The design of the horizontal alignment, which consists of level tangents connected
by circular curves, is influenced by design speed and superelevation of the
curve itself. Crash rate for horizontal curves are higher than for tangent sections,
with rates ranging between 1.5 and 4 times greater than on straight sections.
Several factors appear to influence the safety performance of horizontal curves,
including: (1) traffic volume and mix, (2) geometric features of the curves,
(3) cross section, (4) roadside hazards, (5) stopping sight distance, (6) vertical
alignment superimposed on horizontal alignment, (7) distance between curves
and also between curves and the nearest intersections or bridges, (8) pavement
friction and finally (9) traffic control devices. The improvement of horizontal
curve design involves three steps. First, problem site must be identified based
on its crash history and roadway conditions. Second, improvement should assess
and implemented. Third, before and after any construction attempts, studies
of crash performance should be conducted to assess the effectiveness of the
changes (Garber and Hoel, 2009).
MATERIALS AND METHODS
External (sectional) factors in horizontal alignment: Sectional factors include section length, section traffic volume and speed, transition curves, gradients, cross-section elements (lane width, shoulder width, median width, climbing lanes pavement friction, pavement surface type, shoulder type), roadway features (stopping sight distance, overtaking sight distance) and roadside features (side slopes, ditches, obstruction, utility poles).
Section length: Sectional factors include section length, section traffic
volume and speed. A section of rural two-lane road may stretch from one county
line to another and may need breaking up for the purpose of analysis. Decreasing
the length of the sections has the attractive merit of ensuring (to some extent)
uniform geometric features, but the smaller a segment gets, the more sparse
the crash data and consequently, the less reliable the analysis will be. Furthermore,
the smaller a segment becomes, the more difficult it is to assign a crash (in
the current crash database) to that segment (Labi and CATS,
Section traffic volume: The traffic volume for each road section is
the Average Annual Daily Traffic (AADT) on the section for a few year periods.
Where the section consists of segments with different AADTs, the weighted average
of the AADT over the entire section is estimated and used for the analysis.
Section AADT is a very influential variable on crash frequencies. All other
factors being equal, higher AADT will result in higher number of crashes, at
least up to the point where capacity is reached. However, inclusion of AADT
in crash modeling must be done with a great deal of circumspection because it
is typically correlated with a number of explanatory variables such as lane
width, shoulder width, shoulder type and pavement friction. In other words,
higher volume roads are likely to have superior geometric characteristics, even
within a given functional class. Such correlations were evident in the preliminary
investigations for the present study.
Speed: Speed is one of the major parameters in geometric design and
safety is synonymous with crash studies as mentioned by Finch
et al. (1994). A recent study concluded that a reduction of 1.6 km
h-1 (1 min h-1) in the average speed reduces the incidence
of injuries by about 5%. Reducing rural speed limits from 100 to 90 km h-1
has been predicted to reduce casualties by about 11% (Yager
and Van Aerde, 1983). It is interesting to note that the relationship between
the design speed and speed limit is not referred to in the geometric design
standards of many countries (OCinneide and McAuliffe,
1993). However, the design speed can be determined from the road standards,
either using the following equation:
where, Vdesign design speed (km h-1), R curve radius in meters, e superelevation or crossfall in percent in meter and f side friction factor, typically 0.15 (for 120 km h-1) to 0.33 (for 30 km h-1) or estimated from the tables.
Lane width: Most studies were limited to two-lane rural roads and showed
that accident rates decreased with increase in width (Hughes,
1995). However, the result of Hearne (1976) suggested
that there was a marginal increase in accident occurrence with an increase in
carriageway width. Hedman (1990) noted that some results
indicated a rather steep decrease in accident with increased width of carriageway
from 4 to 7 m, but that little additional benefit is gained by widening the
carriageway beyond 7 m. This is supported by the Transportation
Research Board (1978) conclusion that there is little difference between
the crash rate for a 3.35 and a 3.65 m lane width. However, studies on low volume
rural roads indicate that crashes continue to reduce for width greater than
3.65 m, though at a lower rate (Hughes, 1995). Yager
and Van Aerde (1983) found that the passage of a vehicle requires a minimum
lane width and that any additional width beyond this minimum allows one to drive
faster and with a greater measure and perception of safety. For lane width from
3.3 to 3.8 m, they reported that the operation speed is decreased by approximately
5.7 km h-1 for each 1.0 m reduction of the roads width.
Transportation Research Board (1978) suggests that widening
lanes from 2.7 to 3.7 m would reduce crash by 32%. Observations made in Denmark
(1981) demonstrated that as the lane width increases, the relative crash
frequency decreases: for road widths of fewer than 6 m, there was an increase
in the risk of both injury crashes and severe injury crashes. This is supported
by Serinivasan (1982) who reported that the crash rate
of a 5 m road was about 1.7 time that of a 7.5 m road. A comprehensive Swedish
study reported that, for roads with 90 km h-1 speed limits and similar
alignments, increase in roadway width (carriageway plus shoulder) up to 13 m
gives significant reductions in crash rates (Brude et
al., 1980). However, a more recent Swedish work concluded that it was
not possible to detect any statically significant differences in crash rates
between wide and narrow roads (Bjorketun, 1982) of the
three road-width classes used (8.5, 9 and 10 to 13 m), the 99 roads had a higher
crash rate irrespective of the decade of construction.
Shoulder width: There have been a number of studies carried out on relationship
between the shoulder width and crash rate. As noted by Hedman
(1990), more recent studies show a decrease crashes with an increase in
width from 0.0 to 2 m and little additional benefit is obtained above 2.5 m.
However, Transportation Research Board (1978) concluded
that, on multi-lane undivided and divided highways, shoulders that will not
accommodate a parked vehicle off the travelled way increase the crash rate.
As Transportation Research Board (1987) noted, the literature
does not provide an entirely consistent model of the simultaneous effects of
lane width and shoulder type on crashes. It also noted that crash rate decrease
with increases in lane and shoulder width and that widening the lanes has a
greater safety benefit than widening the shoulders.
Transition curves: Some studies have concluded that transition curves
are dangerous because of the drivers underestimation of the severity of
the horizontal curvature (Stewart and Cjfudworth, 1990;
Simpson and Kerman, 1982). Stewart
(1994) reports of a California Department of Transportation study involving
a study of roads without transitions curves which showed that roads with transitions
curves had, on average 73% more injury accidents (probability <1) than the
others. Also the Department report Accidents on spiral Transition Curves in
California warns against any use of these curves. However, it is understood
that recent studies in Germany and the UK have concluded that the impact of
transitions on safety is neural.
Gradients: Steep gradients are generally associated with higher crash
rates. Hedman (1990) quoting Swedishs research
stated that grades of 2.5 and 4% increase crashes by 10 and 20%, respectively,
compared with near-horizontal roads. Glennon et al.
(1985) after examining the results of a number of studies in the United
States concluded that grade sections have higher accident rates than level section;
steep gradients have higher accident rates than mild gradients and down gradients
have higher accident rates than up gradients. Department of
Transportation (1981) included a graph related to the base accident rate
to that on gradients which concurs with Glennon (1985)
conclusions. Simpson and Kerman (1982) noted that the
overall accident implications of steep gradients are not serving as it would
appear first, since steep gradients have shorter length. Transportation
Research Board (1978) concluded that the accident rate increases with gradients
Internal factors in horizontal alignment: Average crash rates are higher on horizontal curves than on tangent sections of rural 2-lane highways. Radius or degree of curvature consistently tops the list of geometry variables that most significantly affect operating speeds and crash experience on horizontal curves. Less consistent results concerning other geometry variables, including length of curve, defection angle, superelevation rate, presence of transition curves and the location of a curve relative to other horizontal curves, suggest that their effects may be statistically significant but lesser in magnitude.
Radius or degree of curvature: Many research efforts have identified
radius or degree of curvature as a strong indicator of crash experience (Krammes
et al., 1993; Glennon et al., 1985;
Terhune and Parker, 1986). The mean radius and degree
of curvature for each category were computed and regressed against the natural
logarithm of mean accident rate within each category. The results support previous
results that the sharpness of curve is significant. The high R results from
the grouping of sites and therefore, does not reflect the variability among
individual sites. Table 1 show the predication model developed
from a Swedish study on road with 90 km h-1 speed limit (Brude
et al., 1980).
Department of Transportation (1984) include graphs which
compared crash rates for horizontal curvature to a base crash rate by means
of a multiplier which agree closely with the Swedish values shown in Table
1. The difference between straight sections and bends becomes significant
at a radius of about 1000 m. The UK data indicates continually increasing accident
rate with reducing radius. This increase in crash rate becomes particularly
apparent at curve radii below 200 m. Simpson and Kerman
(1982) noted that radius curves result in much shorter curve lengths and
that the overall implications for accidents may be as it would appear.
|| Crash reduction factors for various increases in horizontal
|*1 m = 3.28 ft. (Brude et al., 1980)
It has been shown in past research that horizontal curves experience crash
rates of up to 4 times the rates on tangent sections, all else being equal (FHWA,
2000; AASHTO, 1994; Zegeer and
Deacon, 1987). Zegeer and Deacon (1987) identified
the following components such as traffic, roadway and geometric features that
influence safety at horizontal curve sections:
||Traffic volume on the curve and traffic mix (such as the percentage
||Curve features (such as degree of curve, curve length, superelevation,
presence of transition curves)
||Cross sectional curve element (such as lane-width, shoulder width, shoulder
type, shoulder slope)
||Curve section roadside hazard features (such as clear slope, rigidity
and types of obstacles)
||Stopping sight distance on curve (or at curve approach)z
||Vertical alignment on horizontal curve
||Distance to adjacent curves
||Distance of curve to nearest intersection, driveway, etc.
||Presence and type of traffic control devices (signs and delineation)
It has been shown by a number of researchers (Glennon et
al., 1985; Zegeer et al., 1991; Glennon,
1987) that milder curves are associated with lower crash rates compared
to sharper curves. For horizontal curves, casualty crashes seem to be more dominant
than PDO (Property Damage Only) crashes. Those researchers also found that horizontal
curves seem to have proportionately more head-on and opposite direction sideswipe
crashes, fixed object, crashes, rollover crashes and night-time crashes compared
to other sections. Glennon et al. (1985) and Fink
and Krammes (1995) determined that the degree of curvature is the best predictor
of crashes at curved sections. Geometric improvements used to improve safety
at deficient horizontal curves include the following:
||Roadway widening at curve sections
||Roadside improvements at curve sections
Also, traffic control devices are typically used to provide warning to curve
approaches and to provide delineation of the pavement. These devices will be
discussed in different section of this study. In their 1983 study, Glennon
et al. (1985) developed a discriminate model to be utilized in identifying
potentially hazardous horizontal curve sites on the basis of geometric, traffic
and roadside features and conditions. The study found that hazardous roadside
designs are the primary cause of crashes at horizontal curve sections. Fink
and Krammes (1995) investigated the effect of degree of curvature, tangent
length and sight distance on accident rates at horizontal curves and found that
crash occurrence at curve sections was significantly influenced by the degree
of curvature (Fig. 1). According to the researchers, variables
not found statistically significant include preceding tangent length, sight
distance, lane width, pavement width and condition.
Study by Zegeer et al. (1991) for the FHWA, the
impacts of various geometric elements on crashes were investigated using a database
comprising over 10,000 curve sections. The findings of this study were generally
consistent with those of past studies as discussed earlier.
Superelevation: Horizontal alignment and superelevation of curves have
an impact on the traffic safety performance of highway sections. Research that
relates traffic safety to roadway horizontal alignment has consistently shown
that traffic accidents increase with increasingly sharper curves. Sharp curves
in segments that otherwise have good alignment, tend to surprise drivers and
create even more hazardous situations. Consistency in design speeds along significant
sections of highways has been advocated by some, as a means of controlling the
incidence of surprise curves in other gentle alignments. However, design speeds
for horizontal curves serve as functions of the maximum superelevation policies
adopted by a design agency. Therefore, a single curve design may be regarded
as having different design speeds by agencies that have different maximum superelevation
policies (AASHTO, 2001).
The superelevation of horizontal curves is used as an input variable in the
HSM methodology for rural two-lane highways. Superelevation is the pavement
cross slope on the horizontal curve provided to counteract the tendency of vehicles
to move toward the outside of the curve. As a measure of cross slope, superelevation
is a ratio of two lengths and is therefore a dimensionless quantity, although
many standard geometric design references assign it units of ft/ft. The HSM
methodology considers the difference between the actual superelevation and the
superelevation recommended by AASHTO policy. Superelevation affects safety in
the HSM methodology only when this difference exceeds 0.01. Superelevation rates
can be determined from existing data in computerized roadway inventory files,
from as-built plans, or from field measurements Highway Safety Manual (HSM,
2008). This study summary of factors effective in crashes on the horizontal
curves in two-line highways shows in the Table 2 classification.
Details of accident data: From data collected we selected seven main roads of two-lane highways in the province of Kohkilouyeh and Boerahmad in Iran. Crashes in the horizontal curves at 200 km in the regions Boerahmad (R4, 5, 6 and 7), Gachsaran, (R2) and Kohkilouyeh (R3), were investigated in terms of accident frequency in 2007. The findings of study about these roads can be generalized to Iran highways. The details of accident data have been collected and obtained from Traffic Safety Department of the traffic police, with information about each horizontal colligated curve. The collected data included number of accidents in the year 2007 and for each case, the cause of the accident, its time, weather, severity, types and location.
The present investigation incorporates examination of horizontal curve geometric
design, design speed, singing, pavement, marking and road safety features. The
selected horizontal curves include seven main roads of two-lane highways which
were observed as explained below. The number of examined horizontal curves was
502 and each variable, included Radius curve (Rc), Degree curve (Dc), Delta
curve (Δc), Length curve (Lct), lane width 3.5 meter per lane, left and
right clearance width 1.0 and 0.0 m regularity, signing (include advance, warning,
directional that are provided), road marking provided with deficiency, road
condition as pavement surface in good condition with main road lighting and
observations such as high travelling speed of vehicles over curves more than
50 km h-1, Table 3 shown summary Data Main Road-Criteria
for Forming a Horizontal Curve in Rural Major Arterial in K.B province of Iran.
|| Factors effective in crashes on the horizontal curves in
|| Summary data main road- criteria for forming a horizontal
curve in rural major arterial in K.B province of Iran
R Software: The required data about 2 line rural (highways) will be collected from Iranian Highway Police headquarter. Then data will be entered into R software statistical package version 3.0 (USA) for descriptive statistical analysis.
RESULTS AND DISCUSSION
The relationship between horizontal curve factors and crash rates is quite
complex and not fully understood. Relatively little information is available
on the relationships between many geometric elements and crash rates, although
it has been clearly shown that very restrictive geometric elements such as very
short sight distances or sharp horizontal curve in considerably contribute to
higher crash rates and that certain combination of element cause an unusually
severe crash problems.
|| Statistical summary of poison regression model
|No. of observations in the fit: 502; Degrees of Freedom for
the fit: 9; Residual Deg. of Freedom: 493; Cycle:2; Global Deviance: 1012.997;
AIC: 1030.997; SBC: 1068.964; GAMLSS-RS iteration 1: Global Deviance = 1012.997;
GAMLSS-RS iteration 2: Global Deviance = 1012.997
However, it appears that significant reductions in the values of some of the
elements specified in geometric design standards do not result in large increases
in crash rates. There is broad agreement on the general relationship between
geometric design elements and crash rates. Consequently, for the purposes of
evaluating safety impacts of lower physical design standards or for comparing
the safety of alternative road alignments, the available information should
provide a reasonable indication of the likely differences in expected crashes.
Table 4 shows the results from Poisson regression model that
an increase in independed variables of degree curve, length total curve, superelevation
curve and offset variable ADT for horizontal curves leads to an increase in
the number of crashes and an increase in independed variables length spiral
curve, shoulder width ends up with a decrease in the number of crashes.
|| Relationship Sw and CR.No
|| Relationship Lsp and CR.No
According to the parameter estimates obtained in this model, the model form
can be written as in Eq. 2:
||No. of horizontal curve-related crashes,
||average daily traffic (veh day-1)
||Degree horizontal curve (°)
||Superelevation horizontal curve (%)
||Length spiral curve (m)
||Shoulder Width (m) and
||Total length segment of horizontal curve (m), equal (two times length
spiral plus length horizontal curve)
The coefficients of full model show that shoulder width has negative sign,
signifying that for a unit increasing in total shoulder width (Fig.
2) and a unit increasing in length spiral curve the car-related crashes
decrease (Fig. 3) constantly by considering the effect of
other variables. Also with increasing in the degree curve, average daily traffic
and superelevation, crashes rate increases (Fig. 4, 5).
The other variables which include grade curve, line width and limited speed
in horizontal curve are over than Pr (>|z|, z=.05).
|| Relationships Dc and CR.No
|| Relationship ADT and CR.No
That rejects in model. Relationships between number of crashes and Horizontal
Curve Elements are shown in the Fig. 2-5.
The result in this study shown with decrease in horizontal curve degree, causes
horizontal curve radius increase. And increase in horizontal curve radius generally
yields sufficiently among crash reduction. That concurs with founds of (Krammes
et al., 1993; Glennon et al., 1985;
Terhune and Parker, 1986; Brude et
al., 1980; Fink and Krammes, 1995; Labi
and CATS, 2006).
Result this study shown with in this model, gradient and speed, indicator variable
which indicates the horizontal curves is found to be insignificant and is not
included in the model. Whereas, Vavilikolanu (2008) showed
that by flattening steep curves, the safety on vertical curves may increase.
And also showed an increase in truck-related crashes as posted speed limits
increase. This may be explained as the speed of the vehicle increases, sight
distance increases and the vehicle travels further in the direction.
There have been a number of studies carried out on relationship between the
shoulder width and crash rate that concurs with found this study that increases
shoulder width in two line highway crashes rate decreases include Transportation
Research Board (1978, 1987) and Hedman
There are many influential factors in traffic crashes which are taken as the criteria for highway safety. Road horizontal curve elements are among these effective factors. As the relationships between highway safety and road horizontal curve elements are considered some relationships can be seen intuitively at first approach. However, the important point is to determine the level of these relationships quantitatively. Although, the relationships show the same tendency, their level vary according to each country`s characteristic conditions.
It was realized in this study that elements related to horizontal curve geometry are more effective on road safety than elements with road geometry. The other influential elements include-according to their importance-cross section elements, vertical geometry, roadside features, traffic volume and sight distances. The study of the relationship between geometric design and safety yielded the following conclusions:
The most important independent effective variables in the horizontal curves crashes based on the analysis of the collected data are: degree of the horizontal curve (Dc), total length segment of horizontal curve (Lct), superelevation of the horizontal curve (Ec), length of the spiral curve (Lsp), shoulder width (Sw) and offset variable average daily traffic (ADT).
Horizontal curves are more dangerous when combined with gradients and surfaces with low coefficients of friction. Horizontal curves have higher crash rates than straight sections of similar length and traffic composition; this difference becomes apparent at radii less than 1000 m. The increase in crash rates becomes particularly significant at radii below 200 m. Small radius curves result in much shorter curve lengths and overall implications for crashes may not be as severe as would first appear.
Recommend continued use of 4, 6, 8, 10 and 12% maximum rates. Promote design consistency with an area of similar climate and character. Develop the minimum radii with normal crown for each of the five maximum superelevation rates. Only presents the minimum radius for a 1.5% normal crown and a maximum superelevation rate of 10%.
There is only a minor decrease in the speed adopted by drivers approaching curves of radii which are significantly less than the minimum radii specified for the design speed. However, curve radii below 200 m have been found to limit the mean speed to 90 km h-1.
Crashes increase with gradient and down-gradients have considerably higher crash rates than up-gradients. However, the overall crash implications a steep gradients may not be severe since steeper gradients are shorter. The geometry of horizontal curves is not known to have a significant effect on crash severity.
There appears to be little erosion of safety resulting from the use of sight distances below the minimum values specified in geometric design standards, although there is a significant increase in the crash rate for sight distance below 100 m.
As the lane width increases above minimum, the crash rate decreases. However, the marginal rate diminishes with increased lane width. On multi-lane highways, the more lanes that are provided in travelled way, the lower the crash rate.
Shoulders wider than 2.5 m give little additional safety benefit. As the median shoulder width increases, crashes increase. The present of a median has the effect of reducing specific type of crashes, such as head-on collisions. Medians, particularly with barriers, reduce severity of crashes.
Most of the than recent studies emphasize on the impact of transition curves in the horizontal curves crashes and recommend use of transition curves with length curve than 75.0 m.
Methods for improving the safety of horizontal curves include: (1) reconstructing the curve to make it less sharp, (2) widening lanes and shoulders on curves, (3) adding spiral transitions to curves, (4) increasing the amount of superelevation (up to allowable maximums of 0.80 and1.0 in urban and rural areas, respectively), (5) increasing the clear roadside recovery distance by relocating utility poles and trees, (6) improving vertical and horizontal alignment by avoiding sharp left hand curves and sharp downgrades, (7) assuring adequate pavement surface drainage on long radius curves and location where cross drainage is longer than on lane in width and (8) providing increased surface skid resistance on downgrade curve sites.
We would like to thank the Sustainable Urban Transport Research Centre/Department
of Civil and Structural Engineering, Faculty of Engineering and Built Environment,
Universiti Kebangsaan Malaysia, 43600 UKM, for supporting the related studies.
Special thanks to Iran Transportation and Terminals Organization (ITTO) for
their earnest cooperation and also to the Kohgilouyeh and Boyerahmad State Police
which provided us with their annual reports which formed our crash database.
I also would like to express my gratitude to all corporations and agencies who
contributed to this study with their maps, studies and highway and transportation
consultations, especially those Iranian corporations such as ETHAD RAH, BRAYAND,
PARSELO, IRAN ASTON and other companies which cooperate with Road and Transport
Department of Kohgilouyeh and Boyerahmad province.