreover, the homogeneity of the subsequent curve radii
is a recommendation/prescription included in several guidelines/standards worldwide [
23
]. Hence,
this result shed additional light on the importance of consistency between adjacent road curves.
The opposite trend is also known from previous research: when a curve is included between sharper
adjacent curves, its safety performance improves [
11
,
12
]. In this study, the lack of consistency was
specifically linked to the ROR FI crash frequency occurrence (at least two ROR FI crashes in four years
of observation). Hence, it can surely be used as an indicator while conducting a road safety audit or
when planning inspections [
20
], specifically in case of a dedicated safety campaign (e.g., [
41
]). On the
Infrastructures 2020,5, 3 13 of 25
other hand, among other characteristics, it seems that the relationship between the length of adjacent
curves and the length of the crash curve is not influential. In practice, the curve minimum length can be
set as a function of its speed (and then its radius) [
29
], but without specifying the relationship between
subsequent curve lengths. In this case, if the radii are consistently designed, then the lengths will also
be consistently designed as a consequence. Moreover, when checked against Italian requirements [
29
]
for minimum curve lengths (which can be traveled in at least 2.5 s), only two crash curves out of 30 did
not meet the minimum requirements. Hence, this can be considered as a minor issue.
Link between geometric and crash features.
As previously discussed, the unexpected nature
of the curve (i.e., with a significantly sharper radius) can lead to sudden maneuvers with undesired
outcomes. Clearly, this process can be further hampered if the driver is distracted or in the case of
non-optimal visibility conditions. Given the available data, some further analyses were conducted
to investigate this aspect in detail. In fact, the number of crash sites in which (a) most crashes had
distraction as a main contributory factor, and (b) the most crashes that occurred during evening/night
have been previously defined (see Table 1for the case of the most frequent together with other factors).
Binary logistic regression was used to establish if the average ratio between the crash curve and the
average adjacent curves radii could predict: (a) the likelihood of being a “distraction” crash site versus
a “non-distraction” crash site, and (b) the likelihood of being a “evening/night” crash site versus a
“morning/afternoon” crash site.
As a result of the binary logistic regression, an increase in the percentage ratio (crash curve to
adjacent curves radius) was associated with a decreased likelihood (odds ratio =0.983, p=0.097) at the
10% significance level of being a site with the most crashes with distraction as a contributory factor.
This is highlighted in the boxplots of the ratios of crash curve radii to adjacent radii in Figure 4for both
the “distraction” and “not distraction” crash sites. This result means that, the greater the difference
between the crash curve radius and the adjacent curve radii, the more the crash site will be related
to “distraction” contributory factors. Distracted drivers, who are driving in an almost unconscious
state (see [
42
]), may be even more surprised than other drivers by an inconsistent radius of curvature
with respect to previous curves to which they are used to. This may occur even if distracted drivers
are more prone to adapt their speeds at sharp curves (i.e., lower speeds) when compared to other
drivers [
43
]. This finding confirms the crucial relationship between road design consistency and road
safety [
23
,
41
,
44
], and the importance of criteria for ensuring geometric design consistency (see [
45
,
46
]).
Infrastructures 2020, 5, x FOR PEER REVIEW 13 of 25
the 10% significance level of being a site with the most crashes with distraction as a contributory
factor. This is highlighted in the boxplots of the ratios of crash curve radii to adjacent radii in Figure
4 for both the “distraction” and “not distraction” crash sites. This result means that, the greater the
difference between the crash curve radius and the adjacent curve radii, the more the crash site will
be related to “distraction” contributory factors. Distracted drivers, who are driving in an almost
unconscious state (see [42]), may be even more surprised than other drivers by an inconsistent radius
of curvature with respect to previous curves to which they are used to. This may occur even if
distracted drivers are more prone to adapt their speeds at sharp curves (i.e., lower speeds) when
compared to other drivers [43]. This finding confirms the crucial relationship between road design
consistency and road safety [23,41,44], and the importance of criteria for ensuring geometric design
consistency (see [45,46]).
Instead, no statistically significant relationships were found between the curve ratios for
evening/night crashes versus morning/afternoon crashes. This means that, even if there is a
significant percentage of evening/night crashes, which may indicate visibility issues (fostering ROR
crashes, see [35]), the effect of inconsistent curve radii with respect to the adjacent ones is not affected
by the day/night condition.
Figure 4. Boxplots of the distribution of crash curve radius to the radius of the adjacent curves’
average ratios for sites with the most crashes linked and not linked to distraction.
3.2.2. Operational Characteristics
General results. Design and operating speeds were inferred for the 30 curves in the analyzed
segments. The results are reported in Table 3 in terms of: (a) the maximum design speeds for both
crash curve C and the average adjacent curves (in dry, wet, and icy conditions), (b) the difference
between the 85th operating and maximum design speeds for both the crash curve and the average
adjacent curves; and (c) the acceleration/deceleration rates in approaching the crash curve C.
Consistently with the results concerning geometric features, the inferred maximum design
speeds for the curve C were lower, on average, than the speeds computed for the adjacent curves. In
fact, this basically depends on the different average radius across the two categories of curves. The
average maximum design speed at crash curves was 65.5 km/h (st. dev. = 20.2 km/h) in dry conditions
and 54.3 km/h (st. dev. = 15.6 km/h) in wet conditions. This means that the equilibrium requirements
(Equation (5)) are theoretically met if those speeds are not exceeded in the respective pavement
condition (dry/wet). However, if ROR crashes occurred at those curves, then it is likely that those
speeds were actually exceeded. There are some cases in which the inferred maximum design speed
Figure 4.
Boxplots of the distribution of crash curve radius to the radius of the adjacent curves’ average
ratios for sites with the most crashes linked and not linked to distraction.
Infrastructures 2020,5, 3 14 of 25
Instead, no statistically significant relationships were found between the curve ratios for
evening/night crashes versus morning/afternoon crashes. This means that, even if there is a significant
percentage of evening/night crashes, which may indicate visibility issues (fostering ROR crashes,
see [
35
]), the effect of inconsistent curve radii with respect to the adjacent ones is not affected by the
day/night condition.
3.2.2. Operational Characteristics
General results.
Design and operating speeds were inferred for the 30 curves in the analyzed
segments. The results are reported in Table 3in terms of: (a) the maximum design speeds for both
crash curve C and the average adjacent curves (in dry, wet, and icy conditions), (b) the difference
between the 85
th
operating and maximum design speeds for both the crash curve and the average
adjacent curves; and (c) the acceleration/deceleration rates in approaching the crash curve C.
Table 3.
Descriptive statistics of the operational features of ROR FI curved crash sites (each statistic
was computed over the total number of curve sites that met the specific requirements considered).
Curve Operational Features Descriptive Statistics
Mean St. Dev. Max. Min.
Dry inferred maximum design speed—curve C [km/h] 165.5 20.2 104.6 38.2
Wet inferred maximum design speed—curve C [km/h] 254.3 15.6 89.1 33.4
Icy inferred maximum design speed—curve C [km/h] 344.4 20.1 58.6 30.1
Dry inferred max. design speed—adjacent curves 4[km/h]177.5 23.8 135.4 39.4
Wet inferred max. design speed—adjacent curves 4[km/h]265.0 19.2 110.7 31.4
Icy inferred max. design speed—adjacent curves 4[km/h]353.8 22.0 85.0 33.8
Dry 85th—max. design speed difference: curve C [km/h]1−3.5 7.2 2.4 −21.9
Wet 85th—max. design speed difference: curve C [km/h] 27.9 4.5 11.7 −6.5
Icy 85th—max. design speed difference: curve C [km/h] 316.0 1.8 17.2 14.7
Dry 85th—max. design speed diff.: adjacent curves 4[km/h] 1−8.0 12.1 2.4 −46.8
Wet 85th—max. design speed diff.: adjacent curves 4[km/h] 24.5 8.2 11.7 −22.0
Icy 85th—max. design speed diff.: adjacent curves 4[km/h] 313.6 11.2 20.0 −3.2
Deceleration in approaching curve C—both directions [m/s2]5−1.6 2.0 -0.4 −9.7
Acceleration in approaching curve C—both directions [m/s2]62.2 - - -
Discordant deceleration/acceleration in approaching curve C in
the two different directions [m/s2]70.3 2.4 2.4 −2.0
1,2,3
Design/85
th
speed inferred for curves at which at least one crash occurred in (1) dry conditions (21 sites), (2) wet
conditions (21 sites), and icy conditions (two sites).
4
Statistics for adjacent curves refer to the average between
the curves following and preceding curve C.
5
In this case, there is deceleration in approaching to curve C in both
directions (20 segments out of 30).
6
In this case, there is acceleration in approaching to curve C in both directions
(one segment).
7
In this case, there is acceleration from one direction, and deceleration from the opposite direction
(nine segments).
Consistently with the results concerning geometric features, the inferred maximum design speeds
for the curve C were lower, on average, than the speeds computed for the adjacent curves. In fact, this
basically depends on the different average radius across the two categories of curves. The average
maximum design speed at crash curves was 65.5 km/h (st. dev. =20.2 km/h) in dry conditions and
54.3 km/h (st. dev. =15.6 km/h) in wet conditions. This means that the equilibrium requirements
(Equation (5)) are theoretically met if those speeds are not exceeded in the respective pavement
condition (dry/wet). However, if ROR crashes occurred at those curves, then it is likely that those
speeds were actually exceeded. There are some cases in which the inferred maximum design speed was
very high and could not be clearly realistic (e.g., the max. dry speed =135.4 km/h). In these cases, it is
likely that some other aspects could have contributed to the crash besides that of only speeding (e.g.,
distraction, see Table 1). However, even if other factors were determinants, speed is still a crucial factor;
if adequate speeds were operated, then a recovery maneuver could have possibly led to avoiding the
Infrastructures 2020,5, 3 15 of 25
crash. While similar remarks are valid for icy conditions, this is not further discussed since they only
were found at two sites.
In dry conditions, the average inferred 85
th
operating speed was lower, but comparable (
−
3.5 km/h)
with the maximum design speed on the crash curve and even significantly lower (
−
8.0 km/h) than the
maximum design speed on the adjacent curves. Clearly, according to the standard deviation values,
there were several cases in which the 85
th
operating speed was higher than the maximum design
speeds. However, in dry conditions, the inferred 85
th
operating speed values did not provide enough
clear evidence that the drivers’ speeds could have been higher than the maximum design speeds for
those curves, even if they were comparable. On the other hand, in wet conditions, the average inferred
85
th
operating speed was significantly higher (+7.9 km/h) than the maximum design speed on the
crash curve as well as on the adjacent curves (+4.5 km/h). Moreover, considering the values of the
standard deviations, in the case of crash curves, most of the operating speeds were consistently higher
than the inferred maximum design speeds. However, operating speed models are usually estimated
considering good weather conditions and are not applicable to the case of wet conditions, even if
previous research has shown that the difference can be not significant [
47
]. It is also important to note
that, if compared with a commonly used method for evaluating the safety of two-way two-lane rural
roads [
23
,
27
], a difference between the operating and design speed of less than 10 km/h (as found here,
on average) should not indicate safety issues.
The most interesting result concerns the deceleration rates. In most cases (20 segments out of
30), based on the operating speeds computed for the geometric elements of the analyzed segments,
a deceleration is likely to occur in approaching the crash curve from both directions. The average
deceleration rate was
−
1.6 m/s
2
(max. =
−
9.7 m/s
2
), which is higher than the average deceleration
rates closer or smaller than the
−
1 m/s
2
found in previous research (e.g., [
48
,
49
]) and considered in the
standards and guidelines (e.g., [29]). It should be pointed out that:
•
In eight cases, the length of the tangents included between the crash and adjacent curves were
sufficient for both acceleration from the previous curve and further deceleration to the considered
curve, with the AR/DR rates computed through Equations (11) and (12) (case 1, Figure 2).
•
In seven cases, both the previous and following tangent lengths were insufficient (based on
Equation (13) for a proper deceleration computed through Equation (12) to occur, and assumed
to possibly occur on tangents only (an experimentally verified usual condition [
48
]). In cases
of insufficient tangent length (case 3, Figure 2), the deceleration rate was computed through
Equation (14).
•
In all other cases, the length of tangents between the crash curve and the adjacent curves were not
sufficient for both acceleration from the previous curve and deceleration to the crash curve to
occur (case 2, Figure 2). Hence, in this case, only the deceleration from the previous curve was
computed (hypothesis of no acceleration).
These results indicate that, even more than the possible incorrect speed at curves (i.e., higher than
the maximum allowed), the sequence of curves implies severe decelerations that may have caused
skidding in approaching the curves. The increase in the average degree of variation of operating speeds
was actually related to an increase in the expected crash rate in previous research [
44
]. Moreover,
considering that wet conditions were the most frequent for crashes, the role of tire-wet pavement friction
in the case of hard braking could have been crucial. Conversely, previous research has shown the
positive effect of short tangents between subsequent curves on crashes on the following curve [
12
,
50
].
However, these tangents are not entirely comparable: the average distance between the curves in [
12
]
was about 300 m, while in this study, it was about half that (150 m). Hence, the issue pointed out in this
study is technically different: very short tangents included between curves having largely different
radii may be of particular concern for ROR FI crashes due to the severe decelerations implied.
In-depth analysis.
Statistical tests were also conducted for the operational features. In detail, speed
differentials (85
th
operating—maximum inferred design speed) at crash curves were compared with
Infrastructures 2020,5, 3 16 of 25
those at adjacent curves on which, in contrast, no crashes have occurred. Given that the distributions
of these speed differentials also do not evidently follow normal distributions, non-parametric tests
were conducted. Moreover, they were considered as paired measures (such as in the previous case of
geometric features), thus leading to the selection of the non-parametric Friedman test. The differences
between (a) the speed differentials (85
th
operating—maximum inferred design speed) in dry conditions
and (b) the speed differentials in wet conditions of the three populations of crash curves C, previous
curves C-1, and following curves C+1 were tested.
As a result of the tests, there was a statistically significant difference at the 10% significance level
in the speed differential in dry conditions depending on the curve type (crash/previous/following
curve),
χ
2(2) =5.943, p=0.051 (see boxplots in Figure 5). Post-hoc analysis with the Nemenyi test
revealed that, in this case, the only statistically significant differences were between crash curves C and
previous curves C-1. Instead, there was no statistically significant difference in the speed differential in
wet conditions depending on the curve type (crash/previous/following curve),
χ
2(2) =3.930, p=0.140.
Infrastructures 2020, 5, x FOR PEER REVIEW 16 of 25
the 85th operating speed at the crash curve is comparable with the maximum design speed at the same
curve, while it is significantly lower than the maximum design speed on adjacent curves. Hence,
drivers who are selecting speeds based on geometric characteristics of adjacent elements, with
enough safety margins in dry conditions (average margin of the 85th speed from the maximum
inferred design speed = −8.0 km/h) may continue to rely on their speed selection process even at the
crash curve, where the safety margin is significantly lower (on average = −3.5 km/h). This could be
crucial for the crash outcome if combined with other potential crash contributing factors (such as the
previously discussed distraction issue). The practical implication of this involves being more cautious
in interpreting the margins between the 85th and design speed (e.g., the <10 km/h margin indicated
as good design practice [23,27]) for the specific case of ROR FI crash-proneness.
In wet conditions, the populations of speed differentials were similar between the crash curve
and the adjacent curves, and average 85th operating speeds were consistently higher than the
maximum inferred design speeds. Hence, there were no particularly evident differences between the
crash curve and the adjacent curves, which may suggest that using this speed differential parameter
is influential in the crash occurrence at that specific curve. In fact, if aggressive drivers consistently
select speeds as suggested by the geometric characteristics, they would surely be in danger of ROR
crashes at all curves along the analyzed segment in wet conditions. Hence, on the crash curve, there
should be other contributory factors that may have fostered the crash to occur.
Figure 5. Boxplots of the distribution of speed differentials (operating 85th—maximum inferred design
speed) in dry conditions for the three populations (previous C-1, crash C, following C+1 curves).
3.2.3. Predicted Safety Characteristics
Crash modification factors (CMFs), which were chosen as indicators of the predicted safety
characteristics, were computed for both the crash curves and adjacent curves. These are synthetic
parameters that may express the crash risk of given curves, based on both their length and radius of
curvature (see Equations (15) and (16)). Descriptive statistics on their computed values are reported
in Table 4.
Table 4. Descriptive statistics of the predicted safety features of ROR FI curved crash sites (each
statistic was computed over the total number of curve sites (30)).
Crash curve Predicted Safety Characteristics Descriptive Statistics
Figure 5.
Boxplots of the distribution of speed differentials (operating 85
th
—maximum inferred design
speed) in dry conditions for the three populations (previous C-1, crash C, following C+1 curves).
Results from the statistical tests showed that there was a significant discrepancy in the speed
differential (85
th
operating—maximum inferred design speed) between the crash curves and adjacent
curves only in the dry condition. The previously discussed general results showed that, in general,
the speed differentials are greater on the crash curve than on the adjacent curves in both dry and wet
conditions. However, this difference seems noticeable only in the dry condition. This confirms that
the 85
th
operating speed at the crash curve is comparable with the maximum design speed at the
same curve, while it is significantly lower than the maximum design speed on adjacent curves. Hence,
drivers who are selecting speeds based on geometric characteristics of adjacent elements, with enough
safety margins in dry conditions (average margin of the 85
th
speed from the maximum inferred design
speed =
−
8.0 km/h) may continue to rely on their speed selection process even at the crash curve, where
the safety margin is significantly lower (on average =
−
3.5 km/h). This could be crucial for the crash
outcome if combined with other potential crash contributing factors (such as the previously discussed
distraction issue). The practical implication of this involves being more cautious in interpreting the
Infrastructures 2020,5, 3 17 of 25
margins between the 85
th
and design speed (e.g., the <10 km/h margin indicated as good design
practice [23,27]) for the specific case of ROR FI crash-proneness.
In wet conditions, the populations of speed differentials were similar between the crash curve and
the adjacent curves, and average 85
th
operating speeds were consistently higher than the maximum
inferred design speeds. Hence, there were no particularly evident differences between the crash curve
and the adjacent curves, which may suggest that using this speed differential parameter is influential
in the crash occurrence at that specific curve. In fact, if aggressive drivers consistently select speeds
as suggested by the geometric characteristics, they would surely be in danger of ROR crashes at all
curves along the analyzed segment in wet conditions. Hence, on the crash curve, there should be other
contributory factors that may have fostered the crash to occur.
3.2.3. Predicted Safety Characteristics
Crash modification factors (CMFs), which were chosen as indicators of the predicted safety
characteristics, were computed for both the crash curves and adjacent curves. These are synthetic
parameters that may express the crash risk of given curves, based on both their length and radius of
curvature (see Equations (15) and (16)). Descriptive statistics on their computed values are reported in
Table 4.
Table 4.
Descriptive statistics of the predicted safety features of ROR FI curved crash sites (each statistic
was computed over the total number of curve sites (30)).
Crash curve Predicted Safety Characteristics Descriptive Statistics
Mean St. Dev. Max Min.
Crash Modification Factor—curve C—Equation (15) [-] 8.6 7.8 36.3 1.2
Crash Modification Factor—adjacent curves 1—Equation (15) [-] 7.3 8.6 39.6 1.1
Crash Modification Factor—curve C—Equation (16) [-] 6.5 8.1 39.5 1.4
Crash Modification Factor—adjacent curves 1—Equation (16) [-] 4.3 6.8 39.5 1.2
1Statistics for the adjacent curves refer to the average between the following and previous curves to curve C.
It is possible to note that the CMFs for crash curve C were higher, on average, than the CMFs for
adjacent curves, especially in the case of the CMFs computed according to Equation (16), where they
were evidently larger. However, the standard deviation was high, suggesting an overlap of the two CMF
populations, especially for the Highway Safety Manual (HSM) CMF (Equation (15)). A Friedman test
conducted on the three populations of CMFs (curves C, C-1, C+1) revealed no statistically significant
differences for the HSM CMF (
χ
2(2) =0.083, p=0.959). The same test conducted on the other
CMF (Equation (16)) instead revealed statistically significant differences at the 5% significance level
(
χ
2(2) =10.564, p=0.005) with the Nemenyi post-hoc test indicating differences between curves C
and the following curves (5% significance level). In addition, in these tests, six adjacent curves on
which a ROR FI crash occurred were excluded to highlight the differences between high-risk curves
and no-crash curves.
First, both CMFs were for the total crashes. This means that, based on the high average CMF
values, most of the curves analyzed in this study (both crash and adjacent curves) could be at risk
of crashes (CMFs indicate the relative number of crashes compared to straight sections), but that
these crashes are not necessarily fatal +injury (FI) and/or ROR. Depending on the local statistics and
injury scales, the FI crashes are usually only a small percentage (i.e., around 17% including only severe
injuries in [
19
] for the same road category). This means that, based on CMFs, property-damage-only
crashes could have occurred even on the adjacent curves at which ROR FI crashes did not occur in
the same period. Moreover, CMFs were developed by using American data and the transferability of
CMFs to other countries is not straightforward [
8
]. Note that an average CMF for horizontal curves
that also includes European countries (but not Italy) can be found in [
8
], even if it is referred to as the
base condition of a curve with R =1000 m (and not to tangents). However, its application would have
Infrastructures 2020,5, 3 18 of 25
revealed significant differences between the ROR FI and no-ROR FI crash curves as well as the CMF in
Equation (16) [12].
It is important to note that the CMF from Equation (16) outperformed the HMS CMF (Equation (15))
in highlighting sites that may have potential for skidding proneness (with a relevant history of ROR FI
crashes). Hence, this CMF, which only depends on the CCR value, could be used to identify high-risk
ROR FI crash curves in the network screening stage (at least based on the analyzed data).
3.3. Practical Implications for Road Safety Management
In this section, the results presented and discussed in the previous sub-sections are used to define
their practical implications for road safety management purposes. Moreover, some practical design
aspects are also discussed that are useful for safety interventions at similar sites.
3.3.1. Recurrent Features Useful for Road Safety Management
Based on the findings from this study, a list of features to be used as indicators of ROR FI
crash-prone rural two-way two-lane curves was proposed. These features can be used during the
network screening stage (typically conducted by highway agencies or public entities) to highlight some
sites that should be studied in more detail (e.g., for on-site inspections or safety-based management).
In particular, in this specific case, network screening can be aimed at reducing specific type of crashes
such as run-off-road FI crashes. In the following list, only the elements that are immediately available
to practitioners are included, considering a scenario in which some sites should be analyzed in more
detail in a large road network managed by the same agency. These features are:
•
The ratio between the curve radius and the radius of the adjacent curves (average between the
previous and the following curves, since the road type is two-way operated). In this study, by
excluding the adjacent curves on which the ROR FI crashes occurred, the average ratio between
the crash curve radius and the average adjacent curve radius (on which ROR FI crashes did not
occur) was equal to 0.59 and the 85
th
percentile of the distribution of ratios for the crash curves
was 0.76. Hence, for road safety management purposes, two-way two-lane rural curves with
RC≤(0.59 ÷0.76)∗ RC+1+RC−1
2!(17)
could be targeted for further investigation while conducting campaigns dedicated to preventing
ROR FI crashes on two-way two-lane rural road curves. The choice between the two values
proposed (the mean and the 85
th
percentile) may depend on the capability for planning further
investigations (e.g., inspections) at curves. The CMF (Equation (16) [
12
]), which has been
demonstrated to have the capability to highlight ROR FI crash sites, only depends on the CCR.
Hence, a suggested measure based on the difference in CMFs would have been redundant, having
already provided the above described relation in Equation (17).
•
The difference between the operating speed and design speed in dry conditions. In dry conditions,
an inferred operating speed significantly close to the maximum inferred design speed (average
margin of
−
3.7 km/h) was found to be associated with ROR FI crashes at curves. In Figure 6,
Equation (3) (85
th
inferred operating speed) and Equation (10) (max. inferred design speed) are
solved. Given the findings from this study, the radii of curvature for which the 85
th
operating
speed is greater or closer than the maximum inferred design speed could be targeted for further
investigation. In this case, the threshold can be set to around 250 m (close to the intersection
between the two curves in Figure 6and roughly corresponding to the same average margin found
in this study). This indication is more conservative than using the conventional 85
th
-design speed
margin of +10 km/h [
23
,
27
] as a threshold, which would correspond to curves with a radius of
less than around 150 m, as based on Figure 6.
Infrastructures 2020,5, 3 19 of 25
Infrastructures 2020, 5, x FOR PEER REVIEW 18 of 25
excluding the adjacent curves on which the ROR FI crashes occurred, the average ratio between
the crash curve radius and the average adjacent curve radius (on which ROR FI crashes did not
occur) was equal to 0.59 and the 85th percentile of the distribution of ratios for the crash curves
was 0.76. Hence, for road safety management purposes, two-way two-lane rural curves with
𝑅≤(0.59÷0.76)∗(
) (17)
could be targeted for further investigation while conducting campaigns dedicated to preventing
ROR FI crashes on two-way two-lane rural road curves. The choice between the two values
proposed (the mean and the 85th percentile) may depend on the capability for planning further
investigations (e.g., inspections) at curves. The CMF (Equation (16) [12]), which has been
demonstrated to have the capability to highlight ROR FI crash sites, only depends on the CCR.
Hence, a suggested measure based on the difference in CMFs would have been redundant,
having already provided the above described relation in Equation (17).
• The difference between the operating speed and design speed in dry conditions. In dry
conditions, an inferred operating speed significantly close to the maximum inferred design
speed (average margin of −3.7 km/h) was found to be associated with ROR FI crashes at curves.
In Figure 6, Equation (3) (85th inferred operating speed) and Equation (10) (max. inferred design
speed) are solved. Given the findings from this study, the radii of curvature for which the 85th
operating speed is greater or closer than the maximum inferred design speed could be targeted
for further investigation. In this case, the threshold can be set to around 250 m (close to the
intersection between the two curves in Figure 6 and roughly corresponding to the same average
margin found in this study). This indication is more conservative than using the conventional
85th-design speed margin of +10 km/h [23,27] as a threshold, which would correspond to curves
with a radius of less than around 150 m, as based on Figure 6.
Figure 6. Maximum inferred design speed Sd (Equation (10)) in dry conditions plotted with the
85th operating inferred speed S85 (Equation (3)) against the radius of curvature.
• Deceleration rates. High inferred deceleration rates were found to be associated with ROR FI
crash curves. This clearly points out that the length of the tangent included between two
subsequent curves (with largely different radii) plays a crucial role. Hence, if the tangent length
does not allow a deceleration compatible with Equation (12) (i.e., the tangent is shorter), then
tangents before curves with a radius of curvature sharper than the previous ones should be
targeted for further investigation. A practice-ready abacus is graphically depicted in Figure 7
and provides the minimum length of the tangent set as equal to the minimum deceleration
length needed from the previous curve (with larger radius) to the following curve (with sharper
Figure 6.
Maximum inferred design speed S
d
(Equation (10)) in dry conditions plotted with the 85
th
operating inferred speed S85 (Equation (3)) against the radius of curvature.
•
Deceleration rates. High inferred deceleration rates were found to be associated with ROR FI crash
curves. This clearly points out that the length of the tangent included between two subsequent
curves (with largely different radii) plays a crucial role. Hence, if the tangent length does not
allow a deceleration compatible with Equation (12) (i.e., the tangent is shorter), then tangents
before curves with a radius of curvature sharper than the previous ones should be targeted for
further investigation. A practice-ready abacus is graphically depicted in Figure 7and provides
the minimum length of the tangent set as equal to the minimum deceleration length needed from
the previous curve (with larger radius) to the following curve (with sharper radius). This can be
used starting from the radius of the previous curve and by reading the value of the necessary
tangent length for different k values (ratio between the radii of the following and previous curve).
Tangents that do not satisfy this minimum criterion should be targeted for further investigation
during the network screening stage.
Infrastructures 2020, 5, x FOR PEER REVIEW 19 of 25
radius). This can be used starting from the radius of the previous curve and by reading the value
of the necessary tangent length for different k values (ratio between the radii of the following
and previous curve). Tangents that do not satisfy this minimum criterion should be targeted for
further investigation during the network screening stage.
• Longitudinal slope. This was highlighted as a critical factor for ROR FI crashes at curves: the
average slope was 4.0% in the study sample. This suggests that, as expected, curves on steep
slopes should certainly be targeted for further investigation. No further detailed indications are
provided in this study since the vertical alignment was considered to a minor extent, given the
available data sources and the need for accurate data.
Figure 7. Deceleration length Ld needed (using Equation (13)) as a function of the radius of curvature
of the previous curve for different values of the k ratio (the following curve radius to the previous
curve radius).
3.3.2. Remarks for Safety Countermeasures on Similar Sites
Based on both the findings from this study and the remarks made in the previous sub-section, a
discussion about possible countermeasures on two-way two-lane ROR crash-prone curves is
provided as follows.
Basically, the possible countermeasures can be differentiated into long-term and short-term
measures, and different sets of countermeasures can be implemented to optimize safety maintenance
interventions [5]. Long-term measures typically involve re-designing the road alignment to strictly
adhere (or tend to) the current regulations/guidelines (i.e., meeting requirements for radii and
transition curves). In several cases, this is not feasible and thus alternative short-term measures can
be implemented in some cases specifically dedicated to the ROR crash type (e.g., [41]). The
elementary short-term measures that can help in this specific case are:
• Speed reducing measures. Clearly since speeding was indicated as a crucial contributing factor,
the importance of reducing speed is paramount. This can be effectively achieved through
transverse rumble strips [51] and traffic speed control (e.g., [52]).
• Perceptual measures. It was extensively shown how the mis-perception of the crash curve or the
drivers’ distraction could have played an important role in the analyzed crashes. Hence,
measures such as curve delineation, warning signs, and sequential flashing beacons can
effectively reduce crashes [53] by acting on the drivers’ perceptual mechanism.
• Physical improvements. It is paramount that one of the most frequent ROR FI crash mechanisms
is the loss of friction (i.e., when the friction demanded exceeds the available friction [9,10]). A
Figure 7.
Deceleration length L
d
needed (using Equation (13)) as a function of the radius of curvature
of the previous curve for different values of the k ratio (the following curve radius to the previous
curve radius).
Infrastructures 2020,5, 3 20 of 25
•
Longitudinal slope. This was highlighted as a critical factor for ROR FI crashes at curves:
the average slope was 4.0% in the study sample. This suggests that, as expected, curves on steep
slopes should certainly be targeted for further investigation. No further detailed indications are
provided in this study since the vertical alignment was considered to a minor extent, given the
available data sources and the need for accurate data.
3.3.2. Remarks for Safety Countermeasures on Similar Sites
Based on both the findings from this study and the remarks made in the previous sub-section,
a discussion about possible countermeasures on two-way two-lane ROR crash-prone curves is provided
as follows.
Basically, the possible countermeasures can be differentiated into long-term and short-term
measures, and different sets of countermeasures can be implemented to optimize safety maintenance
interventions [
5
]. Long-term measures typically involve re-designing the road alignment to strictly
adhere (or tend to) the current regulations/guidelines (i.e., meeting requirements for radii and
transition curves). In several cases, this is not feasible and thus alternative short-term measures can be
implemented in some cases specifically dedicated to the ROR crash type (e.g., [
41
]). The elementary
short-term measures that can help in this specific case are:
•
Speed reducing measures. Clearly since speeding was indicated as a crucial contributing factor, the
importance of reducing speed is paramount. This can be effectively achieved through transverse
rumble strips [51] and traffic speed control (e.g., [52]).
•
Perceptual measures. It was extensively shown how the mis-perception of the crash curve or the
drivers’ distraction could have played an important role in the analyzed crashes. Hence, measures
such as curve delineation, warning signs, and sequential flashing beacons can effectively reduce
crashes [53] by acting on the drivers’ perceptual mechanism.
•
Physical improvements. It is paramount that one of the most frequent ROR FI crash mechanisms is
the loss of friction (i.e., when the friction demanded exceeds the available friction [
9
,
10
]). A design
friction coefficient varying with speed was assumed in the calculations made throughout the
paper, since no direct measurements were available. However, considering drivers travelling
at the inferred 85
th
operating speeds in sharp radii curves (higher than then maximum inferred
design speeds, see Figure 6for R shorter than about 225 m), the friction used is higher than the
friction computed in the case of design speed. The actual friction used can be computed through
the following equation (obtained by rearranging Equation (5), where q=q
max
=0.07 due to the
assumed sharp radii):
ft(S85)=S85 2
127 ∗RC
−qmax (18)
The cross friction coefficients used (light grey dashed line in Figure 8) were significantly higher
than the design cross friction coefficients in wet conditions (black dashed line in Figure 8). In fact,
a threshold for indicating an unacceptable design condition could be a difference between the
used and design cross friction coefficients of more than 0.04 [
23
,
27
]. This means that treatments
for improving skid resistance should be implemented where there is noticeable evidence that
this condition could occur, especially in the case of sharp radii. Another solution could be an
increase in the cross slope (superelevation) up to 10% (as suggested in particular cases, e.g., in [
31
]).
In this case, no skid resistance treatments are needed (that is, still assuming the design cross
slope is valid) and can be applied to radii of curvature roughly down to 300 m (see black solid
line in Figure 8) where q=0.10 is reached. However, a similar treatment should be considered
with extreme cautiousness, especially in the presence of notable vertical grades and possible icy
pavements. In fact, the compound slope is often limited by design guidelines, thus resulting in the
unfeasibility of implementing cross slopes equal to 10%. Finally, considering the implementation
of both increased superelevation and skid resistance treatments does not dramatically reduce the
Infrastructures 2020,5, 3 21 of 25
need for increased available friction, especially for very sharp radii (compare dashed light grey
line with dashed grey line in Figure 8).
Infrastructures 2020, 5, x FOR PEER REVIEW 20 of 25
design friction coefficient varying with speed was assumed in the calculations made throughout
the paper, since no direct measurements were available. However, considering drivers travelling
at the inferred 85
th
operating speeds in sharp radii curves (higher than then maximum inferred
design speeds, see Figure 6 for R shorter than about 225 m), the friction used is higher than the
friction computed in the case of design speed. The actual friction used can be computed through
the following equation (obtained by rearranging Equation (5), where q = q
max
= 0.07 due to the
assumed sharp radii):
𝑓
(𝑆)=𝑆
127∗𝑅 −𝑞 (18)
The cross friction coefficients used (light grey dashed line in Figure 8) were significantly higher
than the design cross friction coefficients in wet conditions (black dashed line in Figure 8). In
fact, a threshold for indicating an unacceptable design condition could be a difference between
the used and design cross friction coefficients of more than 0.04 [23,27]. This means that
treatments for improving skid resistance should be implemented where there is noticeable
evidence that this condition could occur, especially in the case of sharp radii. Another solution
could be an increase in the cross slope (superelevation) up to 10% (as suggested in particular
cases, e.g., in [31]). In this case, no skid resistance treatments are needed (that is, still assuming
the design cross slope is valid) and can be applied to radii of curvature roughly down to 300 m
(see black solid line in Figure 8) where q = 0.10 is reached. However, a similar treatment should
be considered with extreme cautiousness, especially in the presence of notable vertical grades
and possible icy pavements. In fact, the compound slope is often limited by design guidelines,
thus resulting in the unfeasibility of implementing cross slopes equal to 10%. Finally,
considering the implementation of both increased superelevation and skid resistance treatments
does not dramatically reduce the need for increased available friction, especially for very sharp
radii (compare dashed light grey line with dashed grey line in Figure 8).
Figure 8. Possible modifications of the cross slope q and the cross friction coefficient f
t
, according to
speed increasing from the design speed S
d
(for which f
t
= f
td
, q = 0.07) to the 85
th
operating speed S
85
considering wet pavement conditions.
4. Conclusions
In this study, Italian two-way two-lane rural road curves on which more than one ROR FI crash
in the observation period of five years occurred were analyzed. The aims of the study were: (a) the
Figure 8.
Possible modifications of the cross slope q and the cross friction coefficient f
t
, according to
speed increasing from the design speed S
d
(for which f
t
=f
td
, q =0.07) to the 85
th
operating speed S
85
considering wet pavement conditions.
4. Conclusions
In this study, Italian two-way two-lane rural road curves on which more than one ROR FI crash
in the observation period of five years occurred were analyzed. The aims of the study were: (a) the
identification of recurrent specific features for ROR FI crashes at curves of the road type analyzed,
(b) the identification of recurrent specific geometric and operational features that may be associated
with the occurrence of ROR FI crashes at curves, and (c) link empirical findings from the study to road
safety practice. These research questions were addressed through a micro-analysis approach involving
accident reconstructions [
16
–
18
,
39
], which allowed for additional insights than traditional macro-level
approaches (e.g., [2,54]).
The following conclusions can be drawn based on the research questions:
•
There were some recurrent features in the ROR FI crash dataset analyzed. In particular, a typical
ROR FI crash is an injury light vehicle crash that occurs to adult drivers (aged between 30–64) in
the afternoon, on wet pavements, with speeding and/or distraction as a contributory factor.
•
Typically, curves with a relevant history of ROR FI crashes have significantly smaller radii of
curvature than the adjacent ones. This finding was associated with possible distraction and great
deceleration rates, based on the data exploration. In fact, crashes in which distraction was a
contributory factor were associated with crash curves having a notably smaller radius than the
previous one. Moreover, several crash curves require high deceleration rates, thus also implying
insufficient tangent lengths before curves. Nevertheless, in dry conditions, the 85
th
inferred
operating speeds are comparable with the inferred design speeds that meet the curve equilibrium,
while they are higher in wet conditions.
•
Some suggestions for road safety management and safety interventions (i.e., reducing speeds,
improving perception and skid resistance) are provided based on the findings. The suggestions
for targeting specific ranges of radii of curvature, ratios between the curve radius and the average
Infrastructures 2020,5, 3 22 of 25
adjacent radii, and previous tangent lengths may be useful in targeting two-way two-lane rural
road curves for further investigation (e.g., while attempting to reduce the ROR crash type).
Concluding Remarks on Strengths and Limitations
This study was based on an Italian dataset. Even if some values included in the Italian road
standards were considered (to be coherent with the local dataset) for calculation purposes, several
aspects of the discussed findings are transferrable. In fact, the discussed relationships between ROR FI
crashes and speeding, distraction, geometric, and operational features are all transferrable. However,
even if some of the proposed practice-ready tools are based on values taken from local models (e.g.,
Figures 6and 7), their frameworks are still valid and transferable once the applied models are adjusted
according to the local environment. Moreover, clearly, the findings and frameworks from this study
could be useful for application on the existing road network for the aim of design enhancement.
Policies and practices for the enhancement of existing road networks may also vary across countries.
Aside from the transferability issue, which is typical of local road safety studies (see e.g., [
55
]),
the present study is not without limitations. First, it was based on geometric data achieved through
online sources in the absence of more accurate tools, and this could have affected the data accuracy
related to each single site. However, the possible generation of inaccuracies is consistent for all of the
considered samples and then their overall effect on averages may be levelled. Due to the same data
source used, information about sight distance and lateral obstacles, which may be relevant for ROR
crashes (see [
2
,
56
]) were not collected. Moreover, detailed information about the vertical alignment,
spiral transition curves, and speed limits of the sections was not available, which may also affect
the drivers’ speed choice. Traffic volumes were not available for the investigated sections, but the
homogeneity of the road category chosen (and the actual location of the segments) may indicate this
lack as a minor issue. Moreover, single-vehicle crashes in which interactions with other vehicles were
null or minor were analyzed and the functional relationship between traffic volumes and ROR crash
frequency may not be trivial (see [2,14]).
However, given the level of resolution of the study, some insights are provided based on our
findings, which may be useful and potentially applicable in practice. The micro-analysis approach
proposed was able to reveal some interesting patterns (e.g., the great deceleration rates involved),
which are not easily revealed in traditional macro-level studies. In fact, a strength of this study is
the level of disaggregation of the analysis, which led to the identification of some patterns that are
otherwise hidden in aggregated statistical analysis. The use of aggregate geometric and operational
predictors of road safety mostly relate to average measures or objective indicators, which do not
take into account the degree of deviation of the individual driver from the ideal behavior. Most of
these unwanted patterns relate to human-based tendencies (e.g., unexpected maneuvers, distracted
driving, hard braking), which could be potentially solved with the advent of self-driving vehicles in
fully autonomous modes (see [
57
,
58
]). In this case, information about the adequate operating safe
speeds [
59
] could be shared between the vehicles and infrastructure through I2V systems (see [
60
]).
Based on the micro-analysis approach used, it may be of interest to replicate similar studies with other
international datasets since ROR FI crashes are a worldwide safety issue.
Author Contributions:
Conceptualization, P.I., N.B., V.R., and P.C.; Methodology, P.I., P.C.; Investigation, P.I.;
Data curation, P.I.; Writing—original draft preparation, P.I.; Writing—review and editing, N.B., V.R., and P.C.;
Supervision, P.C. All authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflicts of interest.
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