Evaluating Safety Effects of Ramp Density and …...shown similar results for curve density AMF and the method documented in Bonneson et al. (4). Bonneson et al. (4) reviewed several

Fitzpatrick, Lord & Park 1

Evaluating Safety Effects of Ramp Density and Horizontal Curve for Freeways Using Texas Data

Kay Fitzpatrick1 Senior Research Engineer

Texas Transportation Institute, 3135 TAMU College Station, TX 77843-3135

phone: 979/845-7321, fax: 979/845-6481 E-mail: [email protected]

Dominique Lord

Assistant Professor Zachry Department of Civil Engineering

Texas A&M University, 3136 TAMU College Station, TX 77843-3136

Phone: 979/458-3949, fax: 979/845-6481 E-mail: [email protected]

Byung-Jung Park

Graduate Research Assistant Zachry Department of Civil Engineering

Texas A&M University, 3136 TAMU College Station, TX 77843-3136

Phone: 979/862-8492, fax: 979/845-6481 E-mail: [email protected]

Date

July 30th, 2009

Total Words 7,414 [5,164 Words, 5 Tables, 4 Figures]

1Corresponding author

2 Fitzpatrick, Lord & Park

ABSTRACT

Increased emphasis has been placed on improving the explicit role of highway safety in making decisions on highway planning, design, and operations. This can be achieved by quantifying the safety effects of geometric design elements for various highway facilities. While great attention has been directed primarily on rural two-lane highways and to a lesser degree, on urban arterials and rural multilane highways, freeway is a highway facility where additional efforts are needed. Despite one of the most critical design elements for freeways, the safety effect of on-ramps or off-ramps has yet to be quantified through research so far. The crash risk is likely to increase when they are combined with sharp horizontal curves. In this context, this study investigated the effect of ramp density on freeway segment crashes both in urban and rural areas, and whether that effect is different for tangent segments than horizontal curves. In addition, the effect of horizontal curves on freeway crashes was also identified using the degree-of-curvature variable. Data available for use in the evaluation included 324.3 centerline miles of freeways in Texas. Negative binomial regression models were used to estimate the effects of independent variables on crashes. The statistical modeling results were geared into the development of the corresponding accident modification factors (AMFs) that can be used for safety prediction for freeways.


INTRODUCTION

Increased emphasis has been placed on improving the explicit role of highway safety in making decisions on roadway planning, design, and operations. To evaluate safety in a quantitative way, it is vital to identify the relationships between safety and various geometric design elements for a highway facility. These geometric design elements may include roadway cross-section (lane width, shoulder width, and pavement width), horizontal alignment (degree of curvature or radius, superelevation, and spiral transition curves), vertical alignment (grade, length of grade, and lengths of crest vertical curves), median width, roadside (clear zone width and sideslopes), etc (1, 2). However, as noted in Bonneson et al. (3), quantitative safety relationships are not available for every geometric element of highway design. To address this need, the Highway Safety Manual (HSM) is being developed under the direction of the Transportation Research Board Highway Safety Manual Task Force. It is envisioned to become a nationwide predictive tool and available to evaluate the safety performance for various highway facilities. The goal is to provide the best available safety knowledge in a condensed and widely usable form for designers and practitioners. With such a tool state highway agencies or others responsible for the road system can identify potential areas of concern on streets and highways which can lead to safety performance improvement associated with those facilities. The first edition of the HSM is expected for public release shortly, and it will contain safety prediction methodologies for rural two-lane highways, rural multilane highways, and urban and suburban arterials. Additional information is available on the HSM website (http://www.highwaysafetymanual.org/). While great attention has been directed primarily on rural two-lane highways and to a lesser degree, on urban arterials and rural multilane highways, freeway is a roadway classification where additional efforts are needed. As part of the Texas Department of Transportation (TxDOT) proactive commitment to improving highway safety, TxDOT is moving toward including quantitative safety analyses earlier in the project development process. An objective of a current TxDOT research project is to develop evaluation tools that can be used by TxDOT designers. A draft of such tool is currently available (3). Specific accident modification factors (AMF) for freeways within the Texas tool have also been identified as deserving additional efforts. The interchange ramps are among them. Despite one of the most critical elements in the design of freeways, the safety effect of on-ramps or off-ramps has yet to be quantified through research so far. On-ramps or off-ramps have a high potential for crashes since they involve a significant speed change along their length and thereby complicate the driving task. The crash risk is likely to increase when they are combined with sharp horizontal curves and steep grade changes. As part of this effort, this study investigated the effects of on-ramps or off-ramps on freeway segment crashes both in urban and rural areas, and whether that effect is different for tangent


segments than horizontal curves. In addition, the effect of horizontal curves on freeway crashes was also identified using the degree-of-curvature variable. The statistical modeling results were geared into the development of the corresponding accident modification factors that can be used for safety prediction for freeways.

PREVIOUS WORK

This section reviews previous statistical modeling efforts for freeway safety which are deemed to be relevant for this study. The previous research results will be used later as a comparative purpose with the findings from this study. Crash Prediction Models Bonneson et al (4) reviewed three previous studies that developed crash prediction models for freeways and rural divided highways: Hadi et al. (5), Persaud & Dzbik (6), and Wang et al. (7). Hadi et al. (5) used negative binomial regression analysis to calibrate a set of safety prediction models using data from Florida roadways. The models were categorized by crash severity, area type (i.e., urban, rural), and number of through lanes. Persaud and Dzbik (6) developed two prediction models using data for urban freeways in Ontario, Canada. Separate models were developed for total crashes and severe (fatal plus injury). Unlike the models by Hadi et al. (5), the models by Persaud and Dzbik did not include variables for specific roadway elements (e.g., lane width, posted speed limit, median width, etc.). Moreover, the freeway segments do not distinguish between those with and those without ramp speed-change lanes. Because speed-change lanes tend to be associated with more crashes than basic freeway segments, the model predictions may overestimate crash frequency for mid-junction segments. Wang et al. (7) developed a safety prediction model for rural multilane divided highways using crash and geometry data from Minnesota. The database does not include data for freeways. However, the behavior of a rural divided highway with few or no access points is similar to that of a rural freeway. The models from these studies were modified by Bonneson et al. (4) so that each predicted severe crashes per year (i.e., fatal and injury crashes). Table 1 lists the revised models and comparisons of the crash prediction models are shown in Figure 1 for a range of traffic volume levels. For model comparison, the values of other model variables were set at typical values for freeways. Trends apparent from the figures are:

• Severe crash frequency increases in a nearly linear manner with traffic volume, • Crash frequency on urban six-lane freeways increase more rapidly than crash frequency

on urban four-lane freeways, • Rural four-lane freeways have fewer crashes than urban four-lane freeways.


Table 1 Safety prediction models from previous studies (4) Hadi Models (5) CRF = 0.25 ADT 0.9599 (1000 L)0.9107 eB-RF (1) B-RF = -14.032 - 0.0407Wis + 0.2127Nx (2) CUF4 = 0.25 ADT 1.1832 (1000 L)0.7733 eB-UF4 (3) B-UF4 = -10.61 – 0.307 Wl – 0.0232 Ws – 0.0154 V + 0.24 Nx – 0.06 (Wm)0.5 (4) CUF6 = 0.25 ADT 1.405 (1000 L)0.93 eB-UF6 (5) B-UF6 = -14.04 – 0.339 Wl – 0.0594 Ws – 0.031 (Wm)0.5 (6) Persaud and Dzbik Models (6) CUF4 = 0.0000354 ADT 1.082 L (7) CUF6 = 0.0000099 ADT 1.206 L (8) Wang Model (7) CRH = 0.000233 ADT 1.073 L1.073 eB-RH (1-0.01 PDO) (9) B-RH = -0.592 – 0.094 Ws – 0.003 Wm (10) Where:

CRF = frequency of mid-junction injury crashes on rural freeways (crashes/yr) CUF4 = frequency of mid-junction injury crashes on urban four-lane freeways (crashes/yr) CUF6 = frequency of mid-junction injury crashes on urban six-lane freeways (crashes/yr) CRH = frequency of mid-junction injury crashes on rural multilane highways (crashes/yr) ADT = average daily traffic (veh/d) L = freeway segment length (mi) Wis = inside shoulder width (ft) Nx = number of interchanges on freeway segment Wl = lane width (ft) Ws = outside shoulder width (ft) V = speed limit (mph) Wm = median width (ft) PDO = percent property-damage-only crashes on rural multilane divided highways (=62.5)


0

5

10

15

20

25

30

0 50 100 150 200Average Daily Traffic Demand

(1000s), veh/d

Sev

ere

Cra

sh F

requ

ency

, cr

ashe

s/yr

Hadi, 6LPersaud&Dzbik, 6 LPersaud&Dzbik, 4LHadi, 4L

0

1

2

3

4

5

0 10 20 30 40 50 60Average Daily Traffic Demand

(1000s), veh/d

Sev

ere

Cra

sh F

requ

ency

, cr

ashe

s/yr

Hadi

Wang et al

(a) Urban (b) Rural

NOTE: Typical values used for model comparison are: inside shoulder width (Wis)=4 ft; outside shoulder width (Ws)=10 ft; lane width (Wl)=12 ft; median width (Wm)=30 ft; speed limit (V)=55 mph; interchanges per mile (Nx)= 0; segment length (L)=1 mile.

Figure 1 Comparison of crash prediction models listed in Table 1

Safety Effect of Horizontal Curves Crash-prediction models for a four-lane, median-divided Italian motorway were developed using 5 years (1999-2003) of crash data and 46.6 km [28.9 miles] of roadway (8). Separate models were developed for severe crashes on horizontal curves and tangents, respectively:

41040863.033793.0ln86881.045703.1ˆ−××+++−

=AADT

RL

HC eλ (11)

]1050628.0[ˆ 41042575.0ln76232.040044.1 4

JAADTee AADTLTan ×××+×= −××+− −

λ (12)

Where:

HCλ̂ = Predicted severe crashes/year on horizontal curve

Tanλ̂ = Predicted severe crashes/year on tangent

L = curve or tangent length (km) R = Radius of curvature (km) AADT = annual average daily traffic (vehicles/day) J = junction presence, 1 if present or 0 if absent


NCHRP 17-29 developed a methodology for estimating the safety performance of rural multilane highway segments (9). The methodology for undivided segments used an accident modification factor defined as the horizontal curve density rather than an AMF with specific horizontal curve design characteristics. At the time the work was completed, detailed AMFs for horizontal curves were not available. Preliminary analyses in the context of an entire assessment project have shown similar results for curve density AMF and the method documented in Bonneson et al. (4). Bonneson et al. (4) reviewed several studies and developed the following horizontal curve AMF for multilane highways:

2580011 ⎟⎠⎞

⎜⎝⎛+=

RIAMF

cHC (13)

Where: AMFHC = Accident modification factor for horizontal curves V = Speed limit (mph) R = Radius of curvature (ft) In later work, Bonneson and Pratt (10) explored the relationship between horizontal curve and crashes. A comparison of available relationships for urban arterial streets and rural, two-lane highways when the speed limit was either 55 mph or 70 mph showed a possible influence of speed on crash frequency. Using a series of assumptions and comparisons, they developed a suggested AMF for horizontal curves that included speed as shown below:

( ) ( )2

24

2.3247.1147.097.01

RVVAMFHC += (14)

Where: AMFHC = Accident modification factor for horizontal curves V = Speed limit (mph) R = Radius of curvature (ft)

DATA COLLECTION

This section describes the data collection activities undertaken to assemble a database suitable for developing ramp density and horizontal curve accident modification factors for freeways.


Roadway Geometric Data An approach to determine if a difference in a roadway element varies in how it affects crashes is to select neighboring sites or pairs of sections. This approach results in a similar driver population and weather conditions at both sites of the pair (i.e., a horizontal curve and a tangent). For this study, the freeway sections were selected to be adjacent to each other on the same roadway to ensure that the pairs are as nearly matched as possible. Additional information on the approach is documented in Bonneson et al. (11). The TxDOT geometric database was used to identify horizontal curves in Texas that were located on freeway and with a curve type of “normal” (i.e., eliminate spiral curves and point curves). Sites were also eliminated if the horizontal curve was longer than 1.5 miles or less than 0.1 mile or degree of curvature information was not available for the curve. The tangent prior to or following the horizontal curve was required to be at least equal to the curve length plus 0.1 miles. The 0.1 mile represents the “buffer zone” that was eliminated from the evaluation to ensure that curve-related crashes are not inadvertently placed on the tangent segment and vice versa. The length of the buffer reflects recognition of the precision of crash location in the crash database. This database locates crashes to the nearest 0.1 mi. Researchers located each potential horizontal curve on an aerial photograph. Preference was to use aerial photographs available from a city or metropolitan planning organization as these photographs were generally of higher quality or resolution. If a high occupancy vehicle lane was found when reviewing the aerial photograph, the site was eliminated. On a few occasions, the data from the database resulted in identifying sites that were not limited access. These sites were frontage road sections that had been constructed before the freeway section. They were eliminated from the study. If the quality of the view available on the photograph was sufficient for data collection, the following segment characteristics were identified for the horizontal curve and for the associated tangent section:

• Number of lanes • Outside shoulder width (ft) • Inside shoulder width (ft) • Median type (e.g., none, grass, TWLTL, flush, curbed) • Median width (without inside shoulders) (ft) • Distance between edge of travel lane to barrier (when barrier is present) (ft) • Presence of barrier (yes or no), • Number of on ramps present within the horizontal curve or tangent segment (ramp was

counted if the gore was within the limits of the segment) [the number of on ramps for both directions was summed and divided by the section length to determine the on-ramp density]


• Number of off ramps present within the horizontal curve or tangent segment (ramp was counted if the gore was within the limits of the segment) [the number of off ramps for both directions was summed and divided by the section length to determine the off-ramp density]

• Degree of curvature: obtained from the TxDOT geometric database

Because data for only a sample of Texas curves could be collected, the researchers selected districts in different regions of Texas. The final dataset for the study included a total of 561 curves. The rural freeway dataset included 75.8 miles of horizontal curves and 75.8 miles of companion tangent sections for a total of 151.7 miles. The urban freeway dataset included 86.3 miles of curves and 86.3 miles of tangent for a total of 172.7 miles. The entire dataset included 561 curve/tangent pairs for a total of 324.3 miles of freeways and 1122 segments. Initial modeling efforts included an indicator variable to account for whether the curve/tangent pair was in an urban area or a rural area. A number of lanes variable was also included. The preliminary results along with a closer inspection of the range of data characteristics resulted in the dataset being subdivided into the following groups:

• Rural, 4-lane freeways (256 curve/tangent pairs, 151.7 miles), • Urban, 4-lane freeways (140 curves/tangent pairs, 90.0 miles), • Urban, 6-lane freeways (96 curves/tangent pairs, 50.5 miles), and • Urban, 8-or-more lane freeways (69 curves/tangent pairs, 32.2 miles).

Table 2 lists the distribution of the section attributes that was the same for both the tangent and horizontal curve sections along with the distribution for the degree of curvature for the horizontal curve sections. Table 3 lists the distributions of ramp densities subdivided by horizontal curve and tangent alignment.


Table 2 Distribution of variables by number of miles and segments common to the tangent and horizontal curve sections and degree of curve for horizontal curve


Table 3 Distribution of on-ramp and off-ramp density by number of miles and sections subdivided by tangent and horizontal curve

Variable Range Rural, 4 Lanes Urban, 4 Lanes Urban, 6 Lanes Urban, 8 or More Lanes

Sections Miles Sections Miles Sections Miles Sections Miles Horizontal

Curve On-Ramp

Density, both directions

(ramps/mile)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9

9-10 >10

199 9

20 6 9 2 5 3 1 1 1

54.9 5.5 9.4 1.7 2.1 0.4 0.9 0.4 0.1 0.2 0.2

87 7

12 11

5 6 3 3 3 0 3

26.0 4.7 6.0 3.4 1.5 1.3 0.6 0.4 0.5

0 0.6

51 1 8

13 5 7 2 3 2 2 2

11.4 0.6 3.6 4.8 1.4 1.7 0.3 0.4 0.5 0.2 0.3

31 0 3 9

13 4 5 3 0 1 0

6.0 0

1.8 2.6 3.4 0.9 0.9 0.4

0 0.1

0 Total 256 75.8 140 45.0 96 25.2 69 16.1

Tangent On-Ramp


(ramps/mile)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9

9-10 >10

211 8

19 5 6 2 1 3 0 1 0

58.0 5.7 8.1 1.4 1.4 0.4 0.3 0.4

0 0.1

0

86 9

14 12

6 8 3 1 0 0 1

23.5 6.7 6.7 4.0 1.4 2.0 0.4 0.1

0 0 0

41 2

11 15

8 6 4 5 0 4 0

8.9 1.1 5.3 5.2 1.8 1.1 0.6 0.7

0 0.5

0

24 1 5

11 9 2 9 1 4 0 3

4.3 0.9 2.1 3.4 2.0 0.4 1.7 0.1 0.7 0.0 0.5

Total 256 75.8 140 45.0 96 25.2 69 16.1 Horizontal

Curve Off-Ramp


(ramps/mile)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9

9-10 >10

199 9

16 9 8 3 7 2 1 2 0

56.1 6.0 6.9 2.5 1.8 0.6 1.2 0.3 0.1 0.3

0

92 5

16 10

2 6 3 2 2 0 2

27.5 3.3 7.6 3.0 0.4 1.5 0.8 0.3 0.2

0 0.4

53 2 7

11 5 5 5 3 1 4 0

11.8 1.1 3.0 4.3 1.4 1.0 1.4 0.5 0.2 0.4

0

30 0 3 9

11 4 7 1 2 2 0

6.2 0.0 1.8 2.6 2.7 0.9 1.4 0.1 0.2 0.2

0 Total 256 75.8 140 45.0 96 25.1 69 16.1

Tangent Off-Ramp


(ramps/mile)

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9

9-10 >10

210 8

19 8 5 2 0 4 0 0 0

57.5 5.8 8.0 2.4 1.2 0.4

0 0.5

0 0 0

82 7

15 12 11

7 3 1 0 0 2

22.5 5.5 6.9 4.5 2.7 1.6 0.8 0.1

0 0

0.4

37 3

10 14 12

8 3 4 1 3 1

7.7 1.6 4.3 4.7 3.4 1.7 0.5 0.5 0.2 0.3 0.1

28 2 5 8

10 2 8 2 3 0 1

5.1 1.5 2.1 2.3 2.5 0.4 1.2 0.3 0.6

0 0.1

Total 256 75.8 140 45.0 96 25.2 69 16.1


Crash Data Crash data for each section were extracted from the Texas crash electronic database. A total of five years of crash data (1997 to 2001) were used. Analyses were performed using only fatal (K), incapacitating-injury (A), non-incapacitating injury (B), and minor injury (C). To be consistent with other AMFs currently included in the Interim Roadway Safety Design Workbook (3), property damage only (PDO) crashes were not used in the analysis. Within Texas, many freeways have a parallel frontage road that provides access to local properties. Access between freeways and frontage roads is by ramps only. Because the frontage road network was not part of this evaluation those crashes associated with the frontage road should not be included in the evaluation. The Texas crash database has a ‘Part of Roadway’ variable. Those crashes that occurred on the following Part of Roadway were included in the dataset: main lane, entrance ramp, and exit ramp. The Parts of Roadway excluded were frontage road, transitway, connection, detour, and other. The values listed in Table 4 are based on crashes that occurred during the five-year period of 1997 to 2001 for the 561 pairs. Table 4 Crash characteristics for horizontal curve and tangent sections based on crashesa over five years (1997 to 2001)

Variable Location Rural 4 Lanes

Urban 4 Lanes

Urban 6 Lanes

Urban 8+ Lanes

Per Section Average Number of

Crashes HC b 1.9 7.0 15.2 27.9 Tan b 1.7 7.0 15.4 30.3

Maximum Number of Crashes

HC 14 69 86 154 Tan 20 78 98 144

All Sections

Number of Miles (mi) HC Tan

151.6 151.6

90.0 90.0

50.4 50.4

32.2 32.2

Sum of Crashes on all Sections

HC 490 977 1461 1927 Tan 424 982 1482 2092

Crash Count (crashes/mile-yr)

HC 1.29 4.34 11.58 23.97 Tan 1.12 4.36 11.75 26.02

Crash Rate c HC 0.23 0.34 0.33 0.50 Tan 0.20 0.34 0.34 0.54

NOTE: a KABC crashes includes fatal (K), incapacitating injury (A), non incapacitating injury (B), and possible injury (C); Part of Roadway includes main lane, entrance ramp, or exit ramp; b HC = Horizontal Curve sections, TAN = Tangent sections; c Crash Rate = Crashes per million vehicle miles (crashes/mvm)


STATISTICAL MODELING

Negative binomial (NB) regression models for cross-sectional data were used for estimating the safety of freeways. An important characteristic associated with the development of NB models is the choice of the functional form linking crashes to the covariates. Flow to a power has been a common functional form used by transportation safety analysts in recent studies. For this study, the functional form in Equation 15 was used. Another important factor that should be considered is how to treat the dispersion parameter in the NB model. Traditionally the dispersion parameter is assumed to be fixed, but recent research in highway safety has shown that it could potentially be dependent on the covariates (12, 13, 14, 15, 16). Therefore, this study adopted the formulation proposed by Hauer (12), in which the amount of dispersion found in the data is dependent upon the segment length. The formulation for the dispersion parameter used in this study is given in Equation 16. It should be also pointed out that the dispersion parameter should be adjusted for the small sample size and low sample mean biases (17). Recent researchers have proposed methods to minimize the biases caused by these two factors (4, 18). This was not done in this work since the focus is on the coefficient of the models rather than the variation found in the data.

∑××= =

+K

kkix

iiii eFLt 10 ββ

αμ (15)

ii Le 0γφ = (16)

Where,

iμ = The estimated number of crashes for it period for site i

it = Time period for modeling (five years in this study)

iF = Flow in vehicles per day (ADT) for segment i (average of five years)

iL = Length of segment i in miles

iφ = Dispersion parameter for site i

x = A series of covariates

Kβββγα ,,,,, 100 K = Coefficients to be estimated


For model estimation the nonlinear modeling procedure (NLMIXED) in SAS (19) was utilized. As the log-likelihood, the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC) values are directly available from NLMIXED procedure, they were used to assist in selecting the best model within each model category.

MODELING RESULTS

Three separate models were estimated by using the entire dataset (1,122 horizontal curve and tangent segments), horizontal curves only (561 segments), and tangents only (561 segments). The latter two models were intended for examining whether the effects of on-ramps or off-ramps on crash occurrence are different for tangent segments than horizontal curves. It is believed that using matched sections should control for the effects of those variables that are similar between the pairs. Variable selection for inclusion in each model was carried out along with different combinations of the variables. At first, the research team started with all variables collected, and then removed the variables if they were not significant at 5% significance level. During this selection process, inside shoulder widths and median width were summed to generate median width with shoulders. When off-ramp density was tested, it was removed from the models because it generally had a p-value of 0.15 or greater indicating that it is not statistically significant. Since the initial evaluations indicated that the number of lanes with whether the segment was located in a rural or urban area was significant, indicator variables representing the urban/rural classification along with the number of lanes were included in the model. Rural 4 lane freeway was used as a base condition. Table 5 shows the final results for three models. The results indicate that crashes on freeway segments are influenced by the ADT, the on-ramp density (for horizontal curves and when horizontal and tangent sections are considered together), the degree of curvature, the width of the median (including the inside shoulder width), the number of lanes (for urban freeways), and whether the freeway is in an urban or rural area. ADT, on-ramp density, and degree of curvature had positive coefficient which indicates that as those values increase the number of crashes also increase. The negative sign for the median width indicates that crashes decrease as the median width increases, which is a desirable finding.


Table 5 Modeling results for freeway crashes Parameter Estimate Standard

ErrorP-value Criteria

Tangents and Horizontal Curves (1122 segments) Intercept

ADTOn_ramp_density

CurvatureMedian_w_swdth

Urban_lane4Urban_lane6Urban_lane8

Dispersion (γ0)

-9.03070.97430.03210.1096

-0.00460.43140.26960.69162.0888

0.46690.04620.01170.03290.00110.07310.11020.12880.0665

<.0001<.00010.00600.0009<.0001<.00010.0146<.0001<.0001

Deviance value = 1244.2Deviance/DF = 1.1169

Pearson Chi-Square =1915.7Pearson Chi-Square/DF = 1.7196

Degrees of freedom = 11142 log-likelihood = -5733.9

AIC = 5751.9 BIC = 5797.1

Horizontal Curves (561 segments) Intercept

ADTOn_ramp_density

CurvatureMedian_w_swdth


Dispersion (γ0)

-8.0962 0.8617 0.0393 0.1997

-0.0031 0.4314 0.3687 0.7851 2.1538

0.62990.06210.01540.05330.00160.09950.15120.17590.0934

<.0001<.00010.01080.00020.0507<.00010.0150<.0001<.0001




AIC = 2908.8BIC = 2947.8

Tangents (561 segments) Intercept

ADTOn_ramp_densityMedian_w_swdth


Dispersion (γ0)

-10.3061 1.1084 0.0224

-0.0057 0.4023 0.1479 0.5673 2.0689

0.69470.06900.01750.00160.10740.15960.18800.0950

<.0001<.00010.19910.00040.00020.35450.0027<.0001




AIC = 2838.5BIC = 2873.1

NOTE: Urban_lane4/Urban_lane6/Urban_lane8 – indicator variables for urban 4, 6, and 8-or-more lane freeways, respectively (1 if present, 0 otherwise); On_ramp_density – on-ramp density (# of on-ramps/mile); Curvature – degree of curvature for horizontal curve (degrees); Median_w_swdth – median width including inside should width (ft); ADT – average daily traffic (vehicle/day).

The coefficients for the indicator variables used to account for rural versus urban area and number of lanes can be used to compare the predicted crashes. The model uses rural 4-lane freeways as the base condition. Comparative crash predictions can be generated by assuming a crash prediction for rural 4-lane freeways as having a value of 1 and the predictions for the other area type/number of lanes determined by using e to the power of the coefficient:


• Rural, 4-lane freeway = 1.00 (base condition) • Urban, 4-lane freeway = 1.54 (=e0.4314) • Urban, 6-lane freeway = 1.31 (=e0.2696) • Urban, 8-and-more-lane freeway = 2.00 (=e0.6916)

The comparison reveals that urban freeways have more crashes than rural freeways. This comparison was expected. The results also shows that 6-lane urban freeways have fewer crashes than 4-lane urban freeways, which could also be expected since the additional lane per direction provides more space for vehicles at a given ADT level. Since 8-and-more-lane freeway has even more pavement width than the 6-lane freeway, one expectation was that it would have fewer crashes than the urban, 4-lane freeway. The results indicated, however, that urban 8-and-more-lane freeways had twice the number of crashes as the rural 4-lane freeway. Freeways with 8-and-more-lanes are associated with highly developed areas and the variable may be a surrogate for other conditions present, such as aggressive drivers or larger number of lane change maneuvers. Note that these predictions assume all other characteristics are the same, for example, same ADT, same on-ramp density, etc. The assumption of the same ADT is important since these facilities have large variations in their associated ADTs. The large variations also limit this observation since the volume levels present at urban 8-and-more-lanes freeways are not common on rural freeways. It turned out from the latter two models that on-ramp density is not significant at all at the 5% level in the model based on tangent only data, while it is highly significant for horizontal curves. This indicates that, assuming everything else the same, the vehicles driving on the horizontal curves are more influenced by the presence of the on-ramps and thereby have a higher likelihood of being involved in crashes than on tangent sections. Thus, it is desirable that designers for freeways should eliminate or minimize the number of on-ramps within the horizontal curves. On the other hand, Figure 2 shows a comparison between the modeling results from this study and the previous research listed in Table 1. The models developed using indicator variables for area type and number of lanes provides a comprehensive representation of the variables and geometric configurations considered in this research effort. The model developed based on the entire dataset (1,122 segments) is represented in the graphs. For rural freeways and urban four-lane freeways, the Texas models predicted higher number of severe crashes. For urban six-lane freeways, the Texas models predicted more crashes at lower ADT values and less crashes at the higher ADTs.


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Figure 2 Severe crash frequencies for freeways (Assume 1.0-mile segment length)

ACCIDENT MODIFICATION FACTORS

An AMF represents the change in safety when a particular geometric design element changes in size from one value to another. An AMF greater than 1.0 represents the situation where the design change is associated with more crashes while an AMF less than 1.0 indicates fewer crashes. In this study, the AMFs were estimated directly from the coefficients of the models, derived in the previous section. This approach for AMF development assumes that (a) each AMF is independent since the model parameters are assumed independent and (b) the change in crash


frequency is exponential. In practice, AMFs may not be completely independent, since changes in geometric design characteristics on highways are not done independently (e.g., lane and shoulder width may be changed simultaneously) and the combination of these changes can influence the crash risk. Nonetheless, experience in deriving AMFs in this manner indicates that the assumptions are reasonable and, with thoughtful model development, the resulting AMFs can yield useful information about the first-order effect of a given variable on safety. Others who have used this approach for developing AMFs include Lord and Bonneson (20) and Washington et al. (21). AMF for Ramp Density An objective of this research effort was to identify the effects of on ramp or off ramps on freeway segment crashes and whether that effect is different for tangents than horizontal curves. Since the off-ramp density was found to be a non-significant variable when building safety prediction models for freeways, we only suggest the accident modification factor for on-ramp density. If a general AMF is desired for freeways in both rural and urban areas, the coefficient from the model using the entire dataset in Table 5 is recommended. AMFOnD(all) = e0.0321 (OnD) (17) Where: AMFOnD(all) = Accident modification factor for freeway on-ramp density based on all freeway

segments available for evaluation OnD = On-ramp density, both directions (on ramps/mi) If an AMF that is more specific to the area type and number of lanes is desired, then the coefficient from the specific area type/number of lane model should be used. To this end additional models were estimated for each area type/number of lane category using both the horizontal curves and their associated tangent segments. Each category comprised 512 segments for rural 4-lane freeways, 280 segments for urban 4-lane freeways, 192 segments for urban 6-lane freeways, and 138 segments for urban 8-or-more-lane freeways. The modeling results were not provided due to space constraints, but the findings are summarized here. The results indicated that crash prediction for rural freeways was not a function of ramp density. A review of the distribution of on-ramp density revealed that, as expected, on-ramp density was lower for the rural sites than the urban sites. Levels of on-ramp density that would be expected to influence crash predictions are more common for urban freeways than rural freeway. For urban freeways, however, crash prediction was a function of either on- or off-ramp density for urban four-lane freeways (at a 10% significance level) and a function of on-ramp density for urban eight-or-more-lane freeways. The coefficients were 0.0456 for urban four-lane freeways and 0.0492 for


urban eight-or-more-lane freeways. Surprisingly on-ramp density was not significant for urban six-lane freeways. Figure 3 shows the AMFs calculated using the different approaches. For example, 3 on-ramps/mile is associated with a 10 percent increase in crashes (AMF=1.10) for a general freeway segment, 13 percent more crashes on freeway horizontal curves, 15 percent more crashes on an urban four-lane segment, or 16 percent more crashes on an urban eight-or-more-lane segment. Note that the on-ramp density findings for urban four-lane freeways were significant at the 10 percent level – usually the 5 percent level is preferred. Because of the mixed results obtained when using unique models for each area type/number of lane combinations, the results using the entire dataset appears to be more reasonable.

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Urban/rural, all num lanes, tangent & horizontal curves, coef=0.0321, p-value=0.0060

Figure 3 Comparisons of AMFs for on-ramp density

AMF for Horizontal Curve Two approaches were considered to develop an accident modification factor for horizontal curves. The first approach is to use a regression coefficient of the degree-of-curvature variable, which was already obtained in Table 5. The second one is, following the suggestion by Bonneson and Pratt (10), to derive the AMF based on the models which include the interaction between the speed and the curve radius. For the second approach, the effect of speeds may be


appreciated by using the Speed_Limit_Max variable which is contained in the TxDOT database. However, this is not a direct measurement of the operating speed on the horizontal curve. Due to such uncertainty associated with that variable, the values of the coefficients from this approach may need additional study. For this reason, the horizontal curve based on the first approach is provided in this paper. The degree-of-curvature variable was significant when using all the freeway data in one model with number of lanes and area type being represented as indicator variables (see Table 5). Therefore, assuming zero degree as a base condition, the AMF for horizontal curve would be: AMFHC = e0.1096 (CD) (18) Where, AMFHC = accident modification factor for horizontal curve on freeways CD = degree of curvature = 5730/R When separate models were estimated for each area type/number of lane category, the degree of curvature was significant for the rural, four-lane freeways at the 5% significance level, was significant for the urban, four-lane freeways at the 10% level, and was not significant for urban, six- or eight-or-more-lane freeways. This observation may indicate that the influence of degree of curvature decreases as the number of lanes (and, perhaps, associated congestion) increase. Unlike on-ramp density, the distribution of degree of curvature was similar for all area type/number of lanes combinations. About 80 percent of each dataset included 2 degree curves or flatter; therefore, the urban, six- or eight-or-more-lane freeway dataset did not include a notable difference in the degree of curvature value. Figure 4 illustrates comparisons between AMFs developed for horizontal curves using different approaches. The figure compares the previously developed model (see Equation 14) by Bonneson and Pratt (10); the findings using rural, divided multilane highway data (22), curve is labeled “Highway”; the findings from this study considering area type/number lanes through the use of indicator variables (labeled “Freeway”); and the findings from additional models for each area type/number of lane combinations. The results have similar patterns with the curve based on rural four-lane data producing notable higher AMFs. For example, a 3000 ft radius curve would have an AMF of 1.96 for rural four-lane freeway, 1.26 for urban 4-lane freeways, and 1.23 when both area type and all number of lane combinations are considered as compared to an AMF of 1.17 determined for rural highways. Note that the graph shows radii up to 18,000 ft which was selected to provide an appreciation of the prediction for a near tangent section. The limits of the data were:


• highway data: 0.25 to 15 degrees (22,920 ft to 382 ft) • freeway data: 0.25 to 5.5 degrees (11,460 ft to 1,042 ft)

As shown in Figure 4, the AMF developed using only the rural four-lane freeway data produces an AMF that is much larger than the values developed from the other datasets. Because this variable was the only variable included in the model, it may be accounting for other conditions at the site not successfully capture with the variables collected in this study. Since the results from Equation 18 appear to be in good agreement with the results from other models and previous study, this equation is recommended for the horizontal curve AMF. However, as mentioned before, it should be noted that the effect of speed cannot be distinguished using this equation.

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Highways (all area type/number of lanes), coeff=0.0831, p-value=0.0312Freeway (all area type/number lanes), coef=0.1096, p-value=0.0009Urban 4 Lane Freeway Model, coeff=0.1208, p-value=0.0898Rural 4 Lane Freeway Model, coeff=0.3528, p-value=<0.0001Bonneson&Pratt, V=60Bonneson&Pratt, V=70

NOTE: Development of the Bonneson&Pratt curves is discussed in (10) and the highway curve material is presented in (22). The freeway curve is based on the results listed in Table 5 while the urban four-lane model and rural four-lane model curves are based on the additional models not presented in this paper.

Figure 4 Comparisons of AMFs for horizontal curves


SUMMARY

The objective of this study was to investigate the safety effects of ramp density and horizontal curves on freeway crashes and to quantify the safety through the accident modification factors. Data available for use in the evaluation included 324.3 centerline miles of freeways in Texas. Negative binomial regression models were used to estimate the effects of independent variables. Variables considered in developing the base models included on-ramp/off-ramp densities, outside shoulder with, median width including the inside shoulder, barrier presence, degree of curvature (or curve radius), segment length, and ADT. Five years (1997-2001) of freeway crashes were examined. Three models were estimated for the entire dataset (horizontal curves plus tangent sections), horizontal curves only, and tangent sections only. Indicator variables representing the urban/rural classification along with the number of lanes were used in the model because of the mixed results for on-ramp/off-ramp densities when using unique models for each area type/number of lane combinations. Off-ramp density was removed from the modeling efforts because it generally produced a high p-value indicating that it was not significant at 5% significance level. The first model indicated that crashes on freeway segments were associated with ADT, on-ramp density, degree of curvature, median width including the inside shoulder, number of lanes (for urban freeways), and whether the freeway is in an urban area or rural area. Reviewing the last two models with respect to on-ramp density revealed that the effect of on-ramp density was significant for horizontal curves but not for tangent sections. It was also significant for some urban models but not the rural model. The on-ramp density and horizontal curve AMFs determined using the entire dataset was recommended. The derived AMF functions were provided in Equation 17 and 18, respectively. Regarding the AMF for a freeway horizontal curve, although a previous study developed a suggested AMF that included speed, because of the uncertainties associated with the speed-limit-max variable in the database, the horizontal curve AMF based on degree-of-curvature only was recommend from the two approaches considered. Additional evaluations regarding the inclusion of speed in a horizontal curve AMF may be necessary in the future work in order to incorporate the effect of speed on the curve.

ACKNOWLEDGMENTS

This report is based on research sponsored by the Texas Department of Transportation and the U.S. Department of Transportation, Federal Highway Administration (FHWA). The research was performed at the Texas Transportation Institute. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein. The


contents do not necessarily reflect the official views or polices of TxDOT or FHWA. The authors gratefully acknowledge the thoughts and comments provided by Jim Bonneson during the development of this paper. The authors also appreciate the comments provided by Elizabeth Hilton who served as the TxDOT project director for the study.

REFERENCES

1. A Policy on Geometric Design of Highway and Streets. American Association of State Highway and Transportation Officials, Washington, D.C., 2001.

2. NCHRP Report 374: Effect of Highway Standards on Highway Safety. Transportation Research Board, National Research Council, National Academy Press, Washington, D.C., 1995.

3. Bonneson, J., K. Zimmerman, and K. Fitzpatrick. Interim Roadway Safety Design Workbook. FHWA/TX-06/0-4703-P4. Texas Transportation Institute. College Station. April 2006.

4. Bonneson, J., K. Zimmerman, K. Fitzpatrick. Roadway Safety Design Synthesis. FHWA/TX-05/0-4703-P1. Texas Transportation Institute. College Station. November 2005.

5. Hadi, M.A., J. Aruldhas, L-F. Chow, and J.A. Wattleworth. Estimating Safety Effects of Cross-Section Design for Various Highway Types Using Negative Binomial Regression. In Transportation Research Record: Journal of the Transportation Research Board 1500. Transportation Research Board, Washington, DC. 1995, pp. 169-177.

6. Persaud, B., and L. Dzbik. Accident Prediction Models for Freeways. Transportation Research Record: Journal of the Transportation Research Board, No. 1401. Transportation Research Board, Washington, DC. 1993, pp. 55-60.

7. Wang, J., W.E. Hughes, and R. Steward. Safety Effects of Cross-Section Design for Rural, Four-Lane, Non-Freeway Highways. Report No. FHWA-RD-98-071. Federal Highway Administration, Washington, D.C. May 1998.

8. Caliendo, C. M. Guida, A. Parisi. A Crash-Prediction Model for Multilane Roads. Accident Analysis & Prevention, Vol. 39, 2007, pp. 657-670.

9. Lord, D., S. R. Geedipally, B.N. Persaud, S.P. Washington, I. van Schalkwyk, J. N. Ivan, C. Lyon, and T. Jonsson. Methodology for Estimating the Safety Performance of Multilane Rural Highways. NCHRP Web-Only Document 126, 2008. (http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp w126.pdf, accessed on June 3 2008).

10. Bonneson, J. and M. Pratt. Calibration of Safety Prediction Models and AMFs for Urban & Suburban Arterial Street Segments in Texas. Draft Technical Memorandum No. 14. TxDOT Project 0-4703. Texas Transportation Institute, College Station, March 2008.


11. Bonneson, J., D. Lord, K. Zimmerman, K. Fitzpatrick, and M. Pratt. Development of Tools for Evaluating the Safety Implications of Highway Design Decisions. FHWA/TX-07/0-4703-4, Texas Transportation Institute, College Station, 2007.

12. Hauer, E. Overdispersion in Modeling Accidents on Road Sections and in Empirical Bayes Estimation. Accident Analysis & Prevention, Vol. 33, No.6, 2001, pp. 799-808.

13. Heydecker, B.G., J. Wu. Identification of Sites for Road Accident Remedial Work by Bayesien Statistical Methods: An Example of Uncertain Inference. Advances in Engineering Software, Vol. 32, 2001, pp. 859-869.

14. Lord, D., S.P. Washington, and J.N. Ivan. Poisson, Poisson-Gamma and Zero Inflated Regression Models of Motor Vehicle Crashes: Balancing Statistical Fit and Theory. Accident Analysis & Prevention. Vol. 37, Number 1, 2005, pp. 35-46.

15. Miaou, S.-P., and D. Lord. Modeling Traffic-Flow Relationships at Signalized Intersections: Dispersion Parameter, Functional Form and Bayes vs Empirical Bayes. Transportation Research Record: Journal of the Transportation Research Board, No. 1840, 2003, pp. 31-40.

16. Lord, D., A. Manar, and A. Vizioli. Modeling Crash-Flow-Density and Crash-Flow-V/C Ratio for Rural and Urban Freeway Segments. Accident Analysis & Prevention. Vol. 37, Number 1, 2005, pp. 185-199.

17. Lord, D. Modeling Motor Vehicle Crashes using Poisson-gamma Models: Examining the Effects of Low Sample Mean Values and Small Sample Size on the Estimation of the Fixed Dispersion Parameter. Accident Analysis & Prevention, Vol. 38, No. 4, 2006. pp. 751-766.

18. Park, B.-J., and D. Lord. Adjustment for the Maximum Likelihood Estimate of the Negative Binomial Dispersion Parameter. Transportation Research Record: Journal of the Transportation Research Board, No. 2061, 2008, pp. 9-19.

19. SAS Institute Inc. Version 9 of the SAS System for Windows. Cary, NC, 2002. 20. Lord, D., and J.A. Bonneson. Development of Accident Modification Factors for Rural

Frontage Road Segments in Texas. Transportation Research Record: Journal of the Transportation Research Board, No. 2023, 2007, pp. 20-27.

21. Washington, S.P., B.N. Persaud, C. Lyon, and J. Oh. Validation of Accident Models for Intersections. Report No. FHWA-RD-03-037, Federal Highway Administration, Washington, D.C. 2005.

22. Fitzpatrick, K., D. Lord, and B-Y. Park. Horizontal Curve Accident Modification Factor with Consideration of Driveway Density on Rural, Four-Lane Highways in Texas. Draft Technical Memorandum No. 15. TxDOT Project 0-4703, Texas Transportation Institute. College Station, May 2008.

Documents

Evaluating Safety Effects of Ramp Density and …...shown similar results for curve density AMF and the method documented in Bonneson et al. (4). Bonneson et al. (4) reviewed several