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Publication Number:  FHWA-HRT-13-077    Date:  January 2014
Publication Number: FHWA-HRT-13-077
Date: January 2014

 

Safety Effects of Horizontal Curve and Grade Combinations on Rural Two-Lane Highways

CHAPTER 3—DATABASE DESCRIPTION

This chapter describes the database used in the analysis. The research was performed with HSIS data for State highways in Washington. This is the only data source that includes system-wide data on curve and grade geometry that can be linked to system-wide roadway characteristics, traffic volume, and crash data.

DATABASE DEVELOPMENT

Research began with a review of available databases that contain roadway data (including horizontal and vertical alignment), traffic volume data, and crash data in a format that could be linked by location, with a primary focus on available HSIS data. The only dataset found with sufficient detail concerning horizontal and vertical alignment was HSIS data for State highways in Washington.

Preliminary data processing was performed to identify the following types of roadways on the Washington State highway system (note that the abbreviations are used in table 2 through table 5):

Roadway segments with atypical features such as passing and climbing lanes as well as roadway segments with transitions between grades identified as angle points were eliminated from consideration. Angle points most likely represent crest or sag vertical curves that were too short or not well enough defined to be measured properly. Finally, a limited set of roadways with obvious data problems, such as successive vertical curves whose lengths appeared to overlap, were also eliminated from consideration. The descriptive statistics for the roadway data shown below are based on the roadway lengths that were retained for analysis after the initial screening.

Next, each roadway segment was classified into categories by its horizontal and vertical alignment. Horizontal alignment was classified as follows:

Vertical alignment was classified as follows:

Figure 1 illustrates the distinction between types 1 and 2 crest and sag vertical curves. Every roadway segment was defined by its horizontal alignment, vertical alignment, and combination of horizontal and vertical alignments. Since there were two horizontal alignment categories and six vertical alignment categories, there were a total of 12 possible combinations of horizontal and vertical alignments. Where horizontal and vertical curves overlap, their beginnings and ends may not coincide; therefore, a new roadway segment began at any point where the horizontal or vertical alignment changed. Thus, some segments might include all of a horizontal or vertical curve, while others might include only part of a horizontal or vertical curve. The length of every roadway segment was determined for use in the analysis as well as the length of any horizontal curve that was wholly or partially within the segment and the length of any vertical curve (LVC) that was wholly or partially within the segment. Additionally, each horizontal curve was characterized by its radius. No data on the superelevation of horizontal curves were available for analysis. Each straight grade was characterized by its percent grade (G). Each vertical curve was characterized by its approach grade (G1) and departure grade (G2), its algebraic difference in grade (A = abs(G1 – G2)) [A = abs(G1 – G2 )]*, and the ratio of its length to its algebraic difference in grade (K = LVC/A).

*Modified on November 16, 2014

Crash data for a 6 year period (2003 to 2008) were obtained and used in the analysis. Each crash was assigned to a particular roadway segment, with particular horizontal and vertical alignment based on its assigned milepost location. Since the results of this research are intended for use in the roadway segment procedures of the AASHTO HSM, only nonintersection crashes were considered. Nonintersection crashes are those that did not occur at an intersection and were not classified by the investigating officer or data coder as related to the operation of an intersection. The traffic volume for each roadway segment was determined from available traffic volume data.

Some of the roadway segments included in the analysis may have contained minor intersections, but crashes occurring at or related to those intersections have been excluded from the analysis. No major intersections were included within a roadway segment because a change in traffic volume along the roadway would have led to the creation of a roadway segment boundary.

Driveway crashes are considered roadway segment crashes. As a result, they were included in the analysis. The amount of driveway access within segments may have varied, but all of the segments were located in areas classified as rural.

DESCRIPTIVE STATISTICS

The following discussion presents descriptive statistics for the roadway sections available for analysis including roadway length (miles), exposure (million vehicle miles traveled in the 6 year period (MVMT)) [million vehicle miles traveled in the 6-year period (MVMT)]*, crash frequencies, and crash rates per MVMT for specific combinations of horizontal and vertical alignment and roadway type. Roadway length, exposure, crash frequency, and crash rate are presented in table 2 through table 5, respectively.

*Modified on November 16, 2014

Of the 6,944 mi of roadway in the entire Washington HSIS database, 4,785 mi (69 percent) are on rural two-lane highways. Of these, 3,457 mi were used for analysis. Rural two-lane highways with passing or climbing lanes and segments with missing or obviously incorrect alignment data (e.g., overlapping curves) were excluded from the study. Therefore, based on data availability, the analysis of the safety effects of horizontal curve and grade combinations in this report focused on rural two-lane highways only.

Table 2. Roadway length (mi) in available data from Washington HSIS database.

Alignment Type

Roadway Element

Rural Highways

Urban/Suburban Arterials

R2U

R4D

R4U

U2U

U3T

U4D

U4U

U5T

Horizontal

Tangent

2,472.1

122.4

4.9

122.1

15.9

24.2

46.3

48.0

Curve

985.0

54.0

1.2

43.3

2.5

6.4

13.1

8.9

Total

3,457.1

176.4

6.1

165.4

18.4

30.7

59.4

56.9

Vertical

Straight grade

2,260.7

107.6

4.0

112.4

12.2

17.6

37.5

36.2

Type 1 crest

364.5

19.9

0.1

14.7

1.7

4.5

6.0

6.3

Type 2 crest

300.8

20.1

0.5

13.3

2.0

2.7

6.1

5.5

Type 1 sag

252.1

12.8

0.5

12.0

1.2

3.7

3.9

5.1

Type 2 sag

279.1

16.0

0.9

13.0

1.3

2.2

5.9

3.8

Total

3,457.1

176.4

6.1

165.4

18.4

30.7

59.4

56.9

Table 3. Exposure (MVMT) in available data from Washington HSIS database (2003–2008).

Alignment Type

Roadway Element

Rural Highways

Urban/Suburban Arterials

R2U

R4D

R4U

U2U

U3T

U4D

U4U

U5T

Horizontal

Tangent

16,675.2

3,648.2

113.5

3,228.2

483.5

1,408.2

2,613.9

2,826.3

Curve

6,194.2

1,587.6

35.1

1,108.8

76.5

351.3

684.0

500.3

Total

22,869.5

5,235.8

148.6

4,336.9

560.0

1,759.5

3,297.9

3,326.5

Vertical

Straight grade

14,847.0

3,216.5

91.6

2,894.0

366.8

991.4

2,072.1

2,091.4

Type 1 crest

2,616.4

636.6

2.3

398.3

54.3

265.9

341.4

375.6

Type 2 crest

1,870.5

521.2

11.9

364.1

62.4

162.4

341.5

322.7

Type 1 sag

1,772.6

392.6

23.4

344.5

38.0

209.3

227.4

309.4

Type 2 sag

1,762.9

469.0

19.4

336.0

38.5

130.5

315.5

227.4

Total

22,869.5

5,235.8

148.6

4,336.9

560.0

1,759.5

3,297.9

3,326.5

Table 4. Fatal and injury (FI), property damage only (PDO), and total 6 year crash frequencies in available data from Washington HSIS database.

Alignment Type

Roadway Element

Rural Highways

Urban/Suburban Arterials

R2U

R4D

R4U

U2U

U3T

U4D

U4U

U5T

FI Crash Frequencies in 6 Years (2003–2008)

Horizontal

Tangent

7,360

865

77

2,564

335

1,557

5,100

2,867

Curve

3,659

353

11

772

55

406

1,017

245

Total

11,019

1,218

88

3,336

390

1,963

6,117

3,112

Vertical

Straight grade

7,347

740

63

2,313

260

1,291

3,570

2,117

Type 1 crest

1,168

125

1

260

25

262

634

323

Type 2 crest

826

97

5

292

39

156

780

222

Type 1 sag

896

108

4

235

29

101

577

304

Type 2 sag

782

148

15

236

37

153

556

146

Total

11,019

1,218

88

3,336

390

1,963

6,117

3,112

PDO Crash Frequencies in 6 Years (2003–2008)

Horizontal

Tangent

10,519

1,403

213

3,753

519

2,841

9,012

4,323

Curve

4,758

621

14

1,264

77

741

1,800

426

Total

15,277

2,024

227

5,017

596

3,582

10,812

4,749

Vertical

Straight grade

10,222

1,273

185

3,451

401

2,259

6,250

3,315

Type 1 crest

1,498

229

10

397

55

527

1,208

461

Type 2 crest

1,264

162

4

437

64

310

1,390

333

Type 1 sag

1,154

177

13

383

37

227

1,037

402

Type 2 sag

1,139

183

15

349

39

259

927

238

Total

15,277

2,024

227

5,017

596

3,582

10,812

4,749

Total Crash Frequencies in 6 Years (2003–2008)

Horizontal

Tangent

17,879

2,268

290

6,317

854

4,398

14,112

7,190

Curve

8,417

974

25

2,036

132

1,147

2,817

671

Total

26,296

3,242

315

8,353

986

5,545

16,929

7,861

Vertical

Straight grade

17,569

2,013

248

5,764

661

3,550

9,820

5,432

Type 1 crest

2,666

354

11

657

80

789

1,842

784

Type 2 crest

2,090

259

9

729

103

466

2,170

555

Type 1 sag

2,050

285

17

618

66

328

1,614

706

Type 2 sag

1,921

331

30

585

76

412

1,483

384

Total

26,296

3,242

315

8,353

986

5,545

16,929

7,861

Table 5. FI, PDO, and total crash rates per MVMT in available data from Washington HSIS database.

Alignment Type

Roadway Element

Rural Highways

Urban/Suburban Arterials

R2U

R4D

R4U

U2U

U3T

U4D

U4U

U5T

FI Crash Rate per MVMT

Horizontal

Tangent

0.441

0.237

0.679

0.794

0.693

1.106

1.951

1.014

Curve

0.591

0.222

0.313

0.696

0.719

1.156

1.487

0.490

Vertical

Straight grade

0.495

0.230

0.688

0.799

0.709

1.302

1.723

1.012

Type 1 crest

0.446

0.196

0.432

0.653

0.460

0.985

1.857

0.860

Type 2 crest

0.442

0.186

0.421

0.802

0.625

0.961

2.284

0.688

Type 1 sag

0.505

0.275

0.171

0.682

0.763

0.483

2.537

0.982

Type 2 sag

0.444

0.316

0.775

0.702

0.961

1.173

1.762

0.642

PDO Crash Rate per MVMT

Horizontal

Tangent

0.631

0.385

1.877

1.163

1.073

2.017

3.448

1.530

Curve

0.768

0.391

0.399

1.140

1.007

2.110

2.632

0.852

Vertical

Straight grade

0.688

0.396

2.020

1.192

1.093

2.279

3.016

1.585

Type 1 crest

0.573

0.360

4.323

0.997

1.012

1.982

3.539

1.227

Type 2 crest

0.676

0.311

0.337

1.200

1.025

1.909

4.070

1.032

Type 1 sag

0.651

0.451

0.555

1.112

0.974

1.085

4.560

1.299

Type 2 sag

0.646

0.390

0.775

1.039

1.013

1.985

2.938

1.047

Total Crash Rate per MVMT

Horizontal

Tangent

1.072

0.622

2.556

1.957

1.766

3.123

5.399

2.544

Curve

1.359

0.614

0.712

1.836

1.726

3.265

4.118

1.341

Vertical

Straight grade

1.183

0.626

2.707

1.992

1.802

3.581

4.739

2.597

Type 1 crest

1.019

0.556

4.755

1.649

1.472

2.967

5.396

2.087

Type 2 crest

1.117

0.497

0.758

2.002

1.650

2.870

6.354

1.720

Type 1 sag

1.156

0.726

0.726

1.794

1.737

1.567

7.097

2.282

Type 2 sag

1.090

0.706

1.550

1.741

1.975

3.158

4.701

1.689

     Note: Crash rates cannot be added; therefore, no totals are shown.

The majority of rural two-lane roadway segments included in the analysis experienced no crashes in the 6 year period. Table 6 shows the percentage of roadway segments with no crashes and with one or more crashes for each roadway and severity type. The data clearly show the highly skewed crash distribution for all severity types and all roadway types. The high percentages of roadway segments without crashes (78 to 89 percent for FI crashes and 72 to 84 percent for PDO crashes) provided a challenge in modeling crash frequencies.

Table 6. Percent of sections with and without crashes on rural two-lane highways in available data from Washington HSIS database (2003–2008).

Vertical and Horizontal Alignment Combination

FI Crashes

PDO Crashes

Total Crashes

Percent of Sections With:

Zero Crashes

1+ Crashes

Zero Crashes

1+
Crashes

Zero Crashes

1+
Crashes

Straight grade

Horizontal curve

84

16

81

19

72

28

Tangent on nonlevel grade

84

16

79

21

71

29

Type 1 crest

Horizontal curve

84

16

82

18

73

27

Tangent on nonlevel grade

84

16

80

20

72

28

Type 2 crest

Horizontal curve

88

12

84

16

78

22

Tangent on nonlevel grade

89

11

84

16

78

22

Type 1 sag

Horizontal curve

86

14

84

16

76

24

Tangent on nonlevel grade

86

14

83

17

75

25

Type 2 sag

Horizontal curve

86

14

84

16

76

24

Tangent on nonlevel grade

86

14

83

17

75

25

Level tangent

Level tangent

78

22

72

28

63

37

VALUE RANGE OF ROADWAY CHARACTERISTICS

Prior to statistical modeling, the parameters of interest were assessed for extreme values (both high and low). This was done using a combination of plots of crash rates per MVMT versus selected parameters and distributions of the individual parameters. The following rules were implemented:

 

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