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This is to certify that the

dissertation entitled

Modeling Freeway Interchange Accidents

presented by 1

Tae Gon Kim \

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Civil Engineering

[Li/KW,” é’ . 42% .41

Major professor/

Date April 14, 1989

MSU is an Affirmative Action/Equal Opportunity Institution 0-12771

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TO AVOID FINES return on or before date due.

 

DATE DUE DATE DUE DATE DUE

 

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MSU Is An Affirmative Action/Equal Opportunity Institution

 

MODELING FREEWAY INTERCHANGE ACCIDENTS

BY

Taegon Kim

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

1989

56/79 2w

ABSTRACT

MODELING FREEWAY INTERCHANGE ACCIDENTS

BY

Taegon Kim

The accident frequency and rate for the various
components of freeway interchanges were identified and
compared using accident data from the State of Michigan for
the years 1982 through 1984. The accident rates at various
types of interchanges were compared, and accident predictive
algorithms for freeway interchange elements were developed.

A master data file which was composed of geometric,
accident and traffic data was constructed by merging existing
data bases. The data were then classified into 3 area types
(urban, rural and fringe) and further classified into
different types of interchanges based.on the interchange type.
The interchange types were grouped into 12 homogeneous groups
based on the accident rate and variance. Accident predictive
linear regression models were constructed and tested against
data not used in calibrating the models. An analysis was made
of those interchange groups exhibiting a value greater than
0.7 in multiple R coefficient.

Based upon the results of this study, the average
accident rates on the ramp units are greater than those on the

mainline and crossroad units; the interchange is a very

important variable in predicting accidents; the average daily
traffic (ADT) has the greatest explanatory power in predicting
the accident frequency; and interchange lighting, freeway over
or under the crossroad, and ramp control demonstrate the
potential of being important variables if sufficient data are

available to make additional stratifications.

To my mother, mother-in-law, brothers

and wife

ii

ACKNOWLEDGEMENTS

I am grateful to Dr. William C. Taylor, my major
professor, for his advice and support throughout my graduate
studies. His intimate guidance and aid throughout this
research.progranlis gratefully'appreciated” I am also grateful
to Dr. Thomas L. Maleck for his interest, advice and support
for this research. Thanks are extended to Dr. Kunwar Rajendra
and Joseph C. Gardiner of my advisory committee for their
advice and suggestions.

I would like to thank Mr. Jack D. Benac and Mr. Al Dewey
for their assistance in collecting the data from the Michigan
Department of'Transportation. Special thanks are also due Fred
Coleman for his advice and help throughout my graduate
studies.

Finally, I wish to express my deepest gratitude to
Meesook, my wife for her understanding, patience and
sacrifices, and Myunggon, my brother for his advice and

support throughout the years of my graduate studies.

iii

TABLES OF CONTENTS

Inge

LIST OF TABLES ........................................ Vi
LIST OF CHARTS ........................................ xi
LIST OF GRAPHS ........................................ xii
CHAPTER I. INTRODUCTION ............................. 1
Statement of the Problem ......................... 2
CHAPTER II. LITERATURE REVIEW ........................ 4
CHAPTER III. DATA ACQUISITION ......................... l7
III-1. Data Needed .............................. 17
III-2. Sample Size ..... ......................... 20
III-3. Unit of Analysis ......................... 24
III-4. Mathematical Inspection .................. 26
CHAPTER IV. PROCEDURE ................................ 30
Models constructed before Data Stratification .... 31

Data Stratification ..... ...... . .................. 33
IV-1. Data File Format ......................... 33
IV—Z. Summary of Results by Groups ............. 43
IV-3. Summary of Results ....................... 58
CHAPTER V. MODELS ................................... 115
Models constructed for the Mainline Unit ......... 115
Models constructed for the Crossroad Unit ........ 122
Models constructed for the On-ramp Unit .......... 126
Models constructed for the Off-ramp Unit ......... 127
Summary of Results ........ ..... ............ ...... 129
CHAPTER VI. CALIBRATION . ............................. 135
Models calibrated for the Mainline Unit .......... 135
Models calibrated for the Crossroad Unit ......... 137
Models calibrated for the On-ramp Unit ........... 140
Models calibrated for the Off-ramp Unit .......... 140
Summary of Results ............................... 140

iv

TABLES OF CONTENTS

Ikmp

CHAPTER VII. SUMMARY and CONCLUSIONS ........... . ...... 179
Summary .......................................... 179
Conclusions ...................................... 184
BIBLIOGRAPHY ........................................ .. 187

IV.2

IV.3

IV.4

IV.5

IV.6a

IV.6b

IV.6c

IV.6d

IV.6e

IV.7

LIST OF TABLES

Accident rate by proximity to interchange ahead
or behind (1)...... ...... .... ....... . ....... ....

Accident rate by interchange unit and area type

(_1_) ............................................

Accident rate by type of freeway ramp (1) ......

Comparison of factors related to accidents on
freeway interchanges .... .......................

Mean accident rate and variance by interchange
type ....................................... ....

Mean accident rate and variance by interchange
group ................................ ... .......

Classification of significance between groups
based on t-test ................................

Total number of accidents by uncollapsed
interchange elements ...........................

Total number of accidents by collapsed
interchange elements ...........................

Total number of accidents by each type accidents
and interchange elements .......................

Total number of accidents by each type accidents
and interchange elements .......................

Total number of accidents by each type accidents
and interchange elements .......................

Total number of accidents by each type accidents
and interchange elements .......................

Total number of accidents by each type accidents
and interchange elements ................. ......

Accident types by Collapsed interchange elements

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

vi

BEE

13

14

15

16

6O

61

62

63

64

65

66

67

68

69

7O

Table

IV.9
IV.10
IV.11
IV.12
IV.13
IV.14
IV.15
IV.16
IV.17
IV.18
IV.19
IV.20
IV.21

IV.22

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of urban

Accident
of rural

Accident
of rural

Accident
of rural

LIST OF TABLES

types
group 1

types
group 2

types
group 3

types
group 4

types
group 5

types
group 6

types
group 7

types
group 8

types
group 9

types
group

types
group

types
group

types
group 1

types
group 2

types by
group 3

Collapsed

interchange

elements

...............................

vii

BEE

71

72

73

74

75

76

77

78

79

80

81

'82

83

84

85

LIST OF TABLES

Table Egg
IV.23 Accident types by Collapsed interchange elements

of rural group 4 ............................ . 86
IV.24 Accident types by Collapsed interchange elements

of rural group 5 ............................... 87
IV.25 Accident types by Collapsed interchange elements

of rural group 6 ............................... 88
IV.26 Accident types by Collapsed interchange elements

of rural group 7 ............................... 89
IV.27 Accident types by Collapsed interchange elements

of rural group 8 ............................... 9O
IV.28 Accident types by Collapsed interchange elements

of rural group 9 ............................... 91
IV.29 Accident types by Collapsed interchange elements

of rural group 10 .............................. 92
IV.3O Accident types by Collapsed interchange elements

of fringe group 1 ............................... 93
IV.31 Accident types by Collapsed interchange elements

of fringe group 2 ............................... 94
IV.32 Accident types by Collapsed interchange elements

of fringe group 3 ............................... 95
IV.33 Accident types by Collapsed interchange elements

of fringe group 4 ............................... 96
IV.34 Accident types by Collapsed interchange elements

of fringe group 5 ............................... 97
IV.35 Accident types by Collapsed interchange elements

of fringe group 6 ............................... 98
IV.36 Accident types by Collapsed interchange elements

of fringe group 7 ................ . .............. 99
IV.3? Accident types by Collapsed interchange elements

of fringe group 8 ............................... 100

viii

Table
IV.

IV.

IV.
IV.
IV.

IV.

IV.

IV.

IV.

IV.

VI.

38

39

4O

41

42

43

44

45

46

47

V1.2

VI.3

LIST OF TABLES

BEE
Accident types by Collapsed interchange elements
of fringe group 9 ........ . ...................... 101
Accident types by Collapsed interchange elements
of fringe group 10 ...... .. ...................... 102
Accident types by urban groups .................. 103
Accident types by rural groups .................. 104
Accident types by fringe groups ................. 105
The average number of accidents per interchange by
units used ...................................... 106
Sample Data File ................................ 107

Comparison of the analysis units by groups based
on the highest and lowest accident rates ........ 108

The average number of accidents per interchange by
sample units .................................... 109

The average accident rate per interchange by
sample units .................................... 110

Classification of signs of variable terms used in
in the models constructed ....................... 132

Number of interchanges for each group of analysis
unit ............................................ 133

Multiple R Coefficient for each group of analysis
unit ............................................ 134

Comparison of Actual and Predicted values of
Total accident frequency in'UM-Group 3 ... ....... 143

Comparison of Actual and Predicted values of
Total accident frequency in UM-Group 5 .......... 145

Comparison of Actual and Predicted values of
Total accident frequency in RM-Group 1 .......... 147

ix

LIST OF TABLES

Table Egg
V1.4 Comparison of Actual and Predicted values of

Total accident frequency in.RM-Group 3 .......... 149
V1.5 Comparison of Actual and Predicted values of

Total accident frequency in.RM-Group 4 .......... 151
V1.6 Comparison of Actual and Predicted values of

Total accident frequency in FM-Group 2 .......... 153
V1.7 Comparison of Actual and Predicted values of

Total accident frequency in FM-Group 8 .......... 155

V1.8 Comparison of Actual and Predicted values of
Total accident frequency in FM-Group 9 .......... 157

V1.9 Comparison of Actual and Predicted values of
Total accident frequency in UC-Group 3 .......... 159

V1.10 Comparison of Actual and Predicted values of
Total accident frequency in‘UC—Group 4 .......... 161

V1.11 Comparison of Actual and Predicted values of
Total accident frequency in RC-Group 1 .......... 163

V1.12 Comparison of Actual and Predicted values of
Total accident frequency in.RC-Group 3 .......... 165

V1.13 Comparison of Actual and Predicted values of
Total accident frequency in RC-Group 6 .......... 167

V1.14 Comparison of Actual and Predicted values of
Total accident frequency in RC-Group 7 .......... 169

V1.15 Comparison of Actual and Predicted values of
Total accident frequency in RC-Group 9 .......... 171

V1.16 Comparison of Actual and Predicted values of
Total accident frequency in FC-Group 2 .......... 173

V1.17 Comparison of Actual and Predicted values of
Total accident frequency in‘UON-Group 2 ......... 175

V1.18 Comparison of Actual and Predicted values of
Total accident frequency in'UOF-Group 2 ......... 177

ME

Chart 4.1
Chart 4.2
Chart 4.3

Chart 4.4

Data file
Data file
Data file

Data file

LIST OF CHARTS

format chart .....................
set by urban groups ..............
set by rural groups ..............

set by fringe groups .............

xi

113

114

 

 

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Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph

Graph

LIST OF GRAPHS

P_ag§_
6 l ............................................. 144
6 2 ............................................. 146
6.3 ............................................. 148
6.4 ............................................. 150
6.5 ............................................. 152
6.6 ............................................. 154
6.7 ............................................. 156
6.8 ............................................. 158
6.9 ............................................. 160
6.10 ............................................ 162
6.11 ............................................ 164
6.12 ............................................ 166
6.13 ............................................ 168
6.14 ............................................ 170
6.15 ............................................ 172
6.16 ............................................ 174
6 17 ............................................ 176
6.18 ............................................ 178

CHAPTER I

INTRODUCTION

Fundamentally, an interchange simply provides an
opportunity for traffic to transfer from one road to another.
As used ixtaatmodern freeway system, an interchange plays a
very important role in providing greater capacity, maintaining
higher operating speeds, and reducing the probability of
vehicular conflicts during this transfer (1).

As the Interstate Highway Systemmwas constructed, a large
number of freeway interchanges were designed and constructed.
The design standards for these freeway interchanges, however,
were not derived from an analysis of past experience, since
there was very little past experience upon which the design
engineer could draw. Instead, most designs were modifications
of existing freeway interchanges, since substantive knowledge
for redesign of freeway interchanges was rather limited in
regard to the performance expected from individual elements
in terms of efficient traffic movement and adequate safety
(2). With many freeway systems approaching their design life,
the data are now available to evaluate the safety attributes
of various freeway configurations and various freeway elements
under traffic conditions.

Some evaluation of the geometric design and operational
characteristics of interchanges has been done using the rate

of traffic accidents as an evaluation parameter (1). However,

these safety analyses were not sufficiently detailed to allow

freeway designers to select an optimal interchange design.
STATEMENT OF THE PROBLEM

In Michigan, freeway interchanges have been in use since
the Davidson Freeway and the Ford Freeway were open to traffic
in the early 1940's. There are approximately 700 interchanges
in the state of Michigan. Of those interchanges, there are
few, if any, exactly alike. The geometric interchange designs
vary from the simple rural diamond interchange with at—grade
intersections of the ramp with the crossroad to the urban
multi-level directional freeway-to—freeway interchange with
lane drops, multi-lane turning roadways, weaving lanes, and
freeflow merges.

Research. has indicated that accident rates are not
uniform for the various interchange types or interchange
elements. One study showed that the accident rate (346/100
mvm) for a rural exit ramp is more than twice that (161/100
mvm) of a rural entrance ramp (1). Interestingly enough, the
reverse is true for urban interchanges with entrance ramps
having an accident rate (718/100 mvm) that is twice that
(378/100 mvm) of the exit ramp (1). While this study
identified accident rates for various elements of a freeway
interchange and compared those accident rates with each other,

it did not compare the accident rate at various types of

 

interchanges, nor did it establish predictive algorithms based
on design features of the freeway interchange elements.

The Michigan Department of Transportation recently
completed a geometric inventory of its freeway interchanges,
and has assigned accidents to elements. Thus, the geometric
data, accident data, and traffic data (such as traffic
volumes, population, no. of ramp lanes) could now be used to
develop standards based upon the minimization of accidents,
if models were available that expressed the relationship among
these variables.

The purpose of this analysis of interchanges in Michigan
is to: compare the accident rates in Michigan with those from
the Interstate System Accident Research Study, Interim Report
11 by Cirillo, J. A. (1); identify accident rates as they
relate to parameters of the interchange elements; and,
finally, to establish interchange accident predictive models
based upon accident rates on the elements which comprise the
interchange.

The results of this study will provide guidance as design
decisions are made during the reconstruction of the freeway

system in Michigan.

I'm...

CHAPTER II

LITERATURE REVIEW,

In an analysis of the effect of location on accident
rates on the interstate highway system, Julie A. Cirillo (1)
used data collected by 20 State Highway Departments to compare
accident rates on various roadway elements. The initial
categorization was between-interchange units and at-
interchange units respectively. These were then further
divided into urban and rural sections. Each mainline unit was
described by its proximity to an interchange. Units which were
located at. the same distance from two interchanges were
divided equally between the two study units (1).

From the results of the between-interchange accident rate
analysis, the results shown in Table 11.1 were reported. Some

of the important conclusions from this study were:

. The accident rate increased on urban sections as the study
unit was positioned closer to an exit ramp with the highest
rate occurring in those sections located less than 0.2 mile
from the exit ramp. Also, as a study unit was stationed closer
to the entrance ramp area, the accident rate increased,
although not uniformly.

. On rural sections, the change in accident rates was not
significantly altered as a unit was positioned closer to the

interchange and in the exit direction it remained constant

The results of the at-interchange accident rates as shown

in Table 11.2, indicated that:

. The accident rate for urban interchanges was substantially
higher than for rural interchanges, as these areas carried
more traffic, making merging and diverging maneuvers more
difficult.

. The exceptionally high accident rate on entrance ramps in
urban areas might be caused by inadequate acceleration lanes,
or lack of them, on many sections, necessitating vehicles to
stop at the bottom of the ramp before moving into the traffic
stream.

. The accident rate on the mainline within the interchange

area decreased after the deceleration lane had been passed

(1) -

The general conclusions of this study were that:
sections in proximity of interchanges experienced a higher
accident rate than other sections; ramps have much higher
accident rates than speed-change lanes; and these, in turn,
have generally higher rates than the other portions of the
main roadways (1).

In a study of the relationship between interchange design

features and traffic safety, Joseph C. Oppenlander and Robert

F. Dawson (1) found that:

. Relatively safer designs were produced when the mainline
freeway passed over the minor facility and when the ramp
terminals were at least 750 ft. from the structure.

. On-ramps became high accident locations in‘ urban areas,
while in rural areas the off-ramps represented the greatest
accident rate locations.

. Entrance terminals were improved with geometric designs that
provided auxiliary lanes or deceleration lanes of 800 ft. or
more. This eliminated traffic friction on the through lanes
which resulted in reduced accident rates.

. Adequate sight distances were essential at entrance and exit
terminals.

. Geometric designs for weaving maneuvers should provide

weaving sections that are at least 800 ft. in length.

In another study of accidents and design features at

interchanges, R. L. Fisher (1) found that:

. There were no accidents that could be ascribed to the
curvature on loops which had radii of over 100 ft.

. Speed-change lanes of adequate length together with careful
treatment of the terminals practically eliminated accidents
at interchanges.

. All of the left-hand entrances and exits had a poor accident

record.

In a comparative freeway study concerning alignment and
accidents at interchanges, John Vostrez and Richard A. Lundy
(1) classified the ramp alignment into 6 types. These
alignments, in order of low to high accident rates were
straight level, straight upgrade, straight downgrade, curved
level, curved.upgrade, and curved.downgrade respectively. They

found that:

. With heavy truck traffic the straight upgrade was more
detrimental than the straight downgrade while all of the
curved classifications were the same.

. Fixed objects were involved in about 28 percent of all
freeway interchange accidents. Piers, abutments and bmidge
rails were apparently the most vulnerable, with signs,
guardrails, and light standards following in that order.

. Ramps associated with diamond-type interchanges were the
safest type, and on-ramps generally had better accident rates
than off-ramps. The downhill on-ramp was the safest type of
on-ramp and the uphill off-ramp was the safest type off-ramp.
Left-hand ramps (enters or leaves the freeway at high speed

lane) had a higher accident rate than any other class.

In an analysis with regard to lighting of interchanges,

M. S. Janoff, M. Freedman, and Decina, L. E. (5) reported

that:

. Complete Interchange Lighting (CIL) systems perform better
than Partial Interchange Lighting (PIL) systems consisting of
one, two, or four luminaries.

. Either CIL or PIL normally perform better than no lighting.
. PIL systems with fewer luminaries (one or two) frequently
perform better than PIL systems with a greater number of
luminaries (four).

. There is a trade-off between cost and traffic operations and
safety factors in the design of freeway interchange lighting
systems.

. Existing CIL systems should not be reduced to PIL systems

if safety and traffic flow are important considerations.

In an investigation of factors affecting the design and
location of freeway ramps from an operational VieWpoint,

William E. Tipton and Charles Pinnel (6) indicated that:

. Standard interchange designs cannot always fulfill the
various desired movements at<iifferent interchanges. Toiobtain
the most efficient operaticwxat.a specific interchange, it may
be desirable to use a diamond type, an X-type, or possibly a
combination of both of these. The X-type interchange includes
an on-ramp upstream of the arterial street and off-ramp down-

stream. of 'the arterial street for' both the inbound and

outbound directions of travel.

. The configuration of an off-ramp located upstream of an on-
ramp has considerable advantages over the reverse
configuration. The studies indicated that an approximately 50
to 70 percent increase in on-ramp capacity could be obtained
by removing traffic in advance of adding traffic to the
freeway.

. The construction of stacked ramps rather than an off-ramp
upstream of an on-ramp was not generally feasible due to the
high cost, the lack of potential for stage construction and
the additional right-of—way required. The stacked ramps,
however, offer the advantages of elimination of‘weaving on the
frontage road and less distance (approximately 460 ft.)
required along the freeway to fit in the design.

. The type of interchange layout which has an off-ramp located
upstream of an on-ramp both upstream and downstream of the
arterial street is the most desirable. The exception would
exist when the freeway capacity is reduced by this design as

the freeway crosses the arterial street.

In a study of safety and operational requirements for

interchanges (1), it was found that:

. Simple ramps (such as the diamond ramp, the Cloverleaf ramp
with C-D roads, and direct connections) can reduce the

accident rates as shown in Table 11.3.

. Sufficient advance information on the type of interchange
exit pattern ahead and path which a driver must follow to
reach his desired destination should be provided.

. The relative safety of entrance terminals is enhanced with
geometric designs that provide a long acceleration lane or
auxiliary lanes, adequate sight.distances for both freeway and
ramp drivers, and freeway lanes on downgrades.

. The types of accidents that occur in the area of the exit
terminal can be reduced if the design of entrance and exit
terminals provides adequate speed—change lanes, control of
access, and.proper sight.distances to encourage smooth traffic

flow at proper operating speeds.

Based upon the literature review, the results are
summarized as shown in Table 11.4. An "X" represents that
researches agree with each other on that factor. From the

results in Table 11.4, it might be summarized that:

. The accident rates for urban interchanges are higher than
those for rural interchanges since urban areas carry more
traffic, making merging and diverging maneuvers more
difficult.

. While the accident rate on entrance ramps is higher than
that on exit ramps in urban areas, the accident rate on exit
ramps is higher than that on entrance ramps in rural areas.

. Ramps have :much. higher' accident rates than the other

10

elements of the interchange.

. Ramp terminals should be positioned at least 750 ft. from
the structures.

. Speed-change lanes of 800 ft. or more in length should be
provided to reduce the accident rates.

. Adequate sight distances should be maintained at entrance
and exit terminals.

. Left-hand exits and entrances should be avoided if possible
because of poor accident rates, and adequate signs in advance
should be provided if they are absolutely needed.

. On-ramps on upgrade are more hazardous than those on
downgrade. Vertical alignment should be considered in the
design of interchanges.

. Ramp type should be simple to reduce accidents related to
confusion with complex ramp types.

. Interchange lighting systems reduce the accident rates on

freeway interchanges.

While these research studies provide some useful
information for the freeway designer, they do not provide a
sufficient basis for detailed design purposes. For instance,
they have not developed analytical tools to assist the
designer in making trade offs between the cost of various
freeway elements and.the difference in the number of accidents
that could be expected with each choice. The studies were

often based upon dichotomous data (i.e., speed-change lanes

11

< 800 ft. versus those > 800 ft.), and thus do not provide
data on accidents related to continuous variables which would
allow an analyst to develop predictive algorithms based upon
design features of the freeway interchange elements.

For example, it may not be possible to extend a speed-
change lane from 700 ft. to 800 ft., but it would still be
desirable to know the effect of lengthening it to 750 ft. The
past studies would not assist in this analysis, since both 700
ft. and 750 ft. are less than the dividing point used in the
preceding analysis. The same is true for other design features
(adequate sight distance versus inadequate sight distance,
ramps with a radius greater than 100 ft. versus those with a
radius less than 100 ft., greater than 750 ft. in distances
between ramp terminals and structures versus less than 750
£12.).

The purpose of this research is to establish accident
predictive algorithms based upon geometric design features of
the freeway interchange elements, and traffic data ( such as

traffic volume, population, no. of ramp lanes).

12

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v.HH ”MAME

CHAPTER III

DATA ACQUISITION
1116;. Data Needed

The objectives of this research were to: 1) compare the
accident rates in Michigan with those from the Interstate
System Accident Research Study II, Interim Report II by J. A.
Cirillo (l) and 2) develop and calibrate accident predictive
models based upon accident rates on the elements which
comprise a freeway interchange.

In the state of Michigan, there are approximately 700
freeway interchanges. The Michigan Department of
Transportation recently completed a geometric inventory of its
freeway interchanges, and merged the accident file to the
geometric file to identify the number of accidents associated
with each interchange element. Thus, the three types of data

needed for this research were available from this file.

Geometric data: Data describing the elements of the freeway
interchanges geometrically. The geometric data were collected
from. the IMichigan Department of 'Transportation's Highway
Accident Master Data file. The geometric data used in this

study are:

1). Interchange Number

17

2). Interchange Element Code

3). Control Section

4). Milepoint

5). Prime Road (PR) Number

6). Beginning PR Milepoint

7). Ending PR Milepoint

8). Beginning Ramp Terminal Milepoint
9). Ending Ramp Terminal Milepoint
10). Geometric and Laneage Code

11). Ramp Terminal or Intersection Code
12). Ramp Terminal Lane Usage Code
13). Interchange Light Code

14). Interchange Type

15). Activity Density

16). Junction Type Code

Traffic data: Data describing the level of use of the freeway
interchange elements. The traffic data are available from the
Michigan Department of Transportation's TVM (Trunkline Vehicle
Miles) Master Data file and Traffic FlOW'Map. The traffic data

needed for this study are:

1). ADT (Average Daily Traffic) on Mainline
2). ADT (Average Daily Traffic) on Crossroad
3). ADT (Average Daily Traffic) on Ramp

4). Population of the county in which the interchange is

18

located

Accident data:
interchanges in Michigan.
from. the IMichigan Department of ‘Transportation's Highway

Accident Master Data file.

study are:

1).
2).
3).
4).
5).
6).
7).

8).

10).
11).
12).
13).
14).
15).
16).
17).

18).

Miscellaneous single vehicle accident

Overturn accident

Hit train accident

Hit parked vehicle accident
Backing accident

Parking accident

Pedestrian accident

Fixed object accident

Other object accident
Animal accident

Bicycle accident

Head-on accident

Angle straight accident
Rear-end accident

Angle turn accident

Side swipe same direction accident
Rear-end left-turn accident

Rear-end right-turn accident

19

Data on accidents that occurred on the freeway

The accident data were collected

The accident data needed for this

19). Other drive way related accident

20). Angle drive way related accident

21). Rear-end drive way related accident
22). Side swipe opposite direction accident
23). Head-on left—turn accident

24). Dual left-turn accident

25). Dual right-turn accident

The accident data used for this study were data from 1982
to 1984. The geometric data base used for this study was
completed by 1984, but many parts of the data base had been
partly created before 1984.

The geometric data base completed in 1984 was used since
the geometry had not changed significantly. The traffic volume
data for 1983 was used since traffic volumes are updated with
a traffic growth factor every 3 years. The population data
based on this same year was used.

The master data file comprises the geometric data and the
accident data. Merging the traffic data into the master data
file and analyzing those data was done by computer programs

(that is, FORTRAN and SPSS).

III-g. Sample size

 

The purpose of sampling is to gain information about the

nature or distribution of elements in a particular population

20

without studying the entire population. In determining a
sample size, there are two major considerations:
First, assumptions must be made about the underlying
distribution of these elements when selecting a sample size.
One common assumption is that the population is normally
distributed. Under the normal distribution the same proportion
of observations will always lie between the mean and a
specified number of standard deviations below or above the
mean. For example, 68.26 percent of the area under the normal
distribution will be within one standard deviation of the
mean, and 95.46 percent, within two standard deviations for
any normally distributed variable.
Second, some.decision must.be made about the acceptable limits
of error for the sample. This is usually done by specifying
that the sample mean for a data item should be within some
value d of the true average for a certain percentage of
samples which is called the level of confidence. This level
of confidence is denoted as 100(1 - a), where a is the
fraction of the area under the normal distribution falling
outside the confidence limits. Thus, in the case that d = 2
and a = 0.05, :2 units around the true value will include the
estimated value 95 percent of the time (8).

There are two} types of equations considered for
determining a sample size: sampling with replacement and
sampling without replacement. Sampling with replacement

assumes that the sample n is small relative to the total

21

 

population size, but sampling without replacement does not.
Under sampling with replacement, the equation for determining
a sample size to achieve a precision of d units with 100(1 -

a) percent confidence is

 

ZZ1-(1/2)a02
n =
d2
where n = sample size
d = tolerable margin of error of mean value
a = standard deviation of population distribution

a = fraction of area under normal curve representing
events not within confidence level (thus, 1 -
a is desired level of confidence)

Z = standard normal statistic corresponding to 1 -

1'(1/2)a

a confidence level

If the standard deviation of the population distribution is
unknown, s(standard deviation of sample distribution) might

be used instead as follows:

 

ZZ1-(1/2)azSZ
n 2
d2
where s = standard deviation of sample distribution

22

 

 

Under sampling without replacement, the equation considered

for determining a sample size is

 

n
In =
1 + n/N
where n = number of sample observations with replacement
In = adjusted number of observations

N = total population

In the state of Michigan, there are approximately 700
freeway interchanges. Suppose that there are an average of 4
ramps per freeway interchange. It is desired to know the

number of accidents per ramp within d (tolerable margin of

error) = 2, 32 (sample variance in accidents per ramp) = 100,
and Z = 1.96, assuming 95 % confidence level. Then,

(l.96)2(lOO)

 

(2)2

96.04

96.04

 

n1:
1 + 96.04/2800

= 92.855

Thus, under sampling with replacement, the sample size is at

least 97 ramps, and under sampling without replacement, the

23

sample size is at least 93 ramps. The actual sample size to
be used in this study will be determined following sufficient

analysis to determine the probable value of the variance.

III-g. Unit of Analysis

 

In the Interstate System Accident Research Study II,
Interim Report II by Cirillo, J. A. (_1_) , the following
analysis units of freeway interchange were included in the

analysis:

. Deceleration lanes including taper

. Acceleration lanes including taper

. Exit ramps

. Entrance ramps

. Mainline units between speed—change lanes

. Combined acceleration-deceleration lanes

Each analysis unit was analyzed based on whether the
analysis unit.was within an urban or rural area. The accidents
occurring between interchanges were coded as a distance from
either the interchange ahead or behind based on the distances
to the exit-ramp nose and the entrance-ramp nose,
respectively. However, in this study all exit ramps were
combined, regardless of length, ADT, number of lanes, type of

interchange, etc. The same was true for entrance ramps and

24

mainline sections. No analysis was made of accidents occurring
on the cross roads. Thus, it is not possible to predict the
total accident frequency or rate for an interchange.

The analysis units for this study will be further
classified based on ADT, the interchange type and the length
of the various elements. The population of the county in which
the interchange exists will be used.as a surrogate measure for
activity density. The elements of the freeway interchanges
will be considered in detail, and the following base analysis

units will be included in this research:

. Mainline unit
. Crossroad unit
. On-ramp unit

. Off-ramp unit

The base units of analysis to be considered were defined

as the following:

. Mainline units start at a point 500 ft. before the
deceleration lane for the off-ramp and end at a point 500 ft.
after the acceleration lane for the on-ramp;

. Crossroad units start at a point 250 ft. before the
intersection of the on-ramp and the crossroad and end at a
point 250 ft. after the intersection of the off-ramp and the

crossroad;

25

. On-ramp units start at the point they meet the cross-road
and end at the end of the acceleration lane;

. Off-ramp units start at the beginning of the deceleration
lane on the freeway and end at the point the ramp meets the

crossroad.

III-4. Mathematical Inspection

using the identified data, sample size, and units of
analysis, models were constructed based upon the following

analysis:

Linear model: The data were first analyzed using linear
models. Suppose that interest lies in a certain (response)

variable p, which is thought to be dependent on the

functionally independent variables Z1, 22' ..., ZS, that is, p
= £(z1, ..., ZS). Then, it is said that p obeys a linear model
if
u = f(Zv , 29
k

=.Z ,6ij(21, ..., ZS)

j=l
where Xj== functions of the Zj only
8,, , Bk = unknown parameters which enter into the above
(2).

26

Regression Analysis: As a statistical tool that utilizes the
relation between two or more quantitative variables,
regression analysis is used to predict one variable from the
other or others. Regression analysis is based on a linear
regression model which fits the scattered observations on a
straight line by the least square method. There are two types
of linear regression models: simple linear regression models
and multiple linear regression models. A linear regression
model which contains only one independent variable is called
a simple linear regression model, while the linear regression
model which contains a number of independent variables is
called a multiple linear regression model. Thus, the simple

linear regression model can be stated as follows:

Y'==‘% + 399 + 5i

where Y. = the value of the response variable in the ith
trial BO and E1 = parameters
Xi = a known constant, namely, the value of the

independent variable in the ith trial

6. = a random error term with mean E(efl == 0 and
variance 02(6fl = 02, eiand ejare uncorrelated
so that the covariance 0(ew 6]) for all i, j;
i is not equal to j

i = 1’ O O O I n

27

Method of Least Sggare: In order to find good estimators of
the regression parameters (i.e., 30 and fig), the method of
least squares was employed. Suppose that there is a sample
observation (Xi, TL). Then the method of least squares

1

considers the deviation of Yi from its expected value:
Y} ’ (30'+ 39%)
In particular, the method of least squares requires that the

sum of the n squared deviations is considered. This criterion

is denoted by Q:

Q = Yi - (pa + fi1xi) }2

IIML'S

. {
l 1

Thus, the estimators of 50 and 61 are those values b0.and b1,
respectively, that minimize the criterion Q for the given

sample observations (xi, Yi) (_1_Q).

Regression Procedure: In selecting a regression procedure,
there are three possible regression procedures which require
the fitting of every possible regression equation. The
backward elimination procedure which determines the "best"
regression using all variables and then determines the best
equation for each step in which the number of variables in the

equation is reduced. The forward selection procedure inserts

28

variables in turn until the regression equation is
satisfactory. The stepwise regression procedure which is an
improved version of forward selection procedure which examines
the variables incorporated into the model at every stage of
the regression, provides a judgement on the contribution made
by each. variable, and removes any 'variable ‘which. has a
nonsignificant contribution at a later stage even if it may
have been the best single variable at the early stage (1;).
The stepwise regression procedure was used for this study.
Using the geometric, traffic and accident data, the
regression models were constructed for each unit of analysis.
In the linear regression models, accident rates based on the
different types of accident (i.e., total accident rate, injury
accident rate, etc.) were the dependent variable, and the
geometric and traffic data were the independent variables. In
those instances where the relationship did not appear to be
linear, the intrinsically linear regression model by

transformation was used.

29

CHAPTER IV

PROCEDURE

This study concerned itself with the development of
linear regression models for predicting accidents occurring
on freeway interchanges. One of the questions investigated in
this research was a determination of whether stratified data
or nonstratified data would result in better accident
prediction models.

The units of analysis for constructing the accident
predictive models for the total freeway interchange were based

on individual predictive models for the following elements:

0 Mainline unit
0 Crossroad unit

0 Ramp unit

Mainline units include the freeway lanes from a point 500 ft.
before the deceleration lane for the off-ramp to a point 500
ft. after the acceleration lane of the on-ramp. Crossroad
units include the roadway from a point 250 ft. before the
intersection of the on-ramp and the crossroad to a point 250
2ft. after the intersection of the off-ramp and the crossroad.
Ramp units include the on-ramp units from the intersection of
the cross-road to the end of the acceleration lane and the

off-ramp units from the beginning of the deceleration lane on

30

the freeway to the intersection with the crossroad.

Models constructed before data stratification

Based upon the above units of analysis, a linear

regression model was constructed using the total data based

on the following formula:

Accidents = f(ADT, Population, Lane mileage, # of

Ramps)

The best linear regression models of accident prediction on

each unit of analysis was as follows:

Model for Mainline Unit

Y = -8.0362 + 0.00021658x1 + 0.05523x2 + 0.000008697X3 +

3.39985X4 - 1.86537XS

where Y = Total number of accidents per unit
)6 = Average Daily Traffic (ADT)
X2== Lane mileage
X3== Population
)6 = Number of Off-ramps

><
Ln
ll

Number of On-ramps

31

For this model, the multiple regression coefficient (R) was

0.5624.

Model for Crossroad Unit

Y = 5.9372 + 0.00019387X1-+ 0.01979X2-+ 0.000004297X3

where Y = Total number of accidents per unit

Average Daily Traffic (ADT)

AX
ll

)9 = Lane mileage

X3== Population

For this model, the multiple regression coefficient (R) was

0.386.

Model for Ramp Unit

Y = -0.8302 + 0.00001575X1-+ 0.02555X2-+ 0.000000671X3-+
0.26683X4
where Y = Total number of accidents per unit
)9 = Average Daily Traffic (ADT)
X2== Ramp lane mileage
)g = Population

X
5
ll

Number of Off-ramps

32

For this model, the multiple regression coefficient (R) was
0.323.
It was obvious that there was more variance in the accident
data than that which could be satisfactorily explained by
these linear regression models. Thus, a systematic method of
stratifying the interchanges to reduce the variance, and
increase the explanatory power of the models was undertaken.
As a simple test to determine whether stratification
might be useful, a model of nighttime accidents on Cloverleaf

freeway interchanges was developed as follows:

Y = -2.4229 + 0.00004974X1-+ 0.05896X2
where Y = Dark accidents
)6 = Average Daily Traffic (ADT)

X2== Lane mileage

For this model, the multiple regression coefficient (R) was
0.724. Thus, it appears that stratifying the data can lead to
improved model reliability. The remaining question is whether
the stratification procedure will result in useful data upon

which design decisions can be made.

Data Stratification

Iv-l. Data File Format

33

As described in the preceding section, the objectives of
this research are to: :1) identify accident rates as they
relate to parameters of the interchange elements; 2) compare
the accident rates in Michigan with those from J. A. Cirillo;
and 3) develop and calibrate interchange accident predictive
models based on the accident rates on elements which comprise
the interchange.

With the above objectives, the data needed were obtained
from the databases of the Michigan Department of
Transportation. After data were obtained, they were merged
into the master data file using Fortran programs. The master
data file contains elements from the geometric data file, the
accident data file and the traffic data file. This master data
file also includes a category code. Thus, the master data file
can be sorted into specific data file sets as needed for
research.

From the master data file, the categories used to format

the data file sets needed for this research were:

. Activity Density
. Interchange Type

. Interchange Element

1). Data file set by Activity Density

For' the activity' density, the 'master' data file ‘was

34

classified into 3 area types of activity density: urban;
rural; and fringe. The number of interchanges and the

percentage of each area type are:

. Urban: 28.07 % (185 out of 659)

. Rural: 49.47 % (326 out of 659)

\

. Fringe: 22.46 % (148 out of 659)

2). Data file set pv Interchange Type

For the freeway interchange type, the master data file
was divided into 30 interchange types with the percentage and

the total number of interchanges for each interchange type:

\

. Diamond: 19.12 % (126 out of 659)

\

. Tight diamond: 11.68 % (77 out of 659)

. Modified diamond: 4.10 % (27 out of 659)

. Modified tight diamond: 4.10 % (27 out of 659)
. Partial diamond: 2.73 % (18 out of 659)

. Partial tight diamond: 4.70 % (31 out of 659)

. Split diamond: .2.28 % (15 out of 659)

o\°

. Diamond plus 1 loop: 2.88 (19 out of 659)

. Parclo A: 2.73 % (18 out of 659)

\

. Parclo A 4 quad: 6.98 % (46 out of 659)
. Parclo B: 3.03 % (20 out of 659)

. Parclo B 4 quad: 1.67 % (11 out of 659)

35

Parclo AB: 4.10 % (27 out of 659)

Parclo AB 4 quad: 1.82 % (12 out of 659)
Cloverleaf: 1.37 % (9 out of 659)

Cloverleaf with CD roads: 1.21 % (8 out of 659)

Cloverleaf minus 1 loop: 0.46 % (3 out of 659)

o\°

Trumpet A: 1.37 (9 out of 659)

o\°

Trumpet B: 1.37 (9 out of 659)

Full directional: 1.52 % (10 out of 659)
Partial directional: 2.12 % (14 out of 659)
Directional Y: 1.21 % (8 out of 659)

General Directional: 0.76 % (5 out of 659)
Partial directional Y: 4.40 % (29 out of 659)
Directional with loops: 1.37 % (9 out of 659)
General: 1.52 % (10 out of 659)

Urban diamond: 6.68 % (44 out of 659)

o\°

SRI-A: 0.15 (1 out of 659)

SRI-B: 0.45

o\°

(3 out 659)

Other: 2.12 % (14 out of 659)

These freeway interchange 'types represent 'the

interchanges in Michigan. Based upon the above

created,

Table IV.1.

interchange types, data files for each interchange type were

number of accidents for each data file was found as shown in

these data files were collapsed into a smaller number of

36

and the total number of accidents and the average

Since many of the sample sizes were too small,

groups based upon a similar mean accident rate and variance.
These groups are shown in Table IV.2; The interchange types

comprising each group are as follows:

. Group 1: Diamond

. Group 2: Tight diamond, Urban diamond

. Group 3: Modified diamond, Modified tight diamond, Parclo
A 4 quad

. Group 4: Partial diamond, Partial tight diamond, Trumpet
A, Partial Directional Y

. Group 5: Split diamond, General directional, Other

. Group 6: Diamond plus 1 loop, Parclo B 4 quad, Trumpet B,
Directional Y

. Group 7: Parclo AB, Partial directional

. Group 8: Cloverleaf, Cloverleaf with CD roads, Cloverleaf
minus 1 loop, Directional with loops

. Group 9: Parclo A, Parclo B, Parclo AB 4 quad

. Group 10: Full directional, General

. Group 11: SRI-A

. Group 12: SRI—B

A "t" test was run to determine if these groups were
statistically significantly different. While not all groups
were different from all other groups, all groups were
different from at least one other group. The result of this

analysis is shown in Table IV.3.

37

3). Data file set by Interchange Element

For the freeway interchange element, the master data file
was classified into 33 elements of the freeway interchange as

follows:

. NB mainline

. SB mainline

. EB mainline

. WB mainline

. Crossroad

. Spread on ramp from crossroad to freeway
. Spread off ramp from freeway to crossroad
. Tight on ramp from crossroad to freeway
. Tight off ramp from freeway to crossroad
. Loop on ramp from crossroad to freeway

. Loop off ramp from freeway to crossroad
. Collector distributor

. On ramp from service road to freeway

. Off ramp from freeway to service road

. Service road from off ramp to crossroad
. Service road from crossroad to on ramp

. On ramp from crossroad to CD

. Off ramp from CD

. Ramp from CD to CD

. Off ramp from CD to service road

. On ramp from service road to CD'

38

. Directional loop ramp

. Directional ramp

. Loop ramp from CD to CD

. Loop ramp from CD to crossroad
. Loop ramp from crossroad to CD
. Off ramp from freeway to CD

. On ramp from CD to freeway

. Turning roadway

. Loop ramp from freeway to CD

. Ramp from service road to service road
. Service road

. Other

These freeway interchange elements represent the freeway
interchange in total. For this research the freeway
interchange elements were collapsed into 4 analysis units

based on the role on the freeway interchange:

. Mainline unit - NB mainline
SB mainline
EB mainline
WB mainline
. Crossroad unit - Crossroad
. On-ramp unit - Spread on ramp from crossroad to freeway
Tight on ramp from crossroad to freeway

Loop on ramp from crossroad to freeway

39

On ramp from service road to freeway
On ramp from CD to freeway
. Off-ramp unit - Spread off ramp from freeway to crossroad
Tight off ramp from freeway to crossroad
Loop off ramp from freeway to crossroad
Off ramp from freeway to service road
Off ramp from freeway to CD

Loop ramp from freeway to CD

The total number of accidents by each element and each group

of elements is shown in Table IV.4 and IV.5 respectively.
4). Da a file set by Agcidgnt Tvpg

With the above-described data file set, the types of

accidents available on the accident data file were:

. Miscellaneous single vehicle
. Overturn

. Hit train

. Hit parked vehicle

. Backing

. Parking

. Pedestrian

. Fixed object

. Other object

40

 

. Animal

. Bicycle

. Head-on

. Angle straight

. Rear-end

. Angle turn

. Side swipe same

. Rear-end left turn
. Rear-end right turn
. Other drive

. Angle drive

. Rear-end drive

. Side swipe opposite
. Head-on left turn

. Dual left turn

. Dual right turn

The number of accidents by type for each interchange element

is shown in Table IV.6a through IV.6e. The number of accidents

by collapsed interchange elements is shown in Table IV.7.

5) . Data file set by Interchange groups with Activity density

Based upon the above interchange types and activity

densities, the following combined data file sets were created:

41

Urban Groups

Urban

Urban

Urban

Urban

Urban

Urban

Urban

Urban

Urban

Urban

Urban

Urban

group
group
group
group
group
group
group
group
group
group
group

group

Rural Groups

Rural

Rural

Rural

Rural

Rural

Rural

Rural

Rural

Rural

Rural

group
group
group
group
group
group
group
group
group

group

10

ll

12

10

42

Fringe Groups

. Fringe
. Fringe
. Fringe
. Fringe
. Fringe
. Fringe
. Fringe
. Fringe
. Fringe

. Fringe

group
group
group
group
group
group
group
group
group

group

_.m’_. ,1. I, ___L_.~ ...; ....

10

These data file sets represent the total data file by freeway

interchange type and the analysis units considered. The total

number of accidents in each cell based upon these categories

was found, and the accident rate (accidents per interchange)

for each analysis unit was also determined as shown in Table

IV.8 through IV.38.

IV-2. Summaryeof Reeults by Groups

1). Summary of accident typee bv collapsed interchange

elements

Based upon the accident types and the interchange

elements described, the total number of accidents for each

43

accident type by each interchange element is shown in Table
IV.39 through IV.41. From the results shown in these tables,
the average number of accidents that occurred on the analysis
units is shown in Table IV.42.

Mainline unit: 4464 accidents out of the total 9534 accidents
that occurred on those analysis units occurred on the mainline
unit (46.82 percent). The major types of accidents and the

percentage of each major accident type were:

\

. Rear-end: 39.83 % (1778 out of 4464)
. Fixed object: 27.76 % (1239 out of 4464)

. Animal: 12.25 ° (547 out of 4464)

o\

. Overturn: 8.2 % (364 out of 4464)

. Miscellaneous single vehicle: 3.3 % (148 out of 4464)

These major types of accidents represent 91.31 percent of the
total accidents on the mainline unit.

Crossroad unit: 2536 accidents out of the total 9534 that
occurred on those analysis units occurred on the crossroad
unit (26.60 percent). The major types of accidents and the

percentage of each major accident type were:

\

. Rear-end: 29.77 % (755 out of 2536)
. Fixed object: 16.56 % (420 out of 2536)
. Angle straight: 9.62 % (244 out of 2536)

. Angle turn: 8.16 % (207 out of 2536)

44

. Rear-end drive: 4.53 % (115 out of 2536)

. Head-on left turn: 3.94 % (100 out of 2536)

These major types of accidents represent 72.59 percent of all
accidents on the crossroad unit.

On-ramp unit: 919 accidents out of the total 9534 accidents
that occurred on those analysis units occurred on the on-ramp
unit (9.64 percent). The major types of accidents and the

percentage of each accident type were:

\

. Fixed object: 36.02 % (331 out of 919)
. Rear-end: 33.51 % (308 out of 919)

. Overturn: 16.32 % (150 out of 919)

These major types of accidents represent 85.85 percent of the
total accidents on the on-ramp unit.

Off-ramp unit: 1615 accidents out of the total 9534 accidents
that occurred on those analysis units occurred on the off-ramp
unit (16.94 percent). The major types of accidents and the

percentage of each accident type were:

\

. Rear-end: 41.24 % (666 out of 1615)

. Fixed object: 30.4 % (491 out of 1615)

\

. Overturn: 10.46 % (169 out of 1615)

These major types of accidents represent 82.11 percent of all

45

accidents on the off-ramp unit.

2 . Summary of Urpan Groups based on Analysis Units

Following stratification, some of the groups were too
small to be modeled. An analysis of the sample size for each

group is discussed below:

Urban Group 1: As shown in Table IV.8, the total number of
accidents was small and the number of interchanges was 5. This
group was excluded from further analysis.

Urban Group 2: As shown in Table IV.9, the number of
interchanges was 50. The accident rate for the mainline unit
was 5.86 accidents per interchange, and the major types of
accidents were rear-end and fixed object. The accident rate
for the crossroad unit was 3.66, and the major types of
accidents were rear-end, angle straight, angle turn, fixed
object, other drive, and angle drive. The accident rate for
the on-ramp unit was 2.26, and the major types of accidents
were rear-end and fixed object. For the off-ramp unit the
accident rate was 2.04, and the major types of accident were
rear-end and fixed object.

Urban Group 3: As shown in Table IV.10, the number of
interchanges was 17. The accident rate for the mainline unit
was 9.53 accidents per interchange, and the major types of

accidents were rear—end and fixed object. The accident rate

46

for the crossroad unit was 6.18, and the major types of
accidents Were rear-end and angle turn. The accident rate for
the on-ramp unit was 3.41, and the major types of accidents
were fixed object and rear-end. For the off-ramp unit the
accident rate was 4.82, and the major types of accident were
rear-end and fixed object.

Urban Group 4: As shown in Table IV.11, the number of
interchanges was 38. The accident rate for the mainline unit
was 5.24 accidents per interchange (the lowest value among the
urban groups), and the major types of accidents were rear-end
and fixed object. The accident rate for the crossroad unit was
3.37 (the lowest value among the urban groups), and the major
types of accidents were angle straight, rear-end and hit
parked vehicle. The accident rate for the on-ramp unit was 1
(the lowest value among the urban groups), and the major types
of accidents were rear-end and fixed object. For the off-ramp
unit the accident rate was 1.63, and the major types of
accident were rear-end and fixed object (the off-ramp value
is also the lowest among the urban groups).

Urban Group 5: As shown in Table IV.12, the number of
interchanges was 21. The accident rate for the mainline unit
was 8.90 accidents per interchange, and the major types of
accidents were rear-end and fixed object. The accident rate
for the crossroad unit was 5.52, and the major types of
accidents were reareend, angle straight, fixed object, and

rear-end drive. The accident rate for the on-ramp unit was

47

2.14, and the major types of accidents were rear-end and fixed
object. For the off-ramp unit the accident rate was 2.71, and
the major types of accident were rear-end and fixed object.
Urban Group 6: As shown in Table IV.13, the number of
interchanges was 10. The accident rate for the mainline unit
was 11 accidents per interchange, and the major types of
accidents were rear-end and fixed object. The accident rate
for the crossroad unit was 6, and the major type of accident
was rear-end. The accident rate for the on-ramp unit was 3.5
(the highest value among the urban groups), and the major
types of accidents were rear-end and fixed object. For the
off-ramp unit the accident rate was 6, and the major types of
accident were rear-end and fixed object (the off-ramp value
is the highest among the urban groups).

Urban Group 7: As shown in Table IV.14, the number of
interchanges was 12. The accident rate for the mainline unit
was 7.75 accidents per interchange, and the major types of
accidents were rear-end and fixed object. The accident rate
for the crossroad unit was 6.5, and the major type of accident
was rear-end. The accident rate for the on-ramp unit was 1.83,
and the major type of accident was fixed object. For the off-
ramp unit the accident rate was 2.5, and the major type of
accident was rear-end.

Urban Group 8: As shown in Table IV.15, the number of
interchanges was 7. This group was excluded from further

analysis.

48

Urban Group 9: As shown in Table IV.16, the number of
interchanges was 8. This group was excluded from further
analysis.

Urban Group 10: As shown in Table IV.17, the number of
interchanges was 11. The accident rate for the mainline unit
was 15.0 accidents per interchange (the highest value for any
urban group), and the major types of accidents were rear-end
and fixed object. The accident rate for the crossroad unit was
7.09 (the highest value for any urban group), and the major
types of accidents were rear-end, fixed object and angle
straight. The accident rate for the on—ramp unit was 1.27, and
the major type of accident was rear-end. For the off-ramp unit
the accident rate was 2.82, and the major types of accidents
were rear-end and fixed object.

Urban Group 11: As shown in Table IV.18, the number of
interchanges was 1. This group was excluded from further
analysis.

Urban Group 12: As shown in Table IV.19, the number of
interchanges was 3. This group was excluded from further
analysis.

The highest and lowest accident rates for each analysis unit

in the urban groups are:

. Group 10 had the highest mainline accident rate (13.75)
. Group 4 had the lowest mainline accident rate (5.24)

. Group 10 had the highest crossroad accident rate (6.5)

49

. Group 4 had the lowest crossroad accident rate (3.37)
. Group 6 had the highest on-ramp accident rate (3.5)

. Group 4 had the lowest on-ramp accident rate (1)

. Group 6 had the highest off-ramp accident rate (6.0)

. Group 4 had the lowest off-ramp accident rate (1.63)

3). Summary of Rural Groups based upon Analysis Units

Rural Group 1: As shown in Table IV.20, the total number of
interchanges was 106. The accident rate of the mainline unit
was 5.03, and the major types of accidents were animal, fixed
object, rear-end, and overturn. The accident rate for the
crossroad unit was 2.25, and the major types of accidents were
fixed object, animal, rear-end, angle straight, angle turn,
and head-on. The accident rate for the on—ramp unit was 0.4
(the lowest value among the rural groups), and the major types
of accidents were fixed object and overturn. For the off-ramp
the accident rate was 1.18, and the major types of accidents
were fixed object, rear-end, overturn, and animal.

Rural Group 2: As shown in Table IV.21, the number of
interchanges was 47. The accident rate for the mainline unit
was 5.57 accidents per interchange, and the major types of
accidents were animal, fixed object and rear-end. The accident
rate for the crossroad unit was 2.74, and the major types of
accidents were fixed object, rear-end, angle.straight, animal,

angle turn. The accident rate for the on-ramp unit was 0.60,

50

and the major type of accident was fixed object. For the off-
ramp unit the accident rate was 1.57, and the major types of
accident were rear-end and fixed object.

Rural Group 3: As shown in Table IV.22, the number of
interchanges was 43. The accident rate for the mainline unit
was 5.93 accidents per interchange, and the major types of
accidents were rear-end, fixed object, animal, and overturn.
The accident rate for the crossroad unit was 4.19, and the
major types of accidents were rear-end and fixed object. The
accident rate for the on-ramp unit was 1.07, and the major
types of accidents were fixed object, overturn and rear-end.
For the off-ramp unit the accident rate was 2.47, and the
major types of accident were rear-end and fixed object.
Rural Group 4: As shown in Table IV.23, the number of
interchanges was 36. The accident rate for the mainline unit
was 4.97 accidents per interchange (the lowest value among the
rural groups), and the major types of accidents were rear-end,
fixed object, animal and overturn. The accident rate for the
crossroad unit was 1.06 (the lowest value among the rural
groups), and the major types of accidents were fixed object
and rear-end. The accident rate for the on-ramp unit.was 0.44,
and the major type of accident was fixed object. For the off-
ramp unit the accident rate was 0.56 (the lowest value among
the rural groups), and the major type of accident was fixed
object.

Rural Group 5: As shown in Table IV.24, the number of

51

interchanges was 7. This group was excluded from further
analysis.

Rural Group 6: As shown in Table IV.25, the number of
interchanges was 27. The accident rate for the mainline unit
was 7.41 accidents per interchange (the highest value among
the rural groups), and the major types of accidents were rear-
end, fixed object, animal and overturn. The accident rate for
the crossroad unit was 2.96, and the major types of accidents
were rear-end and fixed object. The accident rate for the on-
ramp unit was 0.74, and the major types of accidents were
overturn and fixed object. For the off-ramp unit the accident
rate was 1.74, and the major types of accidents were rear-end
and fixed object.

Rural Group 7: As shown in Table IV.26, the number of
interchanges was 17. The accident rate for the mainline unit
was 6.94 accidents per interchange, and the major types of
accidents were fixed object, rear—end, animal and overturn.
The accident rate for the crossroad unit was 4.24, and the
major types of accidents were rear-end and fixed object. The
accident rate for the on-ramp unit was 1.18 (the highest value
among the rural groups), and the major types of accidents were
overturn and fixed object. For the off-ramp unit the accident
rate was 2.53 (the highest value among the rural groups), and
the major types of accidents were rear-end and fixed object.
Rural Group 8: As shown in Table IV.27, the number of

interchanges was 8. This group was excluded from further

52

analysis.

Rural Group 9: As shown in Table IV.28, the number of
interchanges was 29. The accident rate for the mainline unit
was 6 accidents per interchange, and the major types of
accidents were fixed object, rear-end, animal and overturn.
The accident rate for the crossroad unit was 4.34 (the highest
value among the rural groups), and the major types of
accidents were fixed object and rear-end. The accident rate
for the on-ramp unit. was 0.90, and the 'major ‘types of
accidents were fixed object and overturn. For the off-ramp
unit the accident rate was 2.31, and the major types of
accidents were fixed object, rear-end, and overturn.

Rural Group 10: .As shown in Table 1V329, the number of
interchanges was 6. This group was excluded from further

analysis.

The highest and lowest accident rates for each analysis unit

in the rural groups are:

. Group 6 had the highest mainline accident rate (7.41)
. Group 4 had the lowest mainline accident rate (4.84)
. Group 9 had the highest crossroad accident rate (4.5)
. Group 4 had the lowest crossroad accident rate (1.03)
. Group 7 had the highest onwramp accident rate (1.18)
. Group 1 had the lowest on—ramp accident rate (0.39)

. Group 7 had the highest off-ramp accident rate (2.53)

53

. Group 4 had the lowest off-ramp accident rate (0.54)

4). Summary of Fringe Groups based on Analysis Units

Fringe Group 1: As shown in Table IV.30, the total number of
interchanges was 13. The accident rate of the mainline unit
was 6, and the major types of accidents were animal, fixed
object and rear-end. The accident rate for the crossroad unit
was 3.85, and the major types of accidents were fixed object,
rear-end, angle straight and angle turn. The accident rate for
the on-ramp unit was 1.38, and the major types of accident
were fixed object and overturn. For the off-ramp unit the
accident rate was 3.23, and the major types of accidents were
rear-end, fixed object and overturn.

Fringe Group 2: As shown in Table IV.31, the number of
interchanges was 25.The accident rate for the mainline unit
was 6.6 accidents per interchange, and the major types of
accidents were rear-end, fixed object, overturn and animal.
The accident rate for the crossroad unit was 3.6, and the
major types of accidents were rear-end, fixed object, angle
straight and angle turn. The accident rate for the on-ramp
unit was 1.24 (the lowest value among the fringe groups), and
the major types of accidents were fixed object and rear-end.
For the off-ramp unit the accident rate was 3.36, and the
major types of accident were rear—end and fixed object.

Fringe Group 3: As shown in Table IV.32, the number of

54

interchanges was 40. The accident rate for the mainline unit
was 7.48 accidents per interchange, and the major types of
accidents were rear-end, fixed object, overturn and animal.
The accident rate for the crossroad unit.was 5.98 (the highest
value among the fringe groups), and the major types of
accidents were rear-end, fixed object, angle turn, angle
straight and rear-end drive. The accident rate for the on-ramp
unit was 2.18, and the major types of accidents were fixed
object, rear-end and overturn. For the off-ramp unit the
accident rate was 3.75, and the major types of accident were
rear-end, fixed object and overturn.

Fringe Group 4: . As shown in Table IV.33, the number of
interchanges was 12. The accident rate for the mainline unit
was 5.5 accidents per interchange (the lowest value among the
fringe groups), and the major types of accidents were rear-
end and fixed object. The accident rate for the crossroad unit
was 1.5 (the lowest value among the fringe groups), and the
major type of accident was nothing to be considered. The
accident rate for the on-ramp unit was 1.25, and the major
types of accidents were rear-end and fixed object. For the
off-ramp unit the accident rate was 1.25 (the lowest value
among the fringe groups), and the major types of accident were
rear-end and fixed object.

Fringe Group 5: As shown in Table IV.34, the number of
interchanges was 6. This group was excluded from further

analysis.

55

Fringe Group 6: As shown in Table IV.35, the number of
interchanges was 11. The accident rate for the mainline unit
was 7.27 accidents per interchange, and the major types of
accidents were fixed object and rear-end. The accident rate
for the crossroad unit was 4.82, and the major types of
accidents were rear-end and fixed object. The accident rate
for the on-ramp unit was 1.73, and the major type of accident
was fixed object. For the off-ramp unit the accident rate was
4.36, and the major types of accidents were rear-end, fixed
object and overturn.

Fringe Group 7: As shown in Table IV.36, the number of
interchanges was 12. The accident rate for the mainline unit
was 5.92 accidents per interchange, and the major types of
accidents were rear-end and fixed object. The accident rate
for the crossroad unit was 3.67, and the major type of
accident was fixed object. The accident rate for the on-ramp
unit was 1.25, and the major type of accident was fixed
object. For the off-ramp unit the accident rate was 2.5, and
the major types of accidents were fixed object and rear-end.
Fringe Group 8: As shown in Table IV.37, the number of
interchanges was 14. The accident rate for the mainline unit
was 13.71 accidents per interchange (the highest value among
the fringe groups), and the major types of accidents were
rear-end and fixed object. The accident rate for the crossroad
unit was 5.71, and the major types of accidents were rear-end

and fixed object. The accident rate for the on-ramp unit was

56

2.93 (the highest value among the fringe groups), and the
major types of accidents were rear-end and fixed object. For
the off-ramp unit the accident rate was 3.79, and the major
types of accidents were rear-end and fixed object.

Fringe Group 9: As shown in Table IV.38, the number of
interchanges was 12. The accident rate for the mainline unit
was 6.92 accidents per interchange, and the major types of
accidents were rear-end, fixed object and.animal. The accident
rate for the crossroad unit was 4.83, and the major type of
accident was rear-end. The accident rate for the on-ramp unit
was 1.92, and the major type of accident was fixed object.
For the off-ramp unit the accident rate was 4.58 (the highest
value among' the fringe «groups), and. the :major' types of
accidents were fixed object and rear-end.

Fringe Group 10: As shown in Table IV.39, the number of
interchanges was 2. This group was excluded from further

analysis.

The highest and lowest accident rates for each analysis unit

in the fringe groups are:

. Group 8 had the highest mainline accident rate (12.8)
. Group 4 had the lowest mainline accident rate (5.5)

. Group 3 had the highest crossroad accident rate (5.98)
. Group 4 had the lowest crossroad accident rate (1.5)

. Group 8 had the highest on-ramp accident rate (2.73)

57

. Group 4 had the lowest on-ramp accident rate (1.29)
. Group 6 had the highest off-ramp accident rate (4.8)

. Group 4 had the lowest off-ramp accident rate (1.25)

 

5). Comparison of the accident rates

From the results of the urban groups, group 4 had the
lowest accident rates for any analysis units, whereas group
6 had the highest accident rates for the ramp units and group
10 had the highest accident rates for the. mainline and
crossroad units. In the rural groups, group 4 again had the
lowest accident rates for any analysis units excluding the on-
ramp unit for which group 1.1nni the lowest accident rate.
Group 6, group 7 and group 9 had the highest accident rates
for the mainline unit, the ramp units and the crossroad unit,
respectively. For the fringe groups, group 4 once again had
the lowest accident rates for the same analysis units as the
rural groups excluding the on-ramp unit for which group 2 had
the lowest accident rate. Group 3, group 8 and group 9 had
the highest accident rates for the crossroad unit, the
mainline and on-ramp units, and the off—ramp unit,
respectively. These groups by the analysis units can be

compared as shown in Table IV.45.

Iv-3. Summary of Regulte

58

Based upon the results from each group of some sample
interchanges, the average number of accidents on the mainline
unit were generally higher than those on the other units as
shown in Table IV.46. However, the accident rates on the ramp
units were higher than those on the mainline unit as shown in
Table IV.47 when the traffic volumes were considered with
those average accidents.

The data file set to be used in modelling will be
selected based on the Charts 4.1 through 4.4. The groups with
less than 10 interchanges were excluded from the analysis.
In the charts, the groups included for further analysis were

marked by **. The sample data file is shown in Table IV.44.

59

 

 

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6.2.26.6 6626266..2.

613

munoaoam monaaouounH ummmuaaoonb an muamcwoom mo Honafia Hmuoa

v .>H OHQMB

 

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m2..z~<x m3
wz..2.<z mm
mz_.z_<z mm
mz..z~<z m2 u>_2: wz_.z.<z

 

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mpop v.2: az<¢-..0
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mhzwo_ou< .0 ¢wmzzz 4<>0h

|
muamaauo omadsoumuaw cmmmuaaoo an muzoowooa no Hones: Hmuoa m.>H canoe

mpzwzw3w muz<=u¢w>z. omma<3600

64

 

 

moF NFN New mvN mhzmo~uo< .0 ¢mm2Dz .<60.
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oz.xo<m .=w> omx¢<. h_z z_<¢F ..z 2¢DF¢m>0 m30wz<..mum.2 mhzm2w.u muz<zu¢mhz_

65

muzoaaaa moaozououaH can muamuwuoa no ooh» some an muaovfloofl no Hanan: Haves

do .>H wand...

 

 

Moo .0 mmON mm mM szmo_uu< .0 ¢wm232 .<.0.
m ¢wzF0 Nv
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0 ><3o<0¢ 02.2¢Dh NM
MF >3. 0F .0 20¢. .2<¢ 20 0M
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o 6 mFN F .2<¢ .<20_h0w¢_o NN
MM .2<¢ .00. .<20_Fuw¢_o ON
on 0» 0¢ wu.>¢mw 20¢. .2<¢ 20 MN
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.
.<2~z< Fuwsmo ¢wzh0 Femsmo omx_. z<_¢Fwwow. uz_¥¢<. szm2w.w wuz<=0¢sz.

66

muaoauam monogamouaH can munmoflooa no «man 50mm ma muzoowoom mo Runes: annoy n6.>H QHQMB

 

 

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266. 6.626 626-6666 .26.66.6 6.626 26-6662 6.6.6.6 6.2.26.6 6626266..2.

67

muaoaoam oozusououna can muzoowoon no omau noun an mucouwoo¢ no nonafln Haves

Oo.>H wands

 

mo m. OFF 00F mo szwomuu< .0 ¢mm202 .<FOF
M ¢m=F0 N6

F m w Q¢ w0_>¢mm Fv
Q¢ m0.>¢mm 0F o¢ w0~>¢mm 20¢. .2<¢ 0M

o0 0F >3. 20¢. .2<¢ .00. NM

><3o<0¢ oz_z¢:F NM

F F >3. 0F 00 20¢. .2<¢ 20 0M

F 00 0F >3. 20¢. .2<¢ ..0 MM

00 0F o<0¢mm0¢u 20¢. .2<¢ .00. «M

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90 0F 00 20¢. .2<¢ .00. 0N

N F M m .2<¢ .<20_Fuw¢_o NN

F F .2<¢ .00. .<20_Fuw¢_o ON

00 0F o¢ w0_>¢wm 20¢. .2<¢ 20 MN

Q¢ w0_>¢mw 0F 00 20¢. .2<¢ ..0 «N

00 0F 00 20¢. .2<¢ MN

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F F .0 OF o<0¢mm0¢0 20¢. .2<¢ 20 FN

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0 M MF FN FF o<0¢mm0¢u 0F .2<¢ ..0 20¢. Q¢ w0~>¢mm 0F
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M N ¢0F:m_¢Fm.o ¢0F0m..00 0F

6 F F o<0¢mm0¢u 0. >3. 20¢. .2<¢ ..0 .00. mF

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FF N F o<0¢wm0¢u 0F >3. 20¢. .2<¢ ..0 o<m¢.m FF

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N m o mz_.z.<2 mm M0

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F M F F FN wz_.z_<2 m2 F0

 

m>_¢o w.oz< w>_¢o ¢m:F0

-

.
qu_¢ ozw-¢<m¢ .... ozm-¢<m¢

-

w2<m m._3mmo_m

szmzm.w woz<=u¢sz~

68

muaoamam moaunououcH can muaocflood no 0..» scam an mucoufiood Ho Hmnafla Hmuoa no.>H manna

 

OM MM OMF ON ooF MszOFOO< ;O ¢mm232 4<FOF
¢m=F0 N«

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90 0F >3; 20¢; a2<¢ moo; OM

><30<O¢ oze¢DF NM

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00 0F O0 20¢; ;2<¢ moo; ON

v N a2<¢ 4<20~F0m¢FO NN

a2<¢ @003 4<203F0w¢FO ON

00 OF O¢ wOF>¢wm 20¢; a2<¢ 20 MN

O¢ w03>¢mm 0F 00 20¢; a2<¢ ;;0 «N

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00 20¢; a2<¢ ;;0 NN

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z¢OF-F:OF¢ 4<0O

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.Oaao w;_3mmO_m

u

m>_¢o O2m-¢<w¢

Msz2m4m moz<=0¢m>z~

69

munoamam mmnmnououcH can unconfined no 00%» comm an muamcfioom mo Hones: dance

00 .>H manna?

 

 

 

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N o N mFFOOQQO m;_3mmo_m MOM
M MFF N m>F¢O ozw-¢<m¢ N¢v
«O N m>_¢O wduz< vcv
No M m>_¢o ¢wzF0 ocq
NM v ¢M FF z¢3F FIOF¢ ozw-¢<m¢ OVM
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NN o NON «F z¢OF maoz< qu
coo OOM MMN ONNF ozw-¢<w¢ NvF
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F_z: ;2<¢-;;0 FFz: a2<¢-20 Fan O<0¢wm0¢0 F_z: mz_42_<2 mwa>F szOFOO<

7O

muamamam omcmnouounfi vanguaaoo kn momma uaouwoon

N .>H ”MAME

0.N o.O M N.M mmuz<=0¢szF ;O u \ szmoFuu< ;0 a

M u mmoz<xu¢szF ;0 ¢mm232

 

 

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7 1

a macho cash: no mucoaoam mmaanuumuafl oommmHHoo an mmmfiu uqmuwoofl m.>H manna

 

«O.N oo.N 00.M OO.M mmOz<zO¢sz_ ;0 % \ szmoF00< ;0 a
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F o z¢DF F;w4 20-0<m: MOM

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F NF m>—¢O Ozw-¢<w¢ Nev

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FFzD a2<¢-;;0

FFZO a2<¢-20

FFZD O<0¢mm0¢0

FFz: wz_az_<2

mwa>F szOFOO<

72

N macho sank: no muzaaoao nonmaoumuaw omeMHaoo ha mama» pamowoom

a .>H QHQdB

 

 

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NF u mmuz<z0¢sz~ ;0 ¢mm232

NO OM MOF NoF szmOFuO< ;0 ¢mm2az 4<FOF
F M z¢OF F20F¢ 4<OO coo
z¢3F F;w4 4<DO Moo

M z¢OF F;w4 20-0<w: McM

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M m>F¢O m4oz< ¢¢¢

m>F¢O ¢sz0 O¢¢

M z¢DF F:O_¢ Ozw-¢<m¢ ovM

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M OF z¢OF waoz< qON
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FFzO szazF<2

ww¢>F FszFOO<

73

m macho dunno no mpnmEoHo omnmnououaw oommmaaoo ha momma unmowoo<

0H .>H ”Hana.

 

mo.F F Fm.m «N.m mmuz<=umszF ;o u \ szNQFQU< ;o a
an n mmoz<=uaszF mo Numzaz

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zmaF FIoFN 4<so oqo

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v m>Fmo awzFo oqq

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q wz<m manmNQFm Nvm

F N zmaF m4uz< qu

mm FN «N NNF ozw-m<m¢ NFF
N «m N quF<NFm m4o2< qu

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N F angu<m mqo
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zF<¢F FF: ONO

n F m o 2N=F¢m>o oFo
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mma>F szOFOO<

711

v macho Guano no munmaoao wounnouounw vomamaaoo kn mama» unmuwoom «H.>H manna

 

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NN u mmoz<=0¢szF ;0 ¢mm232

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z¢DF F:O_¢ 4<DO eve

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F OFFMOQQO m;_3mwOFm MqM

OF w>F¢O O2m-¢<w¢ Nee

F w>~¢o mauz< qvc

N w>_¢O ¢wzF0 Ovv

F 2¢DF F:O_¢ Ozw-¢<m¢ ovM
o z¢DF F;m4 Ozm-¢<w¢ MvM

F N m2<m w;_3mwo_m NvM
F v 2¢OF w402< QQN

0M 0N O¢ FOF Ozw-¢<w¢ NcF
N F FN M FIOF<¢FM waoz< ¢vF
N N 20-0<w: FQF

.m40>u_m OOO

F 4<2_z< OOO

F Fumwmo ¢sz0 ONO

FF O MF «M Fumwmo owXF; OOO
N z<F¢meoma OMO

F OzFx¢<m ovO

F c Ozqu<m OQO

F M M m40_:w> Ow¥¢<a FF: OMO

z_<¢F FF: ONO

o M NF z¢DF¢w>0 OFO
F M m40F2w> mJOsz m30mz<44wOMF2 OOO

 

FFZD a2<¢-;;0

FFzO a2<¢-20

FFz: O<0¢wm0¢0

FFZO wz_az_<2

wwa>F szo~00<

75

m msoum manna mo mucoaoao ooausouoqu vommmHHoo an mama» nzmvwoom

Nd .>H QHQMB

 

 

o M.M o FF mmOz<=0¢wFZF ;0 a \ szmOFuu< ;0 %
OF u mmuz<=u¢mF2F ;0 ¢mm232
O0 MM O0 OFF MF2OOFOO< ;0 ¢mm232 4<FOF
F z¢OF FIOF¢ 4<DO oqo
z¢OF F;w4 4<DO Mvo
F N 2¢3F F;m4 20-0<mz MwM
N mFFmoaao w;_3wmo_w MwM
N m>_¢o ozm-¢<m¢ Nce
M w>_¢O w4oz< «v9
F w>F¢O ¢sz0 qu
F F z¢OF F:OF¢ ozm-¢<m¢ eqM
F N z¢3F F;w4 Ozwu¢<m¢ MoM
F N w2<m w;_3mmo_m NvM
N F N z¢OF w402< «#N
am FF 0F MM ozw-¢<m¢ NcF
F N O FIOF<¢Fm w4oz< ch
M F M 20-0<w: FqF
F w40>OFO OOO
M 4<2~z< OOO
F F F Fumwmo ¢m=>0 ONO
MF NF O FM Fumwmo Ome; OOO
F N F z<F¢meOwa OMO
N uzFx¢<a ovO
F F ozF¥0<m OvO
M F OOO—:w> wa¢<a FF: OMO
z_<¢F FF: ONO
M M ¢ z¢DF¢w>0 OFO
o OOO—zm> maosz w00mz<44mum~2 OOO
F —
FFZO a2<¢-;;0 FFZO a2<¢-zO FFZD O<0¢mm0¢0 FFZO mz_42_<2 wwa>F FszFOO<

76

o macho away: no muaoaoao omnmnouousw umeMHHoo an mama» uaoowoo¢

Md .>H GHQMB

 

 

 

m.N MO.F m.o mF.F OOO2<=OOOF2F OO O \ szmOFOO< OO O
NF u mmoz<xu¢szF mo NszOz
Om NN ON no szmOFOO< OO OOOzOz O<FOF
zOOF FOOFO O<OO OOO
F zOOF FOOO O<OO OOO
F F zOOF FOOO 2O-O<m= OOO
NFFOOOOO OOFzmmO_w MOO
F O>FOO Ozm-m<mm NOO
m O>ONO OOO2< OOO
m m>FOO OOOFO OOO
N m N szF FOOFO Ozw-m<mm oqm
N szF FOOO Ozm-a<ua mam
wz<m OOFOONOFO NON
O ZOOF OOO2< «ON
mF O mm mm Ozm-m<mm NOF
F O F FOOF<NFO OOO2< OOF
F F 2O-O<m: FOF
F F NOOFO_O OOO
m O<zOz< OOO
FOOFOO NOOFO OFO
o FF 0 ON FOOFOO OmeO OOO
z<FOmeOOO OmO
ongN<O OOO
ongO<O OOO
F F F OOO_=O> Om¥¢<¢ FOO OMO
zF<¢F FF: ONO
m N F N ZOOFOO>O OFO
F F q OOOF=O> OOOsz OOOmz<OOwOm_x OOO
\q
FFzO Oz<O-;OO FFzO Oz<¢-zo FFzO O<OOOOOOO FFzO OzFOzF<z OOOFF FzOOFOO<

7'7

N macho Guano mo mquEoHo moamsououaw commmaaoo an mmmhu unmu«004

vH .>H 0HQMB

 

 

FN.N M¢.M 0N.o M.OF mwoz<=0¢sz_ ;0 n \ MFszFOO< ;0 u
N u mmuz<=u¢mF2_ ;0 ¢mm232
OF «N Mo NN szmOFUU< ;0 ¢mm20z 4<FOF
z¢DF F:OF¢ O<Oo owe
z¢OF F;w4 4<DO Mqo
F F z¢OF F;m4 20-0<w: MvM
wFFmoaao w;_3mmo_m M¢M
F m>F¢O Ozm-¢<m¢ Nae
F m>_¢o maoz< qu
m>~¢O ¢m:FO 04v
F F F z¢OF on~¢ Ozm-¢<w¢ OvM
z¢DF F;w4 O2m-¢<m¢ MOM
w2<m m;_3mmO_m NvM
F N z¢OF wqoz< qu
o M OM MM Ozm-¢<m¢ NvF
N F F:O_<¢Fm waoz< qu
z0-0<w: FqF
w40>0~m OOO
M O<2_z< OOO
F Fumamo ¢meO ONO
M FF 0F FN Fuwamo Ome; OOO
2<F¢Fwwowa OMO
F Oz_x¢<; OQO
F OZF¥O<O OOO
F F mau_zm> Om¥¢<a FF: OMO
z_<¢F FF: ONO
N N M M z¢DF¢w>O OFO
F M OOO—zw> NJOZFO m00m2<44m0m_2 OOO
= a
FFz: ;2<¢-;;0 FFZD ;2<¢-20 FFzD O<0¢mw0¢0 FFz: wz_42_<2 mwa>F Fzmo_00<

78

a macho away: no munoamam mocngouounw cmeMHHoo an mwmmu unmvwoo¢

m." .>H 0HDMB

 

 

mF.m mF.O F mF.O mmOz<=O¢mF2_ “O a F szwOFOO< OO O
O u mmoz<OOOOFzF OO OOOzOz
FO Om Om OF szmOFOO< OO OOOzOz O<FOF
zOOF FOO.“ O<OO OOO
zOOF FFOO O<OO OOO
O F zOOF FOOO zO-O<m= OOO
OFFOOOOO OOFOOOOFO NOF
F F O>F¢O Ozm-O<mO FOO
O>FOO OOO2< OOO
m w>FOO OOOFO OOO
N ZOOF FOOFO Ozm-O<mm OOm
F N F ZOOF FOOO O2O-O<OO OOO
F F F wz<m OOFOOOOFO NOm
F N F zOOF OOO2< OON
FF OF ON Fm O2O-O<m¢ FOF
F O F F:O_<¢Fm OOOz< OOF
m F zO-O<m: FOF
F OOOFOFO OOO
F O<zF2< OOO
F F m FOOFOO OOOFO OFO
O mF m ON FOOOOO waFO OOO
z<FOFwOOmO OOO
OzFxOOO OOO
F F OngOOO OOO
F N OOOFOO> OOgO<O FF: OmO
zF<¢F FF: ONO
O O F zaOFOm>O OFO
n F OOOFIO> OOOsz OOOmz<OOmOOFz OOO
J- .—
FFzO Oz<¢-OOO FFzO Oz<a-zo FFZO O<OOmmOOO FFzO szOzF<z OOOFF FzOOFOO<

753

a macho away: no magmaoam moaugououafi cmmmMHFoo an mmmwu uamuwoo<

OH .>H GHAUB

 

 

OM.N NF.F OM.o MN.MF mmoz<=0¢w>z~ ;0 fi \ MFzmoFuO< ;0 n
NF n msz<xu¢szF ;O ¢wm2az
FM OF ON MoF szwOFOO< ;0 ¢mm2az 4<FOF
z¢DF FIOF¢ 4<DO OOO
F z¢OF F;m4 4<OO MOO
N z¢OF F;w4 20-0<m= MOM
F OFFOOQQO waF3mwOFm MOM
w>F¢O ozw-¢<w¢ va
F m>F¢O w402< OOO
F m>_¢O ¢m=>0 OOO
F z¢OF F:0_¢ Ozm-¢<m¢ OOM
O 2¢OF F;m4 ozw-¢<w¢ MOM
O m2<m ma~3mwOFw NOM
o z¢3F m402< «ON
FF 0 MM No Ozw-¢<m¢ NOF
M F NF F qu~<¢Fm maoz< OOF
N F F 20-0<wz FOF
w40>OFO OOO
O<2Fz< OOO
N Fumwmo ¢wzF0 ONO
OF N MF 0M Fuwwmo waF; OOO
F z<F¢meOma OMO
N ozFx¢<a OOO
oz~x0<m OOO
F N F w40_:w> Om2¢<a FF: OMO
z_<¢F FF: ONO
N N O z¢DF¢w>0 OFO
F q MOO—:w> waoz_m m30wz<44mumF2 OOO
. a‘ F
FFz: a2<¢.;;0 FFzO ;2<¢-20 FFzD O<0¢wm0¢0 FFz: wz_az_<2 mm¢>F szOFOO<

80

ca macho Guano no munoaoam omnusououafi commaduoo ha momhu unmofioo<

NH .>H OHQflB

M F O O mmoz<xu¢mFZF ;0 O \ szmOFOO< ;O n

F n mmuz<zu¢sz_ ;0 ¢mm232

M F O O MFszFOO< ;0 ¢mm232 4<FOF

 

z¢DF F:O_¢ 4<OO OOO

2¢DF F;m4 4<DO MOO

z¢OF F;M4 20-0<m: MOM
mF_m0;ao wa~3mwoFm MOM

z¢3F

m>F¢O ozm-¢<m¢ NOO
m>~¢o wduz< OOO
m>~¢a ¢m=FO OOO
F:O_¢ ozw-¢<w¢ OOM

z¢DF F;m4 Ozm-¢<w¢ MOM

w2<m maF3me~m NOM
2¢DF mgoz< OON
Ozwu¢<w¢ NOF
F:OF<¢FM mduz< OOF
20-0<m: FOF
OJO>OFO OOO

O<2Fz< OOO

Fumnmo ¢sz0 ONO
Fumwmo Ome; OOO
z<F¢meOma OMO
ozFX¢<m OOO
oz~20<m OOO

81

mgquw> Ow¥¢<a FF: OMO

zF<¢F FF: ONO
z¢DF¢m>0 OFO

F MOO—:w> NOOZFO m00mz<44wOOF2 OOO

 

FFz: ¢2<¢-;;0 FFZO ;2<¢-20 FFZO O<0¢wm0¢0 FFzD wz~gz_<2 mma>F szOFOO<

|

Ad macaw gonna no magmaoam omamnouounw commmaaoo an mama» uamcfloofl

OH .>H ”Anna.

M F O O mmOz<zu¢sz~ ;0 n \ MszOFOO< ;0 O

F u mmoz<20¢szF ;0 ¢mm20z

M F O O MFszFOO< ;0 ¢mm2zz 4<FOF

 

z¢OF F=OF¢ 4<DO OOO

z¢DF F;w4 4<DO MOO

z¢DF F;w4 20-0<w: MOM
NFFMOQQO mm~3mmo_w MOM

2¢DF

m>~¢o O2m-¢<m¢ NOO
w>F¢O wauz< OOO
w>F¢O ¢sz0 OOO
F=OF¢ ozm-¢<m¢ OOM

z¢DF F;m4 ozw-¢<w¢ MOM

w2<m wa_3mmo_w NOM
z¢DF wauz< OON
O2m-¢<w¢ NOF
FIOF<¢FM m402< OOF
20-0<m: FOF
w40>OFO OOO

4<2Fz< OOO

Fuwnmo ¢w=F0 ONO
Fuwwmo OmXF; OOO
z<F¢meowa OMO
02F¥¢<a OOO
OszO<O OOO

81

m40~xw> Om¥¢<¢ FF: OMO

z~<¢F FF: ONO
2¢OF¢m>0 OFO

F m40~1w> wgosz w00w2<44mOOF2 OOO

 

F—z: a2<¢-;;0 FFZD ;2<¢-20 FFz: O<0¢mm0¢0 FFz: m2_42_<2 mwa>F szOFO0<

NH macho guano no munaaoao mononououaw oommmaaoo ha mama» uaovwoom

OH .>H GHDMB

MM.M MM.O FF OF mmoz<10¢mFZF ;0 u \ szmoFOO< ;0 n

M u mmuz<=u¢MFZF ;0 ¢wm232

OF 0F MM OM MFszFOu< ;0 ¢um232 4<FOF

 

z¢OF F:OF¢ 4<OO OOO

z¢OF F;mg 4<DO MOO

z¢DF F;m4 20-0<wz MOM
OFFMOOQO ma—3mmon MOM

N

z¢DF

~OO1’1-I-

m>F¢O ozmu¢<w¢ NOO
m>F¢O MOO2< OOO
w>F¢O ¢sz0 OOO
F:O_¢ ozw-¢<m¢ OOM

z¢DF F;w4 ozwu¢<m¢ MOM

m2<w w;_3mmo_w NOM
z¢OF w402< OON
ozw-¢<w¢ NOF
FIOF<¢Fm waoz< OOF
20-0<m: FOF
w40>unm OOO

4<2Fz< OOO

Fumwmo ¢wzF0 ONO
Fumamo Ome; OOO
2<F¢meoma OMO
OzF¥¢<a OOO
Ozqu<m OOO

82

F F NOOFzm> omx¢<a FF: OMO

zF<¢F FF: ONO
z¢OF¢m>0 OFO

OOO—:w> mOOsz m30mz<44wOOF2 OOO

 

FFz: a2<¢-;;0 FFZO a2<¢-20 FFZD O<0¢mm0¢0 FFZD mz_42_<2 wwa>F szo_00<

«a macho Gonna no muamaoaa monasouounw cannoaaoo ha momwu uaovfioom

OH .>H QHQUB

 

OF.F 0M.O FN.N O0.0 mmuz<=0¢szF ;0 n \ szmo_uu< ;0 &
OOF u mmoz<zu¢szF ;0 ¢mm222

MNF NO QMN MMM MFszFOO< ;0 ¢mm2nz 4<FOF
F F z¢DF F:OF¢ 4<OO OOO
z¢DF F;w4 4<OO MOO

O z¢DF F;m4 zO-o<w: MOM

F wFFmoamo maF3wwon MOM
N w>F¢O O2m-¢<m¢ NOO

O m>F¢O maoz< OOO

N F w>F¢O ¢wzF0 OOO

M F z¢DF F:O~¢ Ozm-¢<w¢ OOM
o N z¢OF F;m4 ozm-¢<w¢ MOM

F M w2<m m;_3mwo_w NOM
MF F z¢OF mauz< OON

OM F MM Mo ozm-¢<w¢ NOF
N NF F F:O_<¢Fm m402< OOF

FF z0-0<m: FOF

F m40>0_m OOO

FF O NM OOF O<2Fz< OOO
F N Fumsmo ¢m=FO ONO

MO NF ON ONF Fumamo ONXF; OOO
F F N z<F¢meOma OMO
F OzFx¢<a OOO

O ozF¥O<m OOO
M F O M mgu_=w> Omx¢<m FF: OMO
z_<¢F FF: ONO

OF NF MF OO z¢OF¢w>0 OFO
O M NF m;0—:m> NOOZFO w30mz<44w0mF2 OOO

 

FF2D ¢2<¢-;;0

FFZO a2<¢uzo

FFzO O<O¢mm0¢u

F—ZO wz_az_<2

mwm>F Fame—OO<

83

a macho Hanna no munoawao moanaonouzfi commaadoo Na monk» unovwooa

0N .>H OHQdB

 

NM.F O0.0 ON.N NM.M mmoz<=u¢mFZF ;0 O \ szmOFOO< ;O a
NO u mmuz<zu¢szF ;0 ¢wm2Dz

ON ON ONF NON szmOFOO< ;0 ¢mm232 4<FOF
z¢OF F2OF¢ 4<DO OOO

F z¢3F F;m4 O<OO MOO

F O z¢DF F;m4 20-0<m: MOM

F OFFmoaao ma_3mwo_m MOM

M w>~¢O ozm-¢<m¢ NOO

M m>~¢O w402< OOO

M w>_¢o ¢w=F0 OOO

M F z¢DF F:O_¢ czw-¢<m¢ OOM
M N z¢0F F;m4 ozm-¢<m¢ MOM

F w2<w wa_3mwo_m NOM
F MF F z¢OF mgoz< OON
0N O 0F OM Ozw-¢<w¢ NOF
OF N F:O_<¢Fm wquz< OOF

F M O 20-0<w: FOF

M m40>OFO OOO

F F MF OO 4<2~z< OOO
o Fumsmo ¢sz0 ONO

0N MF FN FN Fumsmo Ome; OOO
z<F¢meOwa OMO

F ozFx¢<a OOO

F N oz~xu<m OOO
M OF OOO—:m> Omx¢<a FF: OMO

z_<¢F FF: ONO

N M O FM z¢DF¢m>0 OFO
N N F NF OOO—:w> mgozuw w30mz<44wum_2 OOO

 

FFZO a2<¢-;;0

FFzD a2<¢uzo

FFZO O<0¢mm0¢u

FFZD wz_42_<2

mwa>F FszFOO<

84

N macho anusm no munmemao omnnaouopnw cmmmmFHoo ha monk» acovwoofl d~.>H manna

 

NO.N NO.F

O =
F_z: m2<¢-;;0 FFZD ;2<¢-20

m msoum Hmuzm uo munwamao

0F.O Mo.M wmuz<xu¢sz_ ;0 a \ szwo~uO< ;O %

MO u mwuz<=u¢szF ;0 ¢mO232

OOF MMN MFszFOO< ;0 ¢mm232 4<FOF

.—

,—
,—

z¢DF

0 N O O O P N

\fv-NN
:—

O MN
N

a =

F 2¢DF F;w4 02m.¢<w¢

N mJOFxm> ONX¢<Q F_z

z¢DF F:O_¢ 4<DO OOO

z¢OF F;m4 4<Do MOO

2¢DF F;m4 20.o<m: MOM
OFFMOQQO m;_3mmo_m MOM

m>_¢O O:w-¢<m¢ NOO
m>~¢o m402< O
m>~¢O ¢sz0 O
F:OF¢ 02m-¢<m¢ OOM
M
N
O

w2<w m;_3mma.m
2¢3F wOOz<
O2m-¢<w¢ NOF
FzOF<¢Fm w402< OOF
20-0<w: FOF
MOO>O_m OOO
4<2_z< OOO
Fumwmo ¢wzF0 ONO
Fumwmo OmXF; OOO
z<_¢meOwQ OMO
O2.¥¢<a o
O2_x0<m OOO
O
O

85

z_<¢F F_:
z¢3F¢m>o OFO

o OOO—xm> OOOZFM m30m2<44wum_2 OOO

F_z: O<0¢mm0¢0 F—z: szgz_<2 mwa>F FZNOFOO<

aoamnuumpnw oommmaaoo an mama» uqfiuwood

NN .>H UHQMH.

_".._n. .

'.'\

 

 

OM.O M0.0 MO.F O0.0 mmoz<zu¢szF ;0 O \ szmOFOO< ;0 %
NM u mwuz<zu¢szF ;0 ¢mm232
ON OF OM ONF szmOFOO< ;0 ¢mm20z 4<FOF
z¢OF quF¢ 4<DO OOO
z¢DF F;m4 4<OO MOO
z¢DF F;m4 20-0<m: MOM
OFFOOQQO wa—3mmOFm MOM
F w>F¢O ozmu¢<m¢ NOO
w>F¢O wquz< OOO
m>F¢O ¢wa0 OOO
z¢OF F:OF¢ ozm-¢<m¢ OOM
N M 2¢OF F;w4 O2m-¢<m¢ MOM
M m2<m waF3mwOFO NOM
F z¢DF mguz< OON
N N OF NM ozw-¢<w¢ NOF
F F:O_<¢Fm m402< OOF
F F 20-0<mz FOF
m40>0Fm OOO
O ON 4<2_z< OOO
N FOOOOO ¢sz0 ONO
OF 0 OF NM Fuwwmo owa; OOO
z<F¢meoma OMO
OzFx¢<a OOO
F N Oz~x0<m OOO
F M wOO_:m> Oux¢<a FF: OMO
zF<¢F FF: ONO
N O M OF z¢DF¢m>0 OFO
F N NOOsz> OOOZFO m00mz<44m0w_2 OOO
\F =
FFZO a2<¢-;;0 FFZD a2<¢-20 FFz: O<0¢mm0¢0 FFZD wz_az_<2 mma>F szOF00<

86

v macho Hanna no muzoamam mosazouounw cmmmmaaoo an mama» ucoowood

MN .>H ”MAME

 

MO.F MM.O MM.M MM.O mmuz<=0¢sz_ ;0 n \ szwOF00< ;0 n
O u mmuz<=0¢szF ;0 ¢wm20z

FF N ON OM szwOFuu< ;0 ¢wm232 4<FOF

 

z¢DF F:OF¢ 4<DO OOO

F z¢DF F;m4 4<3O MOO

z¢DF F;m4 20-0<m: MOM

OFFOOOQO maF3mwoFm MOM

N w>F¢O ozw-¢<m¢ NOO

F m>FOO OOO2< OOO

w>_¢O ¢sz0 OOO

F z¢DF FIOF¢ Ozw-¢<w¢ OOM

F zOOF FOOO Ozm-m<w« mOm

m2<m maF3meFM NOM

N z¢DF wAOz< OON

m m NF Ozm-m<w¢ FOF
O F F2OF<¢FO wauz< OOF

F zo-o<w: FOF

w40>OFO OOO

N o O<ze< OOO

F FuwamO ¢m=F0 ONO

M F N FN Fuwwmo OmXF; OOO
F z<OOFmOOOO OOO

Oz_y¢<a OOO

F O2F2O<O OOO

F OOO—:w> Omx¢<a FF: OMO

z_<¢F FF: ONO

n F zOOF¢m>O OFO
O w;u_:w> mgozmm m00mz<44w0m~2 OOO

£37

 

FFzO ¢2<¢-;;0 FFZO ¢2<¢-20 FFZO O<0¢wm0¢0 FFZD wz~42_<2 wwa>F szOFOO<

m macho Hanna «0 muaoaoam mvansououaw oommmaaoo an many» unmuwoo¢ v~.}m canny

 

ON.F ON.O Oo.N FO.N mmO2<xu¢szF ;0 n \ MFszFOO< ;0 u
NN u wmuz<:0¢sz_ ;O ¢wm232

NO ON OO OON OFZMOFOO< ;0 ¢mm232 4<FOF
F 2¢DF F:O_¢ 4<OO OOO
z¢OF F;m4 4<OO MOO

F z¢DF F;m4 20-0<m: MOM

F OFFMOOQO maF3mmO~w MOM

M m>F¢O ozw-¢<w¢ NOO

M m>F¢O m40z< OOO

M m>F¢O ¢sz0 OOO

F z¢OF F:O_¢ Ozm-¢<m¢ OOM

F O F z¢OF F;m4 Ozw-¢<w¢ MOM

M w2<m wa_3wmo_m NOM

M z¢DF wOOz< OON

OF M OF OM Ozw-¢<w¢ NOF
M 0 M F:O_<¢Fw mauz< OOF
M F 20-0<m: FOF

w4u>03m OOO

O F M OM 4<2_z< OOO
N FOmOOO ¢sz0 ONO

OF O OF OM Fumsmo OmXF; OOO
N z<F¢Fwwowa OMO

OzF¥¢<a OOO

OZFxO<m OOO

F O NOO—:m> ow2¢<a FF: OMO
z~<¢F FF: ONO

O N M ON z¢OF¢m>0 OFO
N N N N OOO—xm> NJOZFO m30w2<44m0m_2 OOO

 

FFzO a2<¢-;;0

F—ZO a2<¢uzo

FFz: O<0¢mm0¢u

F_zD mz~gz_<2

wwa>F szOFOO<

88

o aaoum Hausa no muaoamao mmaosououaw commaaaoo ha mumhu uaoowoo¢ n~.>H wands

MM.N OF.F ON.O Oo.O mmuz<=0¢szF ;0 n \ szmOFOO< ;0 u
NF u wmoz<zu¢mFZF ;0 ¢mm202

MO ON NN OFF szwOF00< ;0 ¢mm232 4<FOF

 

zOOF FOOFO OOOO OOO

zOOF FOOO OOOO OOO

F O zOOF FOOO 2O-O<O= OOO

OFFOOOOO OOFOOOOFO OOO

O O>FOO O2O-¢<OO FOO

N O>F¢O OOOzO OOO

F O>FOO OOOFO OOO

F F zOOF F=OFO O2O-O<OO OOO

O zOOF FOOO OzO-O<OO OOO

F Oz<O OOFOOOOFO NOO

F o zOOF OOO2< OON
FF m ON Om O2O-O<OO FOF
N F F F=O_<OFO OOO2< OOF
F O O zO-O<O= FOF
OOOFOFO OOO

F OF O<z_z< OOO

F m FOOOOO OOOFO OFO
MN m OF om FOOOOO OOxFO OOO
z<FOFOOOOO OOO

OzF¥O<a OOO

F F OzF¥O<O OOO

N OOOFOO> Omxm<a FF: OOO

zF<OF FF: ONO

O o N FF zOOFOO>O OFO
F F OOOF=O> OOozFO OOOO2<OOOOOFz OOO

2&9

 

FFz: a2<¢-;;0 FFZO a2<¢-20 FFzO O<0¢mm0¢0 F.23 wz_42_<2 mwa>F Fzmo~O0<

N macaw Hausa no munoaaao ammunououafl commuauoo an mama» unovwood o~.>H wanna

 

NM.O OF.M ON.O MO.NF mmoz<zu¢sz_ ;0 O \ szmomuu< ;0 u

N u wmoz<zu¢sz_ ;0 ¢mm232

 

 

OO Om OO NNF OFzOOFOO< OO OOOzOz O<FOF
zOOF FOO.“ O<OO OOO
zOOF FOOO O<OO OOO
zOOF FFOO zO-O<O= OOO
OFFOOOOO OOFOOOOFO OOO
O>FOO O2O-O<OO FOO
N O>FOO OOO2< OOO
N O>F¢O OOOFO OOO
F zOOF FOOFO O20-0<OO OOO
F zaOF FOOO O2O-O<OO OOO
F N Oz<O OOFOOOOFO NOO
F O F zOOF OOO2< OON
O O OF FO O2O-O<OO FOF
O F FOOO<OFO OOO2< OOF
F zO-O<O: FOF
OOOFOFO OOO
N N o O<2F2< OOO
FOOOOO OOOFO OFO
FF OF FF OO FOOOOO OOxFO OOO
F zOFOFOOOOO OOO
ozFxO<O OOO
OzFxO<O OOO
O N OOOF=O> OOgO<O FF: OOO
zF<OF FF: ONO
OF 0 o ZOOFOO>O OFO
O N F OOOFOO> OOozFO OOOO2<OOOOOF2 OOO
a a d d
FFzO Oz<0-0FO FFzO Oz<x-zo FFzO O<OOOOOOO FFzO OzFOzFOz OOOFF FzOOFOO<

9()

o msouo Hausm no muaoamao mmnmsououaw cmmmnaaoo an momma unoUfloom N~.>H manna

 

0M.N Mo.O OM.O FN.O mwuz<zu¢mFZF ;0 n \ szmOFOO< ;0 %
ON u wwoz<=o¢szF ;0 ¢mm20z

NO ON ONF ONF MFszF00< ;0 ¢mm20z 4<FOF
F F 2¢DF F1OF¢ 4<Oo OOO
2¢DF F;m4 4<Oo MOO

O z¢OF F;m4 20-0<w: MOM

F OFFOOAQO mm~3wwomm MOM

N m>~¢o ozwa¢<w¢ NOO

M F m>_¢O mguz< OOO

O m>F¢O ¢sz0 OOO

F M 2¢3F onF¢ ozm-¢<m¢ OOM
F O F z¢DF F;m4 Ozw-¢<w¢ MOM
w2<m mmF3wwOFO NOM

F O 2¢OF wauz< OON
OF N ON OO Ozw-¢<w¢ NOF
N M F:OF<¢Fw mguz< OOF
F O M 20-0<w: FOF

N wau>0~m OOO

N O OM 4<2_z< OOO
M Fumsmo ¢szO ONO

NN FF NM FM Fumsmo OOXF; OOO
F z<F¢meomm OMO
F czFx¢<a OOO

F Oz_¥u<m OOO

N N O OOO_:m> OOX¢<m FF: OMO
2_<¢F FF: ONO

OF N N NF z¢DF¢m>0 OFO
F M N FF m40_zm> mOOzFO w30w2<44w0mm2 OOO

 

FFZO m2<¢-;;0

FFzO m2<¢-20

FFz: O<0¢ww0¢0

F—ZO szJzF<2

mma>F FszFuu<

91

a macho Hauam no muaoamao oonasououcw 00mmuaaoo an mmmhu unouwoom m~.>H manna

M0.0 MM.O NO.F N0.0

wmuz<zu¢mF2_ ;0 n \ szwOFOO< ;0 n

O u wmoz<zu¢szF ;0 ¢mm232

szwoF00< ;0 ¢mm2az O<FOF

 

‘—

O

2¢DF F:O_¢ 4<Do OOO
z¢DF F;w4 4<Do MOO
z¢OF F;w4 20-0<m= MOM
m>~m0mm0 ma~3mwon MOM
m>~¢O ozm-¢<w¢ NOO
m>F¢O mdoz< OOO

m>F¢O ¢m=FO OOO

z¢3F F:O_¢ Ozm-¢<w¢ OOM
z¢DF F;m4 Ozw-¢<w¢ MOM
m2<m mm~3wmo_m NOM
2¢3F maoz< OON
Ozm-¢<m¢ NOF

FzOF<¢Fm w402< OOF
20-0<w: FOF

w40>umm OOO

4<2Fz< OOO

Fumamo ¢wzF0 ONO
Fuwsmo OOXF; OOO
z<F¢meOmm OMO

oz_x¢<; OOO

oz—u0<m OOO

wgumzm> owx¢<m FF: OMO
z_<¢F FF: ONO

z¢DF¢m>0 OFO

m40_:m> NOOZFO m30wz<44w0m_2 OOO

92

 

FFZO m2<¢-;;0 FFZO a2<¢-20 F_z: O<0¢mm0¢u F_z: wz_42_<2

mmm>F szOFOO<

oa maoum Huuam no munoamao monmnououzw commuaaoo an momma unocwoo¢ m~.>H manna

MN.M

NO

OM.F

OF

mO.M

OM

O muoz<=0¢MFzF ;0 u \ szwOF00< ;0 O
MF u mmuz<xo¢szm ;0 ¢mm232

ON szmOFOO< ;0 ¢wm232 4<FOF

 

ON

NQNFMFQ—c—t—

OF

z¢OF F:OF¢ O<OO OOO

z¢OF F;m4 O<OO MOO

z¢OF F;mO z0-0<m= MOM

wFFwoaao wanmwOFO MOM

m>F¢O Ozw-¢<m¢ NOO

w>FmO mOoz< OOO

w>F¢O ¢wzF0 OOO

z¢OF F:OF¢ Ozm-¢<w¢ OOM

z¢OF F;m4 Ozm-¢<w¢ MOM

m2<m manwwoFm NOM

zmaF mOuz< OON

FN Ozméfim FOF
F F:O_<¢Fw wqoz< OOF
20-0<w: FOF

mOu>uFm OOO

NN O<2Fz< OOO
F FOmOmo aszo ONO
FN FOOFOO OOx: OOO
z<F¢FwwOma OMO

F uz_y¢<; OOO
uzmxu<m OOO

O mOqum> Omx¢<a FF: OMO
zF<¢F FF: ONO

O z¢OF¢m>O OFO
M wqumzw> wguzmm w00w2<44m0mmz OOO

 

FFZO a2<¢-;;0

FFz: ;2<¢-20

FFzO O<0¢mm0¢u

sza mz_42_<2 mmm>F Fsz~00<

93

H macho oonaum no munmamam unannououafi ommmmaaoo an momhu unmowoom

0m .>H “MAME

 

 

OM.M ON.F MN.M O0.0 mmO2<zu¢mFZF ;0 n \ szwOFOO< ;0 u
ON u mmoz<z0¢szF ;0 ¢mm232

OO FM O0 mOF szmOF00< ;0 ¢wm232 4<FOF
z¢DF F:OF¢ O<OO OOO

F F z¢DF F;m4 4<OO MOO
M z¢OF F;m4 20-0<m: MOM

mFFMOQQO wa—3mwOFO MOM

O w>F¢O O2m-¢<m¢ NOO

N w>_¢O mdoz< OOO

N w>_¢O ¢sz0 OOO

N F 2¢OF F:OF¢ ozm-¢<w¢ OOM
M z¢OF F;m4 ozwn¢<w¢ MOM

F w2<m mam3mmo~m NOM

N F OF F z¢OF wguz< OON
OO FF ON NN O2m-¢<m¢ NOF
F F FF F:O_<¢Fw mauz< OOF
F F O 20-0<m: FOF
M NOO>OFO OOO

M FF 4<2~z< OOO

F N FOOOOO ¢uzF0 ONO

NN NF OF 0O Fumsmo OmXF; OOO
z<F¢meOmm OMO

Ozmx¢<m OOO

M F F N Oz~¥u<m OOO
F F N F NOO—:m> Omx¢<a FF: OMO
zF<¢F FF: ONO

O O OF z¢DF¢w>0 OFO
F M M w40_=m> OOOzmm m30m2<44wummz OOO

 

FFz: m2<¢-;;0

FFZO m2<¢-20

FFZO O<0¢mw0¢0

FFzD wz_42_<2

mmm>F szOFOO<

94

N macho omnwnm no manuamam wmnmnouounw cummmHHoo an mmmhu unocwoo¢ Hm.>H manna

 

MN.M OF.N O0.M OO.N mmoz<xu¢szF ;0 u \ szmOFOO< ;0 O
OO u mmOz<10¢szF ;0 ¢mm20z

OMF NO OMN OON szmOFOO< ;0 ¢mm2Dz O<FOF
O F z¢OF F=OF¢ 4<OO OOO
F F z¢DF F;w4 O<OO MOO
O F z¢DF F;w4 20-0<w: MOM

M OFFOOQQO maF3mmomm MOM

OF w>~¢O ozm-¢<m¢ NOO

o w>F¢O w402< OOO

O m>F¢O ¢sz0 OOO

O N O 2¢DF F2OF¢ Ozm-¢<m¢ OOM
F O F z¢OF F;m4 Ozw-¢<m¢ MOM
F N m2<m mm~3mmomm NOM

N 0N F z¢OF wOOz< OON
0O NN NO OMF Ozwu¢<m¢ NOF
F ON F F:OF<¢Fm wauz< OOF

F F o M zouo<w2 FOF
O ma0>0Fm OOO

M F N MF 4<2~z< OOO
F F N FOOOOO ¢sz0 ONO
OM FM FM ON Fumwmo OmXF; OOO
N O z<F¢meOmm OMO

N O2_x¢<m OOO

O F F OzFx0<m OOO
O M O w;u.:w> owx¢<m FF: OMO
zF<¢F FF: ONO

MF FN O 0N z¢OF¢w>0 OFO
M N OF mOO_:m> wOOzFO m00wz<44wOOF2 OOO

 

FFzO ;2<¢-;;0

FFz: a2<¢-20

FFzO O<0¢mm0¢u

F32: mz_42F<2

wwa>F szOFOu<

95

m macho conflum no muaaaouo moauzououaw commmdaoo an momma unoUOOOG

NM .>H manna.

 

 

 

ON.F ON.F m.F m.m OOOZOOONOFzF OO O \ OFszFOO< OO O
NF u OOO2<=OOOF2F mo OOOzOz
mF OF OF OO OFszFOO< OO OmOzOz O<FOF
zNOF FOOFN O<OO OOO
F ZNOF FOOO O<OO OOO
szF FOOO zO.O<O: OOO
OF_OOOOO OOFOOOOOO OOO
N O>FOO Ozm-m<mm FOO
O>FOO OOO2< OOO
F O>_OO OOOFO OOO
ZNOF FOOFN Ozw-N<ON OOO
F F ZOOF FFOO Ozm-x<mm OOO cu
F m Nz<O OO_3OOO_O NOO n9
N szF OOOz< OON
O O O ON O2O-O<ON FOF
O N FIOF<OFO OOO2< OOF
F zO-O<O: FOF
F OOOFOOO OOO
N O<ze< OOO
F FOOOOO OOIFO OFO
O m ON FOOFOO OOxFO OOO
F F F zOFOFOOOOO OOO
OZFOOOO OOO
F F OZFOOOO OOO
N F OOOFOO> Omxm<a F_= OMO
2F<OF FF: ONO
N F F m zOOFOO>O OFO
F NOOF2O> OOOzFO OOOO2<OOOOO_2 OOO
— = =
FOZO az<N-OOO FFzO Oz<m-zo FFzO OOONOOOOO F_zO OzOOzF<z

wma>F FszFOO<

 

v msoum omnfiuh no mucoEuaa mmzmsoumuaw vommmHHoo fin

momku unmUwood

mm .>H 0HQMB

M.O M.N MO.M NF.0 mmoz<=u¢mF2_ ;0 n \ MFszFOO< ;O O

O u muoz<zu¢szF ;O ¢mm232

 

 

NN MF MM MM szmOFOO< ;0 ¢mm232 4<FOF
F 2¢OF F:O_¢ O<OO OOO
F z¢DF F;w4 O<OO MOO
F O z¢OF F;m4 20-0<m= MOM
mFFOOOmO ma_3mmo_m MOM
M m>F¢O Ozw-¢<m¢ NOO
F m>~¢O mOOz< OOO
F w>_¢o ¢sz0 OOO
F z¢OF FzOF¢ Ozw-¢<m¢ OOM
N z¢DF F;m4 Ozm-¢<m¢ MOM
m2<m mam3mwOFm NOM
N M z¢DF m402< OON
FF M NF ON Ozmu¢<m¢ NOF
N FIOF<¢FM wOOz< OOF
F 20-0<mz FOF
w40>u_m OOO
F O<2Fz< OOO
FOmOmO ¢wzFO ONO
O O M FN FONOOO ONXF; OOO
z<F¢meowa OMO
Ozmy¢<a OOO
F ozFxO<m OOO
F F NOO—:w> Om¥¢<a FF: OMO
zF<¢F FF: ONO
N F O 2¢OF¢m>O OFO
F mOOsz> NOOzFO w30m2<44w0m_2 OOO
F F F F
FFZO ¢2<¢-;;0 FFz: ;2<¢-zO sz: O<0¢mm0¢0 FFz: szOzF<2 mwa>F szOFOO<

97

m macho omnwuh mo muaoamam mmzmnoumunw ummmmaaoo an momhu uzouwoom vm.>H manna

 

 

O0.0 Oo.F OM.M O0.0 mmuz<=u¢szF ;0 u \ szmOFOO< ;O %
OF u mmoz<x0¢MFzF ;O ¢mm232
OO 0F MM OO szwOFOO< ;0 ¢mm20z 4<FOF
z¢DF F:OF¢ O<OO OOO
F 2¢DF F;m4 O<OO MOO
O z¢OF F;m4 20-0<m: MOM
F NFFMOQQO NQF3MNOFO MOM
M w>_¢O Ozm-¢<m¢ NOO
N w>F¢O mOOz< OOO
F m>F¢O ¢sz0 OOO
N z¢OF F:O_¢ O2m-¢<w¢ OOM
M F z¢DF F;m4 ozm-¢<w¢ MOM
m2<m ma_3mwomm NOM
F M 2¢DF waoz< OON
OF N MF ON Ozm-¢<w¢ NOF
F O M FIOF<¢FO waoz< OOF
F M 20-0<w: FOF
w40>OFO OOO
N o 4<2_2< OOO
F Fuwwmo ¢wzF0 ONO
MF MF O ON Fuwwmo OwXF; OOO
F z<F¢meOma OMO
Oz_¥¢<a OOO
N ozFx0<O OOO
M NOOF=N> Omx¢<a FF: OMO
zF<¢F FF: ONO
OF F O z¢OF¢w>0 OFO
O NOO—:w> wOOzFO w30mz<44w0mF2 OOO
F F
FFZO a2<¢-;;0 F—ZO a2<¢uzo FFz: O<0¢wm0¢0 FFz: mz_42_<2 mwa>F szOFOO<

98

O msouo omawuh mo muaoeoao monunoumunfl oommmHHoo an momNu unocwood

mm .>H QHQMB

 

M.N MN.F NO.M NO.M mmOz<zu¢szF ;0 a \ szmOFOO< ;0 O
NF u mwoz<zo¢mFZF ;0 ¢wm232

OM MF OO FN szmOFO0< ;O ¢mm2Dz 4<FOF
F F z¢OF F:O_¢ O<OO OOO

F z¢DF F;w4 O<OO MOO

F O z¢OF F;w4 z0-0<w: MOM

mF_m0;m0 m;_3wmomm MOM

M m>F¢O Ozm-¢<w¢ NOO

w>F¢O maoz< OOO

N m>F¢O ¢sz0 OOO

F z¢OF F=OF¢ ozmu¢<w¢ OOM

F z¢OF F;m4 Ozw-¢<w¢ MOM

m2<m ma_3mmo_m NOM

N z¢OF wOOz< OON

N M O OM Ozmu¢<m¢ NOF
N FIOF<¢Fw mauz< OOF

N F F 20-0<w: FOF
w4u>0_m OOO

F O O<2Fz< OOO
FOOOOO ¢me0 ONO

FF M NF 0F Fuwamo Ome; OOO
F N z<F¢meOma OMO

OzFu¢<a OOO

F Oz_x0<m OOO
M OOO—zw> wa¢<m FF: OMO

zF<¢F FF: ONO

O M M o z¢OF¢m>0 OFO
O F F NOO—:m> NOOZFO m00wz<OOwOwF2 OOO

 

FFz: a2<¢-;;0

FFZO a2<¢-20

FFZO O<0¢mm0¢0

sza mz_42_<2

mwa>F szOFOO<

99

N macho mmawum no magmamao monogamouaw vommmHHoo an momma uncowoom

Om .>H 0HQMB

 

 

O0.0 OF.N O0.0 OO NF OOOzOFOFOFzF FO n \ OFzOOFOO< OO O
OF u OOO2<=OOOF2F FO OmOzOz
OO FO OO NOF OFzOOFOO< OO OOOtOz F<FOF
N zOOF FOOFO O<OO OOO
zFOF FFOF F<OO OOO
N F zFOF FOOO 2O-O<O= OOO
OFFOOOOO OOFOOOOFO OOO
O F O>FOO O20-0<OO FOO
O F O>FOO OFOz< OOO
O O>FOO OOFFO OOO
N F zFOF FFOFO O20-F<OO OOO
F FOOF FFOF O2O-O<OO OOO
O Oz<O OOFzmmOFO NOO
O O ZOOF OFO2< OON
ON OF NO OF O2O-O<OO FOF
F F O FOOF<FFO OFO2< OOF
F N zo-O<O= FOF
F OOOFOFO OOO
F F N o O<ze< OOO
F FOOOOO OOFFO OFO
OF OF FN OO FOOOOO OOxFO OOO
F z<FOFOOOOO OOO
OzF¥O<O OOO
F OngO<O OOO
O OOOFFO> OOFO<O FF: OOO
ZF<OF FF: ONO
O O O o zOOFOO>O OFO
O O O OFOF=O> OFozFO OOOO2<FFOOOF: OOO
4 = J—
FFzO Oz<0-0FO FFzO Ox<x-zO FFzO O<OOOOOOO FFzO OzFOzF<z OOOFF FzOOFOO<

100

m macho oonfiuh mo muamaoao ooznsououcw commMHHoo an mmmhu unmuwood

hm.>H OHQMB

 

MO.M OO.F 0N.M MO.M wmoz<zu¢szF ;0 u \ szmOFOO< ;0 O
OF H wmoz<zu¢szF ;0 ¢mm232

MM MN MM MO szmOFOO< ;0 ¢mm232 O<FOF
z¢0F qu~¢ 4<DO OOO

z¢OF F;m4 O<OO MOO

M z¢OF F;w4 20-0<m: MOM

mF_w0aa0 mmF3meFw MOM

O m>_¢O ozmu¢<m¢ NOO

N m>F¢O mOOz< OOO

N m>_¢O ¢wzF0 OOO

z¢OF F:OF¢ ozm-¢<m¢ OOM

N 2¢OF F;w4 ozwu¢<w¢ MOM

F N m2<m NQF3ONOFO NOM

M N F z¢3F wOOz< OON
NF N MF NM ozm-¢<m¢ NOF
N F:O_<¢Fm wdoz< OOF

F F 20-0<w: FOF

mFO>0FO OOO

N OF 4<2Fz< OOO
F F Fuwamo ¢wzF0 ONO

FN MF N ON Fumwmo ONXF; OOO
F z<F¢meOma OMO
F OzFx¢<m OOO

F F F, OZFxO<m OOO
F m40_:m> wa¢<m FF: OMO

zm<¢F FF: ONO

O O N M z¢OF¢m>O OFO
O M O NOO—zm> NFOZFO m30mz<44w0wF2 OOO

 

FFz: a2<¢-;;0 FFz: m2<¢-20

a macho ooawum no munaaoam monunoumunw 00mmmHHoo an momwu unocwoom mm.>H wands

FFz: O<0¢wm0¢0

FFZD mzmdz_<2

mwm>F szOFOO<

101

M.N M.M O M.ON mmOz<IO¢wF2_ ;0 n \ szmOFOO< ;0 a

N u mmuz<=0¢szF ;0 ¢wm232

M N O FO szmOFOO< ;O ¢mO20z O<FOF

 

z¢OF F:O_¢ O<DO OOO

z¢OF F;m4 4<0O MOO

z¢OF F;w4 20-0<m= MOM
memoaao ma~3mmo~w MOM

N z¢DF

m>m¢o ozm-¢<m¢ NOO
m>F¢O mOOz< OOO
w>F¢O ¢w=FO OOO
FIOF¢ Ozw-¢<m¢ OOM

z¢OF F;m4 ozm-¢<m¢ MOM

w2<m wa_3wwo~m NOM
2¢OF wacz< OON
ozw-¢<w¢ NOF
FIOF<¢Fm wguz< OOF
20-0<w: FOF
m40>OFO OOO

4<2Fz< OOO

Fuwwmo ¢sz0 ONO
Fuwwmo owa; OOO
2<F¢meowa OMO
Osz¢<a OOO
ozF¥0<m OOO

F OOO—:w> owx¢<a FF: OMO

z_<¢F FF: ONO
z¢DF¢m>0 OFO

NOO—:m> OOOZFO m00mz<44uum_2 OOO

 

F_z: m2<¢-;;0 FFZO a2<¢-20 FFZO O<0¢wm0¢0 FFZD wz_42_<2 wwm>F szOFOO<

on maouo umcwum no muamaoam ovamsoumunw commuaaoo an mmmhu uamuwood

mm .>H manna.

102

 

 

OOF OM NFM OON NON MMM OOM 0OO OMM FNO MONF MN szwOFOO< ;0 ¢mm232 F<FOF
N F F O N z¢OF F:OF¢ F<DO OOO
N N F N N N O FF 2¢OF F;m4 F<OO MOO
O M N M O O N O OF z¢OF F;mF 20-0<mz MOM
F N N F F F F mFFm0;aO mam3mmOFO MOM
M N M N M NF M M 0F w>F¢O Ozw-¢<w¢ NOO
N F F M M F O M OF m>F¢O wFOz< OOO
N F M M F O M O m>F¢O ¢me0 OOO
O M M O M N FF O MN z¢OF F:O_¢ Ozw-¢<w¢ OOM
N M O M M 0F MF N OO M z¢OF F;mF Ozw-¢<m¢ MOM
N NF M N M N N M ON m2<m mQF3mmOFO NOM
M O OF M NF N NF OF OF MO O z¢OF mFuz< OON
MO 0F 0ON OOF FMF NMF MMF MOM MON OFN NOM OF Ozm-¢<m¢ NOF
FF F NM FF O 0F MF OO MO NF 0FF F FIOF<¢Fw mFoz< OOF
0 O M N M N M 0 20-0<m: FOF
F N F M F O FF m40>u_m O0O
F M M M F N O N 0 F<2FZ< OOO
N M M N M F N O N F Fumwmo ¢szO ONO
ON O MMF OO O0 MO OO ONF O0 FOF 0OF MN FqumO ONXF; OOO
N M M O F NF F z<F¢meowa OMO
N N F N M OF M F O2_x¢<a 0OO
O M O F N NF M O OF O2F20<m OOO
M 0 M O M O OF OF O MN N wFO~xm> Omx¢<a FF: OMO
2F<¢F FF: ONO
M F NN NF MN MF OF 0N MF OF OF O 2¢OF¢w>0 OFO
F O O O N O O FF O MF M NOO—:m> mFOZFO m30mz<44mum_2 OOO
F1 4 F F 14 F F F F F F F
NF a30¢c FF m30¢o OF OOO¢O 0 a30¢o O a30¢o N a30¢o O a30¢o M ODO¢O O a30¢o M ¢30¢O N a30¢u F QOO¢O mmm>> FszFOO<

mmaoum away: On momma unocwoom ov.>H manna

103

 

 

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111

Urban

Data

Set

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-— Group 1

—+ Group 2 **
—% Group 3 **
—~ Group 4 **
—a Group 5 **
—4 Group 6 **
—fi Group 7 **
—u Group 8

—— Group 9

~—4 Group 10**1
HA Group 11
La Group 12

L L L L L L L L L L L . 1

 

 

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On°ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On—ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Chart 4.2 Data file set by Urban Groups

112

Rural

Data

 

 

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Data

file set by Rural Groups

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

113

Fringe

Data

 

 

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Data file set by Fringe Groups

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit
Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

Mainline Unit
Crossroad Unit
On-ramp Unit

Off-ramp Unit

114

CHAPTER V

MODELS

Having determined that models constructed on the total
data base did.not produce results sufficiently reliable to use
in selecting alternative design parameters, the stratified
data set was used for further analyses. As described in
chapter IV, the data had been stratified by activity density
(urban, rural and fringe) and by interchange design groups.
The data records were divided into cells representing this two
way classification, and models were constructed for each of
the analysis units within a cell. Only those cells with at
least 10 interchanges were modeled. These models were based

upon the following formula:

Y = f(X1, X2, x3, x,, X5)

where Y = Number of accidents on road segment (i)

__><
ll

Population (in 1000's) of the county

)9 = Lane mileage of the analysis unit (in 0.01 mile

units)
)5 = Number of on-ramps
)Q = Number of off-ramps
)g = Average Daily Traffic (ADT)

v.1 Models constructed on the Mainline Unit

115

Using stepwise linear regression, the following models

- provided the highest (R2) value for each group.

A. Models constructed based on the total accidents on the

mainline units

1. Model of urban group 2

Y = -l9.9lO + 0.000816X5

where Y = Total number of Accidents on road segment (i)

X5:= Average Daily Traffic (ADT)

From the above linear regression model, the multiple
regression coefficient (R) was 0.5441, based on 19

interchanges (38 road segments).

2. Model of urban group 3

Y = -l4.551 + 0.00115X5

where Y = Total number of accidents on road segment (i)

)g = Average Daily Traffic (ADT)

From the above linear regression model, the multiple
regression coefficient (R) was 0.9025, based on 11

interchanges (22 road segments).

116

3. Model of urban group 5

Y = -42.267 - 0.038X1-+ 0.00215X5
where Y = Total number of accidents on road segment (i)
)9 = Population (in 1000's) of the county
)8 = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.7839, based on 11

interchanges (28 road segments).

4. Model of rural group 1

Y = 0.937 - 0.00880X1-+ 0.000657XS

where Y = Total number of accidents on road segment (i)

X1 Population (in 1000's) of the county

)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.7336, based on 50

interchanges (99 road segments).

5. Model of rural group 2

117

Y = 4.650 + 0.000258X5

where Y = Total number of accidents on road segment (i)

X5== Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.3547, based on 27

interchanges (54 road segments).

6. Model of rural group 3

Y = -5.007 + 0.03OX2 + 0.000354X5
where Y = Total number of accidents on road segment (i)
X2== Lane mileage
)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.7150, based on 25

interchanges (49 road segments).

7. Model of rural group 4

Y = 3.435 + 0.06ox2 - 8.534X3-+ 0.000289xS

where Y = Total number of accidents on road segment (i)

118

)9 = Lane mileage

)9 = Number of on-ramps

)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.8262, based on 23

interchanges (55 road segments).

8. Model of rural group 6

Y = 0.182 + 0.000410XS

where Y = Total number of accidents on road segment (i)

)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.4087, based on 18

interchanges (48 road segments).

9. Model of rural group 7

Y = -6.247 + 0.069X2-+ 0.000316XS
where Y = Total number of accidents on road segment (i)
X2== Lane mileage

)g Average Daily Traffic (ADT)

119

From the above linear regression model, the multiple
regression coefficient (R) was 0.6497, based on 12

interchanges (26 road segments).

9. Model of rural group 9

Y = -27.865 + 11.561X3-+ 0.000585X5
where Y = Total number of accidents on road segment (i)
)g = Number of on-ramps

)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0. 6290, based on 19

interchanges (38 road segments).

10. Model of fringe group 2

Y = 7.932 - 0.067X2-+ 0.000685X5

where Y = Total number of accidents on road segment (i)
X2:= Lane mileage
)% = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.8200, based on 14

120

interchanges (28 road segments).

11. Model of fringe group 3

Y = -9.340 - 0.00629X1 + 0.062X2 + 0.000566X5
where Y = Total number of accidents on road segment (i)
X1== Population (in 1000's) of the county
)9 = Lane mileage
)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.6872, based on 26

interchanges (52 road segments).

12. Model of fringe group 8

Y = —7.127 + 0.149x2
where Y = Total number of accidents on road segment (i)
X2==-Lane mileage
From the above linear regression model, the multiple
regression coefficient (R) was 0.7452, based (Ni 10

interchanges (26 road segments).

121

13. Model of fringe group 9

Y = 5.488 + 0.077x2

where Y = Total number of accidents on road segment (i)

X2== Lane mileage
From the above linear regression model, the multiple
regression coefficient (R) was 0.7162, based on 10
interchanges (20 road segments).

v.2 Models conetructed on the crossroed unit

Using stepwise linear regression, the following models

provided the highest (R?)'value for each group.

A. Models constructed based on the total accidents on the

crossroad units

1. Model of urban group 3

Y = -57.966 + 0.553x2-+ 0.00257xS
where Y = Total number of accidents on road segment (i)
)9 = Lane mileage

XS

Average Daily Traffic (ADT)

122

From the above linear regression model, the multiple
regression coefficient (R) was 0.8590, based on 11

interchanges (11 road segments).

2. Model of urban group 4

Y = -21.355 + 0.425x2-+ 0.00167xS
where Y = Total number of accidents on road segment (i)
X2== Lane mileage
X5== Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.8656, based on 11

interchanges (11 road Segments).

3. Model of rural group 1

Y = -3.654 + 0.00348xS

where Y = Total number of accidents on road segment (i)

X5== Average Daily Traffic (ADT)

From the above linear regression model, the multiple

regression coefficient (R) was 0.7063, based on 50

123

interchanges (50 road segments).

4. Model of rural group 2

Y = 1.959 + 0.00246x5

where Y = Total number of accidents on road segment (i)

)g = Average Daily Traffic (ADT)

From the above linear regression model, the multiple
regression coefficient (R) was 0.6711, based on 27

interchanges (27 road segments).

5. Model of rural group 3

Y = 0.257 + 0.00235XS

where Y = Total number of accidents on road segment (i)

)g = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.8034, based on 25
interchanges (25 road segments).

6. Model of rural group 6

Y = ~175.947 + 0.373X2-+ 48.619X4

124

where Y = Total number of accidents on road segment (i)

)9 = Lane mileage

)9 = Number of off-ramps
From the above linear regression model, the multiple
regression coefficient (R) was 0.8795, based on 12

interchanges (12 road segments).
7. Model of rural group 7
Y = 4.597 + 0.00144X5

where Y = Total number of accidents on road segment (i)

)9 = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.8525, based on 10
interchanges (10 road segments).
8. Model of rural group 9

Y = -O.514 + 0.00384X5

where Y = Total number of accidents on road segment (i)

)9 = Average Daily Traffic (ADT)

125

ms-

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From the above linear regression model, the multiple
regression coefficient (R) was 0.8356, based on 19
interchanges (19 road segments).

9. Model of fringe group 2

Y = 4.077 + 0.00283x5

where Y = Total number of accidents on road segment (i)

)9 = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.7534, based on 14
interchanges (14 road segments).

v.3 Models constructed on the on-ramp units

Using stepwise linear regression, the following models

provided the highest (R2) value for each group.

A. Model constructed based on the total accidents on the on-

ramp units

1. Model of urban group 2

126

Y = 4.723 - 0.00118XS
where Y = Total number of accidents on road segment (i)

)9 = Average Daily Traffic (ADT)
From the above linear regression model, the multiple

regression coefficient (R) was 0.5051, based on 17

interchanges (18 on-ramps).

B. Models conetructed based on the fixed object accidents on

the on-ramp units

1. Model of urban group 2
Y = 0.883 + 0.039X2 - 0.000605XS

where Y = Total number of accidents on road segment (i)

X2== Lane mileage

)9 = Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.7388, based on 17

interchanges (18 on-ramps).

v.4 Models conetructed on the off-ramp unit

Using stepwise linear regression, the following models

127

 

provided the highest (R2) value for each group.
A. Model constructed based on the total accident rate on the
off-ramp unite
1. Model of urban group 2

Y = 8.236 - 0.00236X1 + 0.271X2 - 0.000565X5

where Y = Total number of accidents on road segment (i)

_?<
H

Population (in 1000's) of the county

)9 = Lane mileage

><
1|

5 Average Daily Traffic (ADT)
From the above linear regression model, the multiple
regression coefficient (R) was 0.9091, based on 17

interchanges (l9 off-ramps).

B. Models constructed based on the fixed obiect accidents on

the off-ramp units

1. Model of urban group 2

Y = 3.226 - 0.00102X1

where Y = Total number of accidents on road segment (i)

X1== Population (in 1000's) of the county

128

From the above linear regression model, the multiple
regression coefficient (R) was 0.5034, based on 1]

interchanges (19 off-ramps).

C. Models conetructed based on the rear-end accidents on the

off-ramp units
1. Model of urban group 2
Y = -O.267 + 0.152X2

where Y = Total number of accidents on road segment (i)

X2== Lane mileage

From the above linear regression model, the multiple
regression coefficient (R) was 0.6195, based on 17

interchanges (l9 off-ramps).
Summary of Reeulte

Based upon the above models, the sign of each variable
term was recorded for each group as shown in Table V.1. Some

general observations that resulted from a review of these

models were as follows:

129

 

1. On the mainline unit of urban freeway interchanges, all the
models have a positive sign in the average daily traffic term
as would be expected.

2. On the mainline unit of rural freeway interchanges, all the
models again have a positive sign in the average daily traffic
term. Also, all the models have a positive sign in the lane
mileage term. This indicates that the number of accidents
increases with the length of the road segment. Most of the
models have a positive sign in the number of on-ramps term,
indicating that the number of accidents on the rural mainline
unit increases where there are more on-ramps.

3. On the mainline unit of fringe freeway interchanges, all
the models again have a positive sign in the average daily
traffic term. This is consistent with the results in the urban
and rural areas. Also, most of the models have a positive sign
in the lane mileage term, indicating that the number of
accidents is greater for the longer fringe mainline units.
4. On the crossroad unit of urban freeway interchanges, all
the models have a pmsitive sign in the lane mileage and
average daily traffic terms, indicating that the number of
accidents increases with the longer crossroad units and
increased traffic.

5. On the crossroad unit of rural and fringe freeway
interchanges, all the models have a positive sign in the
average daily traffic term.

6. There were an insufficient number of models of the on-ramp

130

 

and off-ramp accident frequency to draw any general
conclusions.

7. Attempts to model specific accident types (fixed object
accidents, rear-end accidents) did not improve the model
accuracy (R2 value). Therefore, models built on predicting
total accidents were retained for further testing.

8. Relatively high values of R were achieved for group 3
interchange mainline and crossroad units in all three
categories (urban, rural and fringe). Group 3 interchanges
include Modified Diamond, Modified Tight Diamond and Parclo
A 4 Quad. Thus, it may be possible to accurately predict the
accidents to be expected at these interchanges.

9. Group 2 interchanges (Tight Diamond and Urban Diamond) were
not easily modeled, with low values of R resulting from the
urban and rural mainline models. The fringe area model fit the
data better, with an R value of 0.8200.

10. In the rural area, group 4 interchange (Partial Diamond,
Partial Tight Diamond, Trumpet A and Partial Directional Y)
models showed a good fit for both the crossroad and the
mainline segments. There was an insignificant sample of this
interchange group in the urban and fringe areas, so no models

were constructed for this interchange groups.

131

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CHAPTER VI

CALIBRATION

In order to test the above models, all models which had
a multiple R coefficient greater than 0.7 and were based on
more than 10 interchanges for the mainline and crossroad units
were considered. However, all the groups for the ramp units
were considered.during the calibration procedure since samples
of ramp data collected were so small. The linear regression
models were constructed for each group of mainline, crossroad
and ramp units based on population (1000's) of the county
(X1), lane mileage (in 0.01 mile unit) of the analysis unit
(X2) , number of on-ramps (X3), number of off-ramps (X4),
average daily traffic (ADT) (X5) and the total number of

accidents.
VI. 1 Modele for the Meinline Unit
1. Model of urban group 3
Y = -14.551 + 0.00115xS

From the above linear regression model, the predicted values
for each interchange not used in constructing the model for
this group were found, and these were compared with the actual

values as shown in Table V1.1.

135

2. Model of urban group 5
Y = -42.267 - 0.038X1-+ 0.00215XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.2.
3. Model of rural group 1
Y = 0.937 - 0.00880X1-+ 0.000657XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.3.
4. Model of rural group 3
Y = -5.007 + 0.030X2-+ 0.000354X5

From the above linear regression model, the predicted values

and the actual values are shown in Table V1.4.
5. Model of rural group 4
Y = 3.435 + 0.06OX2 - 8.534x3 + 0.000289XS

From the above linear regression model, the predicted values

136

and the actual values are shown in Table VI.5.

6. Model of fringe group 2

Y = 7.932 - 0.067X2-+ 0.000685XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.6.

7. Model of fringe group 8

Y = -7.127 + 0.149X2

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.7.

8. Model of fringe group 9

Y = 5.488 + 0.077X2

From the aboVe linear regression model, the predicted values

and the actual values are shown in Table V1.8.

v.2 Modele for the croeeroed unit

1. Model of urban group 3

137

Y = -57.966 + 0.553x2-+ 0.00257xS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.9.

2. Model of urban group 4

Y = -21.355 + 0.425x2-+ 0.00167xS

From the above linear regression model, the predicted values

and the actual values are shown in Table V1.10.

3. Model of rural group 1

Y = -3.654 + 0.00348XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.11.

4. Model of rural group 3

Y = 0.257 + 0.00235X5

From the above linear regression model, the predicted values

and the actual values are shown in Table V1.12.

138

5. Model of rural group 6

Y = -175.947 + 0.373X2-+ 48.619X4

From the above linear regression model, the predicted values

and the actual values are shown in Table V1.13.

6. Model of rural group 7

Y = 4.597 + 0.00144XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.14.

7. Model of rural group 9

Y = -0.514 + 0.00384XS

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.15.

8. Model of fringe group 2

Y = 4.077 + 0.00283x5

From the above linear regression model, the predicted values

139

 

and the actual values are shown in Table V1.16.

v.3 Models for the on-ramp unit

1. Model of urban group 2

Y = 4.723 - 0.00118X1

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.17.

v.4 Modele for the off-ramp unit

1. Model of urban group 2

Y = 8.236 - 0.00236x1 + 0.271x2 - 0.000565x.5

From the above linear regression model, the predicted values

and the actual values are shown in Table VI.18.

Summary of Results

Based upon the results of model calibration, the

following conclusions were drawn:

1. Out of the urban and rural mainline groups, group 3 which

140

comprises the interchange types of Modified Diamond, Modified
Tight Diamond and Parclo A 4 Quad predicts the observed values
well as shown in Graphs 1 and 4. These models indicate that
the number of accidents on the urban freeway interchanges of
Modified Diamond, Modified Tight Diamond and Parclo A 4 Quad
types depends primarily on the average.daily traffic (ADT) and
increases with increased traffic. However, models to predict
the number of accidents on the rural freeway interchanges of
the same types also include the lane mileage variable with the
accident frequency increasing with the length of the road
segment.

2. Out of the fringe mainline groups, group 2 and group 8
demonstrated good prediction capability as shown in Graphs 6
and 7. Group 2 comprises Tight Diamond and Urban Diamond
types. Groupi8 comprises Cloverleaf, Cloverleaf'with.CD roads,
Cloverleaf minus 1 loop and Directional with loops types. In
group 2, the models indicate that the number of accidents on
these types of interchanges depend on the lane mileage and
average daily traffic (ADT). However, in group 8, the number
of accidents on these types of interchanges depends only on
the lane mileage and increases with the length of road
segment.

3. Out of the rural crossroad groups, group 3 and group 7
predict the observed values well as shown in Graphs 12 and 14.
Group 3tcomprises Modified Diamond, Modified Tight Diamond and

Parclo A 4 Quad. Group 7 comprises Parclo AB and Partial

141

Directional. The number of accidents on these types of
interchanges depends on the average daily traffic (ADT) and
increases with the increased traffic. This is consistent with
the results of other groups.

4. Out of the urban off-ramp groups, group 2 which comprises
Modified Diamond, Modified Tight Diamond and Parclo A 4 Quad
types has a good prediction for the observed values as shown
in Graph 18. The number of accidents on these types of
interchanges depends on the population, lane mileage and
average daily traffic (ADT), and increases with less
population, longer length and reduced traffic.

5. Out of the remaining groups, 3 groups had at least one
negative predicted value and most of the remaining groups gave
poor predictions for the observed values. This might.be result
of the existence of outliers within the data. If the outliers
are removed, better predictions for the remaining groups could

be expected.

142

Table VI.1. Comparison.of.Actual and Predicted values of Total
accident frequency in UM-Group 3
_

 

 

Actual Values Rank Predicted Values Rank
100 3 118.32 3
167 2 215.62 1
173 1 129.36 2
89 4 68.88 4

 

 

 

 

 

 

 

143

 

 

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Table VI.2 Comparison of Actual and Predicted values of total
accident frequency in UM-Group 5
—

 

 

Actual Values Rank Predicted Values Rank
72 2 154.60 2
229 1 280.08 1
15 3 -24.34 4
8 4 71.80 3

 

 

 

 

 

 

 

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Table VI.3 Comparison of Actual and Predicted values of Total
accident frequency in RM-Group 1

 

 

 

Actual Values Rank Predicted Values Rank
23 3 16.36 7
O 17 54.40 1
21 5 16.32 8
11 10 15.50 9
3 15 7.34 17
45 1 35.28 2
l3 9 26.84 3
7 13 15.14 10
18 8 26.06 4
11 10 9.60 14
22 4 17.00 6
27 2 20.32 5
8 12 9.44 15
3 15 12.32 13
7 13 9.38 16
20 6 12.84 12
19 7 14.28 11

 

 

 

 

 

 

 

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Table‘VI.4 icomparison.of Actual and Predicted values of Total
accident frequency in RM-Group 3

 

 

 

 

 

Actual Values Rank Predicted Values Rank
52 l 29.68 2
39 2 24.33 3
19 5 10.58 6
26 3 12.94 5
11 6 7.78 7
11 6 6.74 9
10 8 7.02 8
21 4 75.96 1
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Table V1.5 Comparison of Actual and Predicted values of Total
accident frequency in RM-Group 4
—

 

 

Actual Values Rank Predicted Values Rank
45 2 14.64 3
5 6 9.30 5
4 7 14.52 4
20 3 19.54 2
6 5 37.70 1
3 8 3.60 8
12 4 4.70 7
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Table v1.6 Comparison of Actual and Predicted values of Total
accident frequency in FM-Group 2

 

 

Actual Values Rank Predicted Values Rank
23 2 45.23 2
17 4 33.17 3
19 3 27.92 4
14 5 21.45 5
60 1 75.59 1

 

 

 

 

 

 

 

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Table V1.7 Comparison of Actual and Predicted values of Total

accident frequency in FM-Group 8
_

 

 

Actual Values Rank Predicted Values Rank
167 1 153.56 1
25 4 77.38 3
124 2 79.67 2
40 3 49.86 4

 

 

 

 

 

 

 

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Table V1.8 Comparison of Actual and Predicted values of Total

accident frequency in FM-Group 9
—

 

 

Actual Values Rank Predicted Values Rank
39 2 38.24 1
42 1 35.69 3
21 3 31.46 4
16 4 37.61 2

 

 

 

 

 

 

 

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Table V1.9 Comparison of Actual and Predicted values of Total
accident frequency in UC-Group 3

 

 

Actual Values Rank Predicted Values Rank
87 2 141.48 1
43 ‘ 3 65.04 3
30 4 -25.20 4
161 1 98.96 2

 

 

 

 

 

 

 

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Table V1.10 Comparison of Actual and Predicted values of'Total

accident frequency in UC-Group 4
—

 

 

Actual Values Rank Predicted Values Rank
46 1 35.85 3
11 3 49.46 1
28 2 45.87 2
4 4 4.22 4

 

 

 

 

 

 

 

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Table V1.11 Comparison of Actual and Predicted values of Total
accident frequency in RC-Group 1
—

 

 

Actual Values Rank Predicted Values Rank
3 10 2.26 16
10 4 16.08 6
4 8 17.23 5
2 12 10.61 7
1 13 2.61 14
12 3 2.37 15
14 2 9.99 8
0 17 5.05 12
37 1 49.94 1
3 10 5.74 11
1 13 6.79 10
4 8 18.62 4
l 13 0.87 17
8 5 22.45 2
1 13 9.57 9
7 6 3.65 13
6 7 22.45 2

 

 

 

 

 

 

 

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Table V1.12 Comparison.of.Actual and‘Predicted values.of Total
accident frequency in RC-Group 3
—

 

 

Actual Values Rank Predicted Values Rank
54 2 24.20 2
6 5 9.42 6
11 3 10.83 4
1 9 1.27 9
7 4 1.29 8
2 7 9.66 5
5 6 4.09 7
67 1 61.12 1
2 7 13.68 3

 

 

 

 

 

 

 

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Table VI.13 Comparison of Actual and Predicted values of Total
accident frequency in RC-Group 6
—

 

 

Actual Values Rank Predicted Values Rank
44 1 29.59 2
1 3 -66.03 4
1 3 -60.81 3
29 2 82.68 1

 

 

 

 

 

 

 

 

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Table‘VI.14 Comparison.of.Actual and.Predicted values of'Total
accident frequency in RC-Group 7

 

 

Actual Values Rank Predicted Values Rank
2 4 9.08 4
11 3 19.72 2
21 2 13.96 3
49 1 30.76 1

 

 

 

 

 

 

 

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Table'VI.15 Comparison of Actual and Predicted values of Total
accident frequency in RC-Group 9
—

 

 

Actual Values . Rank Predicted Values Rank
16 1 19.72 2
16 1 17.92 3
2 6 16.57 4
2 6 2.44 6
3 5 9.47 5
5 3 22.53 1
4 4 2.17 7

 

 

 

 

 

 

 

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Table‘VI.16 Comparison.of.Actual and Predicted values of Total
accident frequency in FC-Group 2

 

 

Actual Values Rank Predicted Values Rank
46 3 32.52 3
56 2 13.30 5
18 4 21.06 4
13 5 50.21 2
75 1 55.44 1

 

 

 

 

 

 

 

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Table‘VI.17 Comparison.of Actual and Predicted values of Total
accident frequency in UON-Group 2

 

 

Actual Values Rank Predicted Values Rank
4 1 2.07 3
1 3 2.07 3
2 2 3.91 1
1 3 2.07 3
1 3 2.07 3
1 3 3.91 1

 

 

 

 

 

 

 

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Table V1.18 Comparison.of Actual and Predicted values of Total
accident frequency in OOF-Group 2

 

 

Actual Values Rank Predicted Values Rank
2 4 5.99 3
2 4 4.61 5
15 l 17.30 1
9 2 1.07 6
1 6 5.15 4
9 2 15.43 2

 

 

 

 

 

 

 

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CHAPTER VI I

SUMMARY and CONCLUS IONS

Summary

Freeway interchanges play' a 'very important role in
reducing the probability of vehicular conflicts during
transfer frem one road to another. However, the number of
accidents on freeway interchanges is increasing with increased
traffic on the freeway.

The purpose of this study was to identify the type of
accidents that occurred on the elements of the interchanges,
compare the accident rates with the results from .1. In
Cirillo's study, and finally construct freeway interchange
accident predictive models based on the elements which
comprise an interchange.

The first step iniconstructing these models was to obtain
geometric data, accident data and traffic data for
interchanges located in the State of Michigan. The data

obtained were:

0 Geometric data describing the elements of the freeway
interchange geometry were obtained from the Michigan
Department of Transportation's Highway Accident Master Data
file.

o Accident data from 1982 to 1984 were obtained from the

179

Michigan Department of Transportation's Highway Accident
Master Data file.

0 Traffic Data describing the level of use of the freeway
interchange elements were available from the Michigan
Department of Transportation's TVM (Trunkline Vehicle

Miles) Master Data file and Traffic Flow map.

These data files were merged to produce a master data
file composed of geometric data, accident data and traffic
data. This file was then stratified into 3 analysis units for
constructing freeway interchange accident predictive models

for each element of an interchange. These analysis units were:

o mainline unit
0 crossroad unit

0 ramp unit

During the study period 4464 out of 9534 accidents occurred
on the mainline unit, 2536 accidents occurred on the crossroad
unit and 2534 accidents occurred on the ramp unit,
respectively.

Based upon the total number of accidents for each
analysis unit, the first attempt was made to construct a
linear regression model using all interchanges in one model.
The multiple regression R coefficient for the mainline unit

was 0.5624, indicating that less than 30 % of the variance in

180

accident frequency was explained by the independent variables
used.

The master data file was then stratified into 3 area
types of activity density (urban, rural and fringe). The
master' data file ‘was further classified into groups of
interchange configurations with similar accident rates. The
interchange type with the lowest average accident rate
(accidents per interchange per 3 years) was 0.91 for the
Partial Diamond type interchanges and the highest value of the
average accident rate was 14.29 for the Full Directional type
interchanges. Interchange types that were similar to each
other in the average accident rate and variance were grouped
for further analysis. The interchanges were classified into

12 groups for each analysis unit:

. Group 1 - Diamond

. Group 2 - Tight Diamond, Urban Diamond

. Group 3 - Modified Diamond, Modified Tight Diamond, Parclo
A 4 Quad

. Group 4 - Partial Diamond, Partial Tight Diamond, Trumpet
A, Partial Directional Y

. Group 5 - Split Diamond, General Directional, Other

. Group 6 - Diamond plus 1 loop, Parclo B 4 Quad, Trumpet B,
Directional Y

. Group 7 - Parclo AB, Partial Directional

. Group 8 - Cloverleaf, Cloverleaf with CD Roads, Cloverleaf

181

minus 1 loop, Directional with loops
. Group 9 - Parclo A, Parclo B, Parclo AB 4 Quad
. Group 10 - Full Directional, General
. Group 11 - SRI-A

. Group 12 - SRI-B

For the classified groups, group 4 had the lowest value of
1.25 acc./int./3 yrs. and group 10 had the highest value of
10.27 acc./int./3 yrs.

The most common accident types occurring on the urban
interchanges were fixed object, rear-end and angle straight
accidents. Groupiz had.the highest percentage of fixed object,
rear-end and angle straight accidents. The accident types on
the rural interchanges were fixed object, rear-end and animal
accidents. Group 1 had the highest percentage of fixed object
and animal accidents, and group 3 had the highest percentage
of rear-end accidents. The predominant accident types on the
fringe interchanges were fixed object, rear-end and animal
accidents. Group 3 had the highest percentage of fixed object
and rear-end accidents, and groupil had the highest.percentage
of animal accidents.

Based on the total number of accidents per interchange
for each analysis unit (considering only groups with more than
10 interchanges), rural group 4 and urban group 10 had the
lowest value of 4.84 acc./int. and highest value of 13.75

acc./int., respectively on the mainline unit. On the crossroad

182

 

unit rural group 4 had the lowest value of 1.03 acc./int., and
urban groups 7 and 10 had the highest value of 6.5 acc./int.
On the on-ramp unit rural group 2 had the lowest value of 0.60
acc./int., and urban group 6 had the highest value of 3.50
acc./int. On the off-ramp unit rural group 4 had the lowest
value of 0.54 acc./int., and urban group 3 had the highest
value of 4.82 acc./int.

From the classified groups, only groups with more than
10 interchanges were selected for constructing linear
regression models. Three fourth.of the stratified data in each
cell were used to construct the model and the remaining 25 %
of the data were used for calibrating the model. Variables
used to construct the models were population (in 1000's) of
the county, lane mileage (0.01 mile units) of the analysis
unit, number of on-ramps, number of off-ramps, average daily
traffic (ADT) for the independent variables and the total
number of accidents for the dependent variable. Models with
greater than 0.7 in multiple R<coefficient.were tested against
the remainder of the stratified data.

The last step in constructing linear regression models
for predicting accidents on freeway interchanges was to
compare predicted and actual accident frequencies for the

acceptable models.

183

Conclueione

The following conclusions concerning modeling accidents

on freeway interchanges were drawn:

The data support the literature which found that the
accident rate on ramp units is higher than on mainline
and crossroad units.

Models with all interchanges in one model are not
reliable, because there is too much variance to be
explained by the variables used in the study. The type
of interchange (configuration) is the most important
variable, with accident rates ranging between 0.91
acc./int. and 14.29 acc./int.
Out of the variables used for constructing accident
predictive models, the average daily traffic (ADT) was
found to be the most significant in modeling freeway
interchange accidents. The number of accidents on the
mainline and crossroad units increased with increased
traffic. However, the number of accidents on the ramp
units tended to decrease with increased traffic.

It is possible to obtain reasonable predictions of the
accident frequency on the elements of some interchange
classes (see R values in Table v.3).

Some of the other variables tested (over or under,

lighting, and ramp control) might improve the model

184

u runab-

 

prediction power, but the data base was not large enough

to make these additional stratifications.

185

BIBLIOGRAPHY

186

 

BIBLIOGRAPHY

Cirillo, J. A., "Interstate System Accident Research
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Oppenlander, J. C. and Dawson, R. F., "Traffic Control
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Fisher, R. L., "Accident and Operating Experience at
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Vostrez, J and Lundy, R. A., "Comparative Freeway Study."
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Janoff, M. S., Freedman, M. and Decina, L. E., "Partial
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187

10.

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3, Session 8, May 1980, pp. 1-13.

Michael D. Meyer and Eric J. Miller, "grbeg
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Irwin Guttman, "Linear Models: An Introduction." John
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John Neter, William Wasserman and Michael H. Kutner,
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N. R. Draper and H. Smith, "Applied Regression Analysis."
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'T. L. Maleck and VL .1. Sproule, "Freeway Interchange
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Dept. of Civil and Environmental Engg., May 1985.

188

Jammy

 

 

 

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