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Publication Number: FHWA-RD-98-133
Date: October 1998

Accident Models for Two-Lane Rural Roads: Segment and Intersections

4. Analysis

New Variables

Accident Variables

Accident data for all data sets includes information on severities. So, in addition to the variable TOTACC for all non-intersection accidents along a segment and all intersection accidents within 250 feet of an intersection, a variable, INJACC, excluding property damage only accidents was introduced. INJACC counts fatal accidents and the various types of injury accidents (fatal + injury + non-incapacitating + possible injury). In the case of Minnesota some logistic modeling of severities was also done to determine the probability that an accident is severe. This made use of a severity variable Y defined on an accident database developed at the same time as the Minnesota segment and intersection data sets. This variable had value 1 if an accident was in one of the first two classes (fatal or injury) and value 0 otherwise (non-incapacitating, possible injury, or property damage only).

Run-off-road accidents are described by the variable RORACC. In Minnesota this is the sum of run-off-road left accidents and run-off-road right accidents. In Washington it was obtained indirectly from the HSIS variable V1EVENT2, as explained earlier.

Traffic Variables

A variable seg_lng, representing segment length in miles, is used to develop an exposure variable EXPO for segments. Seg_lng is obtained from true_beg and true_end in Minnesota and from begmpr and endmpr in Washington data (begmpr and endmpr are begmp and endmp with 250 feet removed if the segment begins or ends at an intersection). The variable EXPO is then given by:

The units of EXPO are millions of vehicle-miles (MVM).

The Minnesota and Washington intersection traffic variables are ADT1 and ADT2. These represent estimated average daily traffic on the major and minor road, respectively. As noted already, for Minnesota these variables are derived by applying growth factors to the Minnesota traffic variables, which tend to be somewhat out of date. In addition, a variable CINDEX, conflict index, is used for Minnesota intersection accident severity modeling. CINDEX is defined to be the ratio of average daily traffic entering the intersection from the minor road to average daily traffic entering the intersection from both minor and major road. CINDEX is given by:

Commercial traffic is represented in both segment and intersection databases by the variable T:

Horizontal Alignment Variables

For horizontal curves DEG{i}, the degree of curve in degrees per hundred feet, is an important variable. It was present in the Minnesota data, while in the Washington data it had to be computed from the familiar formula:

where the radius is in feet.

Various criteria were considered to determine how horizontal curves that were not entirely within a segment would be treated. One possible approach was to restrict attention to horizontal curves whose midpoints lie in the segment. This possibility was explored. However, the approach ultimately adopted was to regard a horizontal curve as eligible if any portion of it overlapped the segment. Variables associated with individual eligible horizontal curves are:

where seg_lngh is the segment length increased by adding on any portions of horizontal curves that fall outside the segment. These dimensionless weights are two different ways of taking into account the fact that horizontal curves may lie partly inside a segment and partly outside (or can even properly contain the segment). If two-thirds of the curve is inside, WH{i} has a numerator equal to two-thirds the numerator of whm{i} while the latter has a denominator equal to the denominator of WH{i} plus one-third the curve length plus lengths of portions of any other horizontal curve that lie outside. These weights are intrinsically non-negative, summing to a number less than or equal to 1.

Although in the final model for segments the variable WH{i} appears explicitly and each horizontal curve makes a separate contribution, in general the curves have to be aggregated in some fashion. The following aggregate variables are used in some segment models:

For the study of horizontal curves at intersections, each intersection was treated as a segment extending ± 250 feet along the major road from the intersection center or sometimes ± 764 feet. Two hundred fifty feet (or approximately 75 meters) is a typical length of an acceleration lane onto the major road, while 764 feet (approximately 233 meters) is a typical distance required for a vehicle turning onto a major road from a minor leg to achieve reasonable speed. Horizontal curves were considered eligible if they met this artificial segment. Aggregate variables of the following form were considered:

where the sum is over the corresponding curves. HI and HEI (E for extended) are the unweighted averages of the degrees of curvature of the corresponding curves.

Vertical Alignment Variables

Vertical alignment variables are subject to some of the same considerations as horizontal alignment variables.

A basic variable associated with each vertical curve is V{j}:

with units of percent per hundred feet. Change of grade g{j} equals g{j} - g{j+1} for the Minnesota data and g{j} - h{j} for the Washington data and l{j} is the length of the curve in hundreds of feet. Likewise a weight is associated with each individual curve that meets a segment, namely WV{j}:

The aggregate variables VC, VM, VMC, and VMCC were used for segment models:

Crest curves are vertical curves for which the grade decreases (positive to negative, positive to less positive, negative to more negative), and crests of type I are crests for which the grade changes sign. The last three variables are unweighted averages of the V{j} variable, and their denominators equal seg_lng plus the length of portions of the corresponding curves that lie outside the segment. The units of the denominators are miles. Variables for sag curves, for vertical curves with grade increases, and for sags of type III (with sign change) were also considered separately in Minnesota, but were not as significant as the crest variables.

For intersections three vertical variables were considered:

These sums are over the stipulated vertical curves, and hence VCI, VI, and VEI are unweighted averages of V{j} for each type of curve.

Complementary to vertical curves are sections of uniform grade and these also were used in the modeling for Minnesota and Washington segments. On such sections there is a constant absolute grade GR{k}. In Minnesota this was readily obtainable, but in Washington there were cases where h{k-1} and g{k} did not agree. Although other options were considered, for simplicity the segment section from e{k-1} to b{k} was treated as if it were of uniform grade with absolute grade GR{k} = |(h{k-1}+g{k})/2|. In addition to GR{k}, each such section had a variable WG{k}:

A composite variable GR was defined:

where the sum is over all uniform grade sections overlapping with the segment.

Angle Variables

An angle variable DEV, representing the average deviation from 90, was defined by:

Two more angle variables are also used. DEV15 is a variable discovered empirically that seems to be negatively correlated with accidents on four-legged intersections. Another intersection angle variable considered in this study, suggested by E. Hauer, is HAU:

The variable HAU is a signed variable. See Figures 4 and 5 below. For a three-legged intersection with the angle to the right of the increasing direction, HAU is positive when the angle is larger than 90, as in 4(a), and HAU is negative when the angle is smaller than 90, as in 4(b). If the angle is to the left of the increasing direction (see Figure 5), 180 minus the angle becomes the new angle and HAU is defined as ((180 - angle) - 90) = (90 - angle), as above. For four-legged intersections, as in 4(c), it is the average of the two three-legged values (and thus 90 cancels out). Figure 5 illustrates the calculation of HAU in a variety of cases. It is thought that turns from the far lane of the major road may be less accident prone in situation 4a) than in situation 4b), so that positive values of HAU correspond to fewer accidents.

Miscellaneous Variables

Some other segment variables included in the study are TOTWIDTH, DD, INTD, STATE, and SPD:

SPD is an amalgam of advisory and posted speeds seen on some roads together with HSIS speeds. Advisory and regulatory speeds, if seen on photologs, were given preference. However, photolog speeds were not collected for some Minnesota segments, were missing for others even when the photolog was searched a few miles outside the segment, and had multiple values in some cases when seen (i.e., changes in speed along a direction, different speeds in opposing directions, a difference between regulatory and advisory speed). Minnesota HSIS speeds were for accident sites only (at the same segment or a nearby one). For Washington data, a posted speed variable was obtained from the HSIS roadway file, together with speeds for each horizontal and vertical curve from the HSIS alignment files. Averaging these to achieve a single number could not be done without some subjectivity.

Other intersection variables are RT and SPDI:

 

SPDI is an amalgam of mainline speeds observed at intersections, averaged by approach where possible.

Finally, two weather variables NONDRYP and SNP were devised for use with the Minnesota data:

 

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