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Material Information
- Title:
- Probablistic Assessment of Bridge Loading Concurrent with Permit Vehicles
- Creator:
- CRIM, MATTHEW
- Copyright Date:
- 2008
Subjects
- Subjects / Keywords:
- Axles ( jstor )
Headway ( jstor )
Histograms ( jstor )
Modeling ( jstor )
Probabilistic modeling ( jstor )
Recordings ( jstor )
Sensors ( jstor )
Travel ( jstor )
Trucks ( jstor )
Vehicles ( jstor )
Miami metropolitan area ( local )
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- University of Florida
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- University of Florida
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- Copyright Matthew Crim. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Embargo Date:
- 5/1/2005
- Resource Identifier:
- 71321858 ( OCLC )
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PROBABALISTIC ASSESSMENT OF BRIDGE LOADING CONCURRENT WITH
PERMIT VEHICLES
By
MATTHEW CRIME
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA
2005
Copyright 2005
by
Matthew Crim
This document is dedicated to my parents who have supported me throughout my
undergraduate and graduate careers.
ACKNOWLEDGMENTS
I would like to thank my committee chair and cochair Dr. Scott Washburn and Dr.
Kurtis Gurley for their continued support and guidance. I would also like to thank Vivek
Pahariya and Seokjoo Lee for their help in writing Visual Basic code.
TABLE OF CONTENTS
page
A C K N O W L E D G M E N T S ................................................................................................. iv
LIST OF TABLES .......................................... viii
LIST OF FIGURES ....................................... ........... ............................ ix
A B S T R A C T ...................................................................................................... ............ x i
CHAPTER
1 IN TR O D U C T IO N ........ .. ......................................... ..........................................1.
P problem Statem ent......... .. ......................................... .................................. . ...1.
B a ck g ro u n d ........................................................ ................................................ 2
B ridg e R ating Sy stem ........................................... ......................... ...............2...
F lorida's W IM P olling System ............................................................ ............... 3
D definition of a Perm it V vehicle ......................................................... ...............3...
P erm it issuance...................................................................................... .. .4
P erm it ty p e s ............................................................................................ 4
Objectives and Tasks .................... .. ........... .........................................5
2 LITER A TU R E R EV IEW .................................................................... ...............6...
Studies Pertaining to B ridge Loading...................................................... ...............6...
FD O T Literature .......................................................................................... . 10
3 PRELIMINARY ANALYSIS OF WEIGH-IN-MOTION DATA: SINGLE
V EH IC LE M O D ELIN G ................................................................. ...............1...... 1
R etrieval of D ata from FD O T ....................................... ........................................ 11
C conversion of D ata .................................................... .. ......................... ............... .. 14
Prelim inary A analysis of W IM D ata .................... ............ ........................................ 15
Initial Analysis of Data from All WIM Stations Combined...............................15
Generating Extreme Value Histograms from WIM Data.................18
Meaning of the extreme value histogram................................................20
Modeling the extreme value histogram ..................................................20
Application of the extreme value model .................................................24
Extensions of the extreme e value m odel................................... ................ 27
D difficulties w ith the W IM D atasets.......................................................... ............... 28
Inconsistent Form atting in W IM D ata Files...................................... ............... 29
Blank Data Files .......... ........ ... .. .............. ........................ 29
Same Vehicle Entry Recorded More than Once.............................................30
End of Month Carryover into the Subsequent Month .....................................31
Multiple Days of Data in a File with No Reset of the Vehicle Count..............32
Naming of Combined Files by the Last Day .................................. ................ 33
R solving Problem s w ith W IM Files ................................................ ............... 33
4 PERMIT VEHICLE ANALYSIS: REGIONAL VEHICLE MODELING ............ 36
F orm atting and P processing .........................................................................................36
Zones for Permit Vehicle Travel ................... ................ 38
Difficulties with the Perm it Vehicle D atasets ....................................... ................ 41
U know n Routes .................... ......................... .. .... ............... 41
Routes through Non-Contiguous Regions...................................... ................ 43
Determination of Multiple Vehicles on a Bridge ...........................................43
Blanket and Trip Perm it Im plications ................................................... 43
Probabilistic Modeling of the Permit Vehicle Data...............................................45
Regional Probabilistic Modeling of the Permit Vehicle Data..........................46
C o n c lu sio n s ......................................................................................................... 4 8
5 ANALYSIS OF WEIGH-IN-MOTION HEADWAY DATA: CONCURRENT
V EH ICLE M OD ELIN G .................................................................. ................ 49
H eadw ay A analysis ............................................................................. ..... .. ........ ..... 49
Identification of WIM Sites to Conduct Headway Analysis ..................52
A analysis of the Four Chosen W IM Sites........................................... ............... 55
B ridge L ength D eterm nation ......................................................... ................ 57
Speed D eterm nation ...................................................... ........ ...... .. ........ .... 57
Headway Determination at the Four W IM Sites ...................................... ............... 58
R e su lts................................................. ... ...... ....................................... ............ ........ 6 0
Generating Concurrent Vehicle Histograms from Headway WIM Data ............63
Modeling the Extreme Value Histogram Concurrent Permit Vehicles ............65
Interpretation of the Extreme Value Histogram .............................................69
Applications of Extreme Value Concurrent Weight Models ..............................70
6 SUMMARY AND RECOMMENDATIONS ............... ...................................72
S u m m a ry ..................................................................................................................... 7 2
Recommendations .......................... ........... .....................................74
APPENDIX
A FDOT CLASSIFICATION SCHEME "F" ...........................................................76
B W IM D A TA SU M M A R Y ............................................ ......................... ............... 78
C SUMMARY OF FILES CONTAINING MULTIPLE DAYS OF DATA..............93
L IST O F R E F E R E N C E S ...................................................................................................98
B IO G R A PH IC A L SK E T C H ...........................................................................................100
LIST OF TABLES
Table page
3-1 O verview of the 37 W IM stations .......................................................... ............... 12
3-2 C ontents of a selected W IM file............................................................. ............... 13
3-3 A key to the column fields for Table 3-2 ............... ....................................14
3-4 Sum m ary of W IM data .................................................................. ............... 17
3-5 WIM stations with an inconsistent file format....................................................29
3-6 WIM stations and years that contain blank files .................................................30
3-7 W IM file 99350110.021 V TR ............................................................ ................ 33
3-8 List of the files with multiple days of data for the site 9921, year 2001 ...............34
4-1 Examples of processed permit vehicle records ...................................................41
4-2 Routes not accounted for in the permit records...................................................42
5-1 H eadw ay data statistics ................................................................... ................ 51
5-2 Results from the ArcMap analysis of bridges .....................................................54
5-3 A average speeds and bridge lengths ..................................................... ................ 57
5-4 Summary of headway results .........................................................61
5-5 Summary of the travel direction of 80,000+ lb vehicles....................................62
5-6 Summary of same direction concurrent permit vehicles compared to all 80,000+
lb v e h ic le s ............................................................................................................. .. 6 2
LIST OF FIGURES
Figure page
3-1 Weight category percentages out of all vehicles over 85,000 lbs.........................17
3-2 W IM station 9932, the full year of data from 2001. ........................... ................ 19
3-3 W IM station 9932 (vehicles greater than 70,000 lbs)......................... ................ 20
3-4 Example of a maximum likelihood function for WIM data as a function of A........23
3-5 Exponential PDF model and normalized histogram (WIM station 9932) ...............23
3-6 First three months of data for 2001 from WIM station 9932 ................25
3-7 Exponential PDF model and normalized histogram (first three months from
W IM station 9932) ............... ................ .............................................. 25
3-8 W IM station 9901, the full year of data from 1998 ............................ ................ 26
3-9 Exponential PDF model and normalized histogram (WIM station 9901) ...............27
4-2 Regional partitioning of Florida for classification of travel for permitted vehicles
greater than 160,000 lbs ............. .............. ................................................ 40
4-3 Histogram of all permit vehicle data excluding weight over 1,000,000 lbs ..........46
4-4 The exponential PDF model on the normalized extreme value histogram ..............46
4-5 Exponential PDF models on the normalized extreme histogram..........................47
5-1 H eadw ay frequency histogram s .......................................................... ................ 52
5-2 Locations of the four WIM sites selected for headway analysis.................. 55
5-3 Detailed view of the four WIM sites selected for headway analysis ............... 56
5-4 Histogram of total weight passing WIM station 9913 in a 3-second interval..........63
5-5 Histogram of total weight passing WIM station 9926 in a 3-second interval ..........64
5-6 Histogram of total weight passing WIM station 9932 in a 2-second interval ..........64
5-7 Histogram of total weight passing WIM station 9936 in a 2-second interval..........65
5-8 Exponential PDF model and normalized histogram (WIM station 9913) ...............67
5-9 Exponential PDF model and normalized histogram (WIM station 9926) ...............68
5-10 Exponential PDF model and normalized histogram (WIM station 9932) ...............68
5-11 Exponential PDF model and normalized histogram (WIM station 9936) ...............69
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Engineering
PROBABALISTIC ASSESSMENT OF BRIDGE LOADING CONCURRENT WITH
PERMIT VEHICLES
By
Matthew Crim
May 2005
Chair: Scott Washburn
Cochair: Kurtis Gurley
Major Department: Civil and Coastal Engineering
Multi-presence factors in the AASHTO bridge code are designed to account for the
occurrence of multiple lanes experiencing maximum standard AASHTO loads. Permit
(overweight) vehicles represent a source of loading that exceeds standard vehicle
weights. The presence of a single permit vehicle in addition to the loads from standard
weight vehicles is arguably accounted for implicitly in the multi-presence factors.
However, there is a concern that such multi-presence factors do not account adequately
for the occurrence of more than one permit vehicle on a given bridge simultaneously.
The objective of this project was to develop a probability-based model to determine
whether the occurrence rate of multiple permit vehicles on a given bridge is significant.
Further, the model delineates the relative probability of the combined weight of
concurrent permit vehicles. The model is site-specific, dependent upon the frequency of
truck travel along a given route.
This project used information from the 37 Weigh-In-Motion sensors around the
state of Florida. Weigh-In-Motion (WIM) sensors are commonly used to obtain truck
weight data on major roadways throughout the state, employing passive weighing
techniques so the operator is unaware that the truck is being monitored. An evaluation of
the Florida Department of Transportation's (FDOT) WIM stations was done. Numerous
irregularities in the data were found during the evaluation process. A major issue that
was encountered was the fact that the WIM sensors did not record any truck weights
greater than 160,000 lbs. An additional source of data was obtained from the FDOT and
used to analyze the permit vehicles records over 160,000 lbs. These vehicles were
evaluated using a regional analysis.
Using multiple years of data from the WIM sensors, a model was created to predict
the presence of multiple permit vehicles concurrently on a bridge. The model was run on
four of the most heavily traveled among the 37 WIM stations. The four particular WIM
stations were chosen because they contained a high volume of trucks passing over the
sensor, numerous trucks over 85,000 lbs, several bridges within a 15 mile radius, and
together the sites represent different regions of the state.
Results indicate a significant number of observations of concurrent permit vehicles
at each of the four analyzed stations. The resultant probability models of combined
weight of concurrent vehicles represent an extreme loading condition with a considerable
chance of occurrence.
CHAPTER 1
INTRODUCTION
Problem Statement
Multi-presence factors in the AASHTO bridge code are designed to account for the
occurrence of multiple lanes experiencing maximum standard AASHTO loads. Permit
(overweight) vehicles represent a source of loading that exceeds standard vehicle
weights. The presence of a single permit vehicle in addition to the loads from standard
weight vehicles is arguably accounted for implicitly in the multi-presence factors.
However, such an assumption needs to be verified based on the specifications for permit
vehicle weights and traffic patterns within the state of Florida. In addition, the presence
of multiple permit vehicles in configurations that result in loads in critical locations may
conceivably exceed the capacity of the bridge.
This study examined the loads (additional trucks or otherwise) that should be
considered concurrent with the different permit loads for the purpose of calculating
appropriate operating ratings. Existing Weigh-In-Motion and other records were
analyzed to develop a probabilistic model of the relative likelihood of various concurrent
vehicle combinations to describe realistic worst case loading configurations. The
outcome will be used by Florida Department of Transportation (FDOT) engineers
evaluating the existing bridge rating system.
This chapter presents a brief background and necessary definitions, followed by the
specific objectives of the research.
Background
Truck travel has steadily increased in the recent years, and the amount of
overweight trucks on the roadways has also increased. Trucks that exceed 80,000 lbs are
considered overweight, and need special permission from the FDOT to operate on state
roadways. Additionally, trucks that exceed length and height limits are rarely allowed to
operate without a permit. Typically, these loads are short haul vehicles such as solid
waste trucks and concrete mixers. Although these vehicles are above the legal limits,
they are allowed to operate on the roadway due to "grandfather" provisions in state
statutes, and are referred to as exclusion vehicles [1].
With the large amount of trucks on the roadway, both over and under the permit
threshold limit of 80,000 lbs, monitoring the truck traffic flow is crucial to preserving
Florida's roadways and bridges. Weigh-In-Motion (WIM) sensors are commonly used to
obtain truck weight data on major roadways throughout the state, employing passive
weighing techniques so the operator is unaware that the truck is being monitored. This
study analyzed the WIM data collected in the state of Florida in order to develop a
statistical model of extreme loads on bridges due to overweight vehicles. More
specifically, WIM data will be used to determine the likelihood of the occurrence of
multiple heavy (permitted) vehicles on a given bridge simultaneously. The outcome of
this study will provide information to FDOT engineers evaluating the state of Florida's
bridge rating system.
Bridge Rating System
Load rating is a component of the bridge inspection process. It consists of
determining the safe load carrying capacity of bridges on an individual basis. The load
rating process estimates the live load capacity of a structure based on its current condition
through analysis or a load test. It determines if specific overweight vehicles can safely
cross the structure, and whether a structure needs to be weight restricted.
In addition, every bridge has an inventory rating and an operating rating. These
factors are used when evaluating the load rating of the bridge. The inventory rating
represents the load level which can safely be placed on an existing structure for an
indefinite period of time. The operating rating represents the absolute maximum
permissible load level to which the structure may be subjected [2].
Florida's WIM Polling System
Florida has implemented a system of software programs that, every night,
automatically poll each of the (approximately 37) WIM monitoring stations throughout
Florida and process the collected data. While the computer is polling the field counters
for their data, it is also processing the data from stations previously captured. All the
binary files are converted to ASCII. Count and classification records are generated from
WIM files. If these data pass some elementary filters, they are summarized by station,
date, and direction and written to the database tables. Once the database is populated, the
data are edited for quality [3]. Count and classification records are generated from WIM
files.
Definition of a Permit Vehicle
According to the Florida Department of Transportation's Trucking Manual, a
permit vehicle is any vehicle that needs special permission to operate on the roadway [4].
An overweight/oversized permit is required to move a vehicle or combination of vehicles
of a size or weight that exceeds the maximum size or weight established by law over state
highways. Except for certain vehicles exempt by law, any vehicle that exceeds the
following size or weight limitations is not allowed to move without a permit:
1. The maximum width of the vehicle or vehicle combination and load exceeds 102
in. or exceeds 96 in. on less than 12 ft wide travel lane.
2. The maximum height of the vehicle or vehicle combination and load exceeds 13 ft
6 in.
3. The maximum length of a single-unit vehicle exceeds 40 ft. The trailer of the
combination unit exceeds 48 ft. A 53 ft trailer with a kingpin distance which
exceeds 41 ft, measured from the center of the rear axle, or group of axles, to the
center of the kingpin of the fifth-wheel connection. The front overhang of the
vehicle extends more than 3 ft beyond the front wheels or front bumper if so
equipped.
4. The gross weight of the vehicle or vehicle combination and load exceeds 80,000
lbs.
Permit issuance
The intent of the law under which the FDOT issues vehicle movement permits is to
protect motorists from traffic hazards caused by the movement of overweight and
oversized vehicles or loads on state highways [4]. This ensures the comfort and
convenience of other motorists on the highways and guards against undue delays in
normal flow traffic. The permit process is also intended to minimize damage to
pavement, highway facilities and structures, thus protecting the investment in the state
highway system. Additionally, the permit process assist persons, companies or
organizations with special transportation needs involving size and weight. Furthermore,
permits are fee based, which will recover the DOT's administrative costs, as well as any
wear caused to the state highway system by the permitted loads.
Permit types
Overweight vehicles require either a trip-based or blanket permit. A trip-based
permit is used to cover a vehicle's move from the origin to the destination for one
particular trip, allowing that trip to occur within five days of permit issuance. However,
if the truck or trailer is oversized in any way, the return trip (empty) may be included on
the permit. Trip based permits are generally issued for vehicles over 160,000 lbs, and
often include route restrictions in which the permit is only valid if traveling over specific
roads. Trip permits are more restrictive than blanket permits.
Blanket permits are issued to vehicles for a twelve month period of time. The
vehicle can make as many trips as needed, as long as it is within the twelve month period.
Blanket permits are generally issued for vehicles under 200,000 lbs.
Objectives and Tasks
The first objective was a literature review. The literature review traced the
development of the current AASHTO provisions for bridge loading, and identified
existing studies on extreme traffic loads, permit vehicle routes, and statistical
characterizations of traffic flow over bridges. The FDOT Weigh-In-Motion and other
data records related to both permit and other vehicles were examined for relevant
information.
The second objective was the identification and classification of specific bridges
within close proximity to WIM stations. The subjects of study for vehicle loading were
bridges, but the available information on vehicle weight and frequency of occurrence
exists at the WIM stations. Identifying bridges close to WIM stations will justify the
extrapolation of WIM-based probability models to the nearby bridges.
The third objective was the development of a probabilistic model of concurrent
vehicles. The collected information on the frequency, routes, and weights was used to
develop a probabilistic model describing the likelihood of concurrent vehicles on bridges
with permit vehicle traffic. This portion of the model (concurrent use) will not directly
address critical locations for loading.
CHAPTER 2
LITERATURE REVIEW
The current AASHTO provisions for bridge loading account for the occurrence of
multiple lanes experiencing the maximum standard AASHTO loads. Permit vehicles
represent a source of loading that exceeds standard vehicle weights. The presence of
multiple permit vehicles on a single bridge is not directly accounted for. A large number
of papers were reviewed to identify any other studies that pertained to the work done in
this study. The following text will summarize the articles that were found.
Studies Pertaining to Bridge Loading
A study by Chou et al. [5] discussed a method to evaluate overweight permit
applications received in the state of Tennessee. A detailed structural analysis was
required for all vehicles with a gross weight over 150,000 lbs. Due to the volume of
overweight permit applications received, this policy resulted in a large demand in man-
hours to perform the structural analysis. Chou et al. developed an empirical method to
efficiently extract any suspicious overweight vehicles requesting a permit. The method
utilized the route type, the combined effect of truck gross weight, axle loads, and axle
spacing to assess the truck's effect on Tennessee highway bridges. An allowable weight
curve was empirically developed to determine whether a permit request should be
granted, rejected, or granted with restrictions. This reduced the detailed structural
analyses required by about 50%. The results of the study also reduced the cost of the
analyses and structural risk.
All states issue special permits for truck loads exceeding the weight limit of the
highway jurisdiction. This causes structural stress levels higher than those induced by
normal truck traffic. A study by Fu and Hag-Elsafi [6] discussed a method to develop
live load models including over-load trucks, associated reliability models for assessing
structural safety of highway bridges, and proposed permit load factors for over-load
checking in the load and resistance factor format. The average bridge safety assured by
the current AASHTO codes was used as the safety target in determining the load and
resistance factors in the proposed procedure. The procedure proposed by Fu et al. will be
useful to U.S. highway agencies as it can be used by engineers responsible for checking
overloads for permit issuance. This method may be included in specifications for bridge
evaluation subject to overweight trucks.
A study by Cohen et al. [7] presented a new method for predicting truck weight
spectra resulting from a change in truck weight limits. This method was needed to
estimate impacts of the change on highway bridges such as accelerated fatigue
accumulation. This model was based on freight transportation behavior, and it was
flexible for both across-the-board and local changes without restriction on the truck types
to be impacted. Using data from Arkansas and Idaho, it was shown that the proposed
method can capture effects of truck weight limit change on truck weight histograms and
on resulting steel bridge fatigue.
A study by Ghosn [8] developed a new truck weight formula that regulates the
weight of heavy trucks and axle groups. The formula was developed based on rational
safety criteria. The procedure used to obtain the proposed formula utilized a reliability
analysis such that the projected truckload effect will produce a uniform reliability index
for existing bridges designed according to current AASHTO criteria.
A sensitivity analysis that was performed in the second of a two paper sequence by
Ghosn and Moses [9] showed how the expected number of bridge deficiencies could be
reduced if different truck weight regulations were adopted, or if different bridge safety
criteria were used in the derivation of the truck weight formula. An analysis of twelve
typical bridge configurations confirmed the results obtained from the generic analysis of
the bridges taken from the National Bridge Inventory (NBI) files. The analysis indicated
few bridges would need rehabilitation if operating stress criteria were used for bridge
evaluation. However, several of these bridges would be considered deficient if working
stress design stresses were used as the rating criteria.
A study by Brillinger [10] studied at risk analysis in a format non-specific to
vehicles and/or bridges. Brillinger looked at low probability-high consequence events,
events that lead to damage, loss, injury, death, and environmental impairment. Based on
his findings Brillinger believes that the demand for risk analysis is growing steadily, in
part because the costs of replacing destroyed structures are growing and in part because
of the steady increase in the population living in hazardous areas. The article had two
examples, the first one was seismic risk analysis and the second was forest fire
probabilities. The method of risk analysis could be applied to predicting when multiple
overweight trucks would appear on a given bridge, a low probability-high consequence
event. Another study by Brillinger et al. [ 11] expanded on the forest fire study done in
the previous paper.
A study by Fu et al. [12] researched the effects that various existing and projected
truck configurations have as live loadings upon bridges which exist on the National
Bridge Inventory (NBI). The study found that the live load truck capacity of existing
bridges on the NBI was highly dependent upon the selection of the AASHTO
Specification alternate, the analysis methodology, and assumptions used in applying the
specification.
A study by Croce and Salvatore [13] presented a general theoretical stochastic
traffic model that can be used in the assessment of existing bridges, as well as the design
and analysis of bridges with less traditional schemes or subjected to particular traffic
conditions. The model is intended for applications, not only to background studies for
calibration of traffic load models in new bridge codes, but also in all those cases where
precise evaluation of traffic effects are required.
A study by Galambos [14] presented a comparison of the AASHTO design live
loadings for bridges with various other loading situations. Situations include normal
permit overloads and abnormal permit loads among other loadings. Galambos concluded
that the bridge load rating process needs to be improved. Also, a standard load rating
vehicle test and method should be employed.
A study done by Kolozsi et al. [15] discussed a computer program that was used to
determine routes for permit vehicles in Hungary. Weigh-In-Motion measuring units were
usually applied along highly trafficked roads and close to major bridges to monitor
weight. A noticeable difference between static mass and the loads of the moving vehicle
were found. The moving vehicle mass was also found to be higher than the considered
factors of the dynamic design specifications.
A study by Fryba [16] looked at the fatigue life of railway bridges. Fryba used the
Palmgren-Miner theory of linear cumulative damage as a basis. Fryba looked at the
effect of different parameters on the estimation of the bridge fatigue life. It was found
that the rise in speeds of the traffic loads has resulted in shortened bridge life. It was also
found that the increase in the number of stress cycles per year, the standard deviation of
stress, and an increase in the mean value of the traffic loads diminish the life of the
bridge.
The majority of articles that were found focus on the effects of overweight trucks
once they are on the bridges. None of the articles were found on the travel patterns of
overweight trucks, and the occurrence of concurrent vehicles on the same bridge.
Nevertheless, each article listed has information that is relevant to this study.
FDOT Literature
Three documents supplied by the Florida Department of Transportation were used
to get a better understanding of the project. The first document was the Bridge Load
Rating, Permitting and Posting Manual [2], which provided information on the load
rating process the FDOT used. The second document was the Automated Editing of
Traffic Data in Florida [3]; it provided insight into the Weigh-In-Motion polling process
used and the editing process that the FDOT used to filter out erroneous data. The third
document was the Trucking Manual [4], it was used to get information on the types of
permits the state of Florida issued along with when, why, and how permits were granted.
CHAPTER 3
PRELIMINARY ANALYSIS OF WEIGH-IN-MOTION DATA:
SINGLE VEHICLE MODELING
The state of Florida has 37 Weigh-In-Motion (WIM) sites dispersed across the
state. The truck data that these sites collect was downloaded to the FDOT central office
in Tallahassee. This chapter focuses on the contents of the WIM data records, examples
of preliminary analysis of these data, probabilistic modeling of the occurrence of a single
vehicle weight, and a discussion on problems identified within the data files.
Retrieval of Data from FDOT
Retrieval of the weigh-in-motion data for the project came from the statistics office
under Richard Reel's supervision. The data were copied onto a hard drive and brought
back to the University of Florida. There were approximately 25,300 files of data that
were collected and stored on the hard drive from January 1998 to August 2003. Each file
consists of the individual samples of WIM data collected during one 24-hour period at
one WIM station. Thus one WIM station could produces 365 files per year. A given file
may range from a few dozen to a few thousand individual samples of vehicle
information. Some WIM sites have data from all five years; others only have data from
part of that time frame. This is due to a specific site not being operational for a period of
time. Another reason for an incomplete five year time period was time constraints in the
collection process at the FDOT.
The data retrieved from the FDOT were in ASCII format. An overview of the 37
WIM sites such as site location, county, and number of lanes can be found in Table 3-1.
12
An example of the contents of any given data file can be seen in Table 3-2. A key
explaining each column in Table 3-2 can be found in Table 3-3. As can be seen in Tables
3-2 and 3-3, the WIM files contain details of the trucks being sampled, including date,
time, and lane of travel (implies direction), vehicle class, travel speed, gross weight, and
weight of each axle.
Table 3-1. Overview of the 37 WIM stations
Site Number Lane Original Existing Date Dates
Site Location County of Lanes Orientation Sensor Sensor Changed Copied
9901 1-10, Monticello Jefferson 4 OE-OW DAW-200 DAW-190 6/1/2003 1/98-12/99; 1/01-8/03
9904 -75, Micanopy Alachua 6 ON-OS DAW-200 DAW-190 4/15/2002 1/01 8/03
1-75, Micanopy-SB DAW-200
9905 SR-9/I-95, Jacksonville Duval 6 OS-ON DAW-190 DAW-190 1/01 8/03
9906 1-4, Deltona Volusia 4 OE-OW ADR-WIM ADR-WIM 1/01 8/03
9907 US-231, Youngstown Bay 4 ON-OS DAW-100 DAW-100 1/01 8/03
9908 US-319, Trk Rt, TLH Leon 4 OE-OW DAW-200 DAW-200 1/98 8/03
9909 US-19, Chiefland Levy 4 ON-OS DAW-200 DAW-190 8/14/2001 1/01 8/03
9913 Trnpk, St.Lucie Co. St. Lucie 4 OS-ON DAW-100 DAW-100 1/01 8/03
9914 SR-9A/I-295, Duval Co. Duval 4 ON-OS ADR-WIM ADR-WIM 1/01 8/03
9916 US-29, Pensacola Escambia 4 ON-OS DAW-190 DAW-190 1/01 8/03
9917 US-41, Punta Gorda Charolette 4 OS-ON DAW-200 DAW-190 5/2/2002 1/01 8/03
9918 US-27, Clewiston Hendry 4 ON-OS DAW-100 DAW-100 1/01 8/03
9919 1-95, Malabar Brevard 4 ON-OS DAW-100 DAW-190 6/23/2003 1/01 8/03
9920 1-75, Sumter Co. Sumter 4 ON-OS ADR-WIM DAW-190 10/2/2003 1/02 8/03
9921 SR-5, Martin Co. Martin 4 ON-OS DAW-100 DAW-190 4/11/2003 1/98- 8/03
9922 1-275, Tampa Hillsborough 6 ON-OS DAW-200 DAW-190 7/21/2003 1/02 8/03
9923 1-95, Jacksonville Duval 4 ON-OS DAW-200 DAW-200 1/02 8/03
9924 1-110, Pensacola Escambia 4 OS-ON DAW-200 DAW-200 1/02 8/03
9925 US-92, Deland Volusia 4 OW-OE DAW-200 DAW-200 1/02 8/03
9926 1-75, Tampa Hillsborough 6 ON-OS DAW-200 DAW-200 1/02 8/03
9927 SR-546, Lakeland Polk 4 OE-OW DAW-200 DAW-200 1/02 8/03
9928 1-10, Walton Co. Walton 4 OW-OE DAW-200 DAW-200 1/02 8/03
9929 US-1, Edgewater Volusia 4 ON-OS DAW-200 DAW-190 4/11/2003 1/02 8/03
9930 US-, Miami -SB Miami-Dade 6 ON-OS DAW-200 DAW-190 3/21/2003 1/02 8/03
9931 Trnpk, Sumter Co. Sumter 4 ON-OS DAW-100 DAW-100 1/01 8/03
9932 Trnpk, Osceola Co. Osceola 4 ON-OS DAW-100 DAW-100 1/01 8/03
9934 Homestead Ext, Dade Miami-Dade 7 (4S,3N) OS-ON DAW-100 DAW-190 6/3/2002 1/01 8/03
9935 US-27, Palm Beach Co. Palm Beach 4 OS-ON DAW-100 DAW-190 4/11/2003 1/98-8/03
9936 1-10/SR-8, Lake City Columbia 4 OW-OE DAW-100 DAW-190 1/30/2003 1/98- 8/03
9937 SR-87, Milton Santa Rosa 4 ON-OS DAW-100 DAW-190 5/23/2002 1/98- 8/03
9938 SR-83/US-331, Freeport Walton 2 ON-OS DAW-100 DAW-100 1/98 8/03
9939 SR-2, Graceville Holmes 2 OE-OW DAW-100 DAW-100 1/98 8/03
9940 SR-267, Quincy Gadsden 4 OS-ON DAW-100 DAW-100 1/98 8/03
9942 SR-85, Laurel Hill Okaloosa 2 ON-OS DAW-100 DAW-100 1/98 8/03
9943 SR-10/US-90, Cypress Jackson 2 OE-OW DAW-100 DAW-100 1/98 8/03
9944 SR-69, Selman Calhoun 2 OS-ON DAW-100 DAW-100 1/98 8/03
9946 SR-363, St. Marks Wakulla 2 OS-ON DAW-100 DAW-100 1/98 8/03
*OW, OE, OS, and ON represent the outside westbound, eastbound, southbound, and northbound
lanes. E.g. OE-OW means lane 1 refers to the outside eastbound lane and lane 4 refers to the
outside westbound lane.
13
Table 3-2. Contents of a selected WIM file (50 columns of data)
1 2 3 4 5 6 7 8 9 10 11 12 13
TAG County Station Lane Date Time Vehicle # Class Violation Speed Length Gross Weight L Axle 1
VTR 59 9946 2 1227/1999 32716 29 9 0 45 6144 28880 4980
VTR 59 9946 2 12/7/1999 33519 31 9 14 38 6144 80340 4170
VTR 59 9946 2 12/27/1999 34414 34 9 0 57 4922 24340 4040
VTR 59 9946 2 12/27/1999 34419 35 9 0 58 4960 27380 4020
VTR 59 9946 1 1227/1999 35433 38 9 0 51 7998 46740 6060
VTR 59 9946 2 1227/1999 35741 40 8 0 65 4812 22220 3610
VTR 59 9946 2 12l27/1999 35751 41 8 0 57 4386 23860 3930
VTR 59 9946 2 1227/1999 42447 46 8 0 48 4529 32920 5180
VTR 59 9946 1 12,27/1999 44215 50 9 1 67 6663 39360 6320
VTR 59 9946 2 12,27/1999 45534 51 9 0 63 4964 40580 6010
VTR 59 9946 1 1227/1999 45732 52 9 0 63 6638 32840 5130
VTR 59 9946 2 12/27/1999 45931 54 9 1 53 6255 45260 6540
VTR 59 9946 2 1227/1999 50813 56 8 0 70 4796 34700 5590
VTR 59 9946 2 12/27/1999 51657 57 8 O 67 4703 30240 4960
VTR 59 9946 2 12/27/1999 52122 60 9 15 59 6267 108740 7680
14 15 16 17 18 19 20 21 22 23 24 25 26
R Axle 1 Total Axle 1 L Axle 2 R Axle 2 Total Axle 2 L Axle 3 R Axle 3 Total Axle 3 L Axle 4 R Axle 4 Total Axle 4 L Axle 5 R Axle 5
4980 9960 2930 2930 5860 3070 3070 6140 1590 1590 3180 1870 1870
4170 8340 8370 8370 16740 8340 8340 16680 8730 8730 17460 10560 10560
4040 8080 3100 3100 6200 1980 1980 3960 1700 1700 3400 1350 1350
4020 8040 3180 3180 6360 2620 2620 5240 1220 1220 2440 2650 2650
6060 12120 4100 4100 8200 3840 3840 7680 4880 4880 9760 4490 4490
3610 7220 3680 3680 7360 1580 1580 3160 2240 2240 4480 0 0
3930 7860 4110 4110 8220 1580 1580 3160 2310 2310 4620 0 0
5180 10360 5480 5480 10960 3870 3870 7740 1930 1930 3860 0 0
6320 12640 3590 3590 7180 3760 3760 7620 3070 3070 6140 2940 2940
6010 12020 4180 4180 8360 4140 4140 8280 2640 2640 5280 3320 3320
5130 10260 2820 2820 5640 2870 2870 5740 3780 3780 7560 1820 1820
6540 13080 4660 4660 9320 4520 4520 9040 3310 3310 6620 3500 3600
5590 11180 5640 5640 11280 3130 3130 6260 2990 2990 5980 0 0
4960 9920 5540 5540 11000 2120 2120 4240 2500 2500 5000 0 0
7680 15360 11230 11230 22460 11080 11080 22160 12190 12190 24380 12190 12190
27 28 29 30 31 32 33 34 35 36 37 38
Total Axle 5 L Axle 6 R Axle 6 Total Axle 6 L Axle 7 R Axle 7 Total Axle 7 L Axle 8 R Axle 8 Total Axle 8 L Axle 9 R Axle 9
3740 0 0 0 0 0 0 0 0 0 0 0
21120 0 0 0 0 0 0 0 0 0 0 0
2700 0 0 O 0 0 O0 0 0 0
5300 0 0 O 0 0 O0 0 0 0
9800 0 0 0 O O 0 0 O 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
5880 0 0 0 0 0 0 0 0 0 0
6640 0 0 0 0 0 0 0 0 0 0
3640 0 0 0 0 0 0 0 0 0 0
7200 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
24380 0 0 0 0 0 0 0 0 0 0 0
39 40 41 42 43 44 45 46 47 48 49 50
Total Axle 9 NS NA WHLB ASP1 ASP2 ASP3 ASP4 ASP5 ASP6 ASP7 ASP8
0 4 5 5174 1381 421 2998 374 0 0 0 0
0 4 5 5096 1319 439 2939 399 0 0 0 0
0 4 5 3993 1311 447 1818 417 0 0 0 0
0 4 5 3975 1335 425 1821 394 0 0 0 0
0 4 5 5260 1773 510 3547 430 0 0 0 0
0 3 4 3824 1434 1981 409 0 0 0 0 0
0 3 4 3367 1311 1639 417 0 0 0 0 0
0 3 4 3530 1210 1942 378 0 0 0 0 0
0 4 5 5510 1395 488 3174 453 0 0 0 0
0 4 5 4032 1344 426 1869 393 0 0 0 0
0 4 5 5409 1475 459 3049 426 0 0 0 0
0 4 5 5278 1389 444 3029 416 0 0 0 0
0 3 4 3897 1493 2040 364 0 0 0 0 0
0 3 4 3871 1465 1988 418 0 0 0 0 0
0 4 5 5134 1361 433 2938 402 0 0 0 0
14
Table 3-3. A key to the column fields for Table 3-2
Column # Field Name Range Units Description Example Translation
1 TAG N/A N/A Identifies what type of file it is VTR Vehicle Truck Record
2 County 1 -94 N/A The county number where the site is located 59 station is in Wakulla county
3 Station 9901 -9946 N/A Station number (99xx) where 99 indicates a 9946 WIM detector #46
WIM station and xx is the site number
4 Lane 1 7 N/A Lane the truck was traveling in 2 vehicle was traveling in the northbound
5 Date 1/1/98 8/11/03 N/A Date surveyed 12/27/1999 date of sample
6 Time 0- 235959 hr, rm, sec Hours, minutes, seconds after 12 OC am 32716 time vehicle went over sensor which is 3
vehicle crossed sensor (32716= 3 27 16 am) hours 27 minutes and 16 seconds after
7 Vehicle # 1 n N/A nth vehicle to cross WIM station since 00 00 00 29 the 29th vehicle to pass over the sensor
8 Class 4- 13 N/A Classification of the vehicle according to 9 3 axle tractor w/ 2 axle trailer or 2 axle
scheme "F" of the DO T classification system tractor w/ 3 axle trailer
9 Violation 0 0 N/A Type of violation 0 no violation
10 Speed Variable* MPH Speed of vehicle 45 45 mph
11 Length Variable* FT Length of Vehicle from bumper to bumper 6144 61 44 ft
(format 99 99 decimal implied)
12 Gross Weight Variable* LB Gross weight of the vehicle 28880 203,B3I0 lb
13 L Axle 1 Variable* LB Left axle 1 weight 4980 4,980 Ib
14 R Axle 1 Variable* LB Right axle 1 weight 4980 4,980 Ib
15 Total Axle 1 Variable* LB Total axle 1 weight 9960 9,960 Ib
16 L Axle 2 Variable* LB Left axle 2 weight 2930 2,930 Ib
17 R Axle 2 Variable* LB Right axle 2 weight 2930 2,930 lb
18 Total Axle 2 Variable* LB Total axle 2 weight 5860 5,860 Ib
19 L Axle 3 Variable* LB Left axle 3 weight 3070 3,070 Ib
20 R Axle 3 Variable* LB Right axle 3 weight 3070 3,070 Ib
21 Total Axle 3 Variable* LB Total axle 3 weight 6140 6,140 Ib
22 L Axle 4 Variable* LB Left axle 4 weight 1590 1,590 lb
23 R Axle 4 Variable* LB Right axle 4 weight 1590 1,590 lb
24 Total Axle 4 Variable* LB Total axle 4 weight 3180 3,180 Ib
25 L Axle 5 Variable* LB Left axle 5 weight 1870 1,870 Ib
26 R Axle 5 Variable* LB Right axle 5 weight 1870 1,870 Ib
27 Total Axle 5 Variable* LB Total axle 5 weight 3740 3,740 lb
28 L Axle 6 Variable* LB Left axle 6 weight 0 only a five axle truck, therefore no data
29 R Axle 6 Variable* LB Right axle 6 weight 0 only a five axle truck, therefore no data
30 Total Axle 6 Variable* LB Total axle B weight 0 only a five axle truck, therefore no data
31 L Axle 7 Variable* LB Left axle 7 weight 0 only a five axle truck, therefore no data
32 R Axle 7 Variable* LB Right axle 7 weight 0 only a five axle truck, therefore no data
33 Total Axle 7 Variable* LB Total axle 7 weight 0 only a five axle truck, therefore no data
34 L Axle 8 Variable* LB Left axle 8 weight 0 only a five axle truck, therefore no data
35 R Axle 8 Variable* LB Right axle 8 weight 0 only a five axle truck, therefore no data
36 Total Axle 8 Variable* LB Total axle 3 weight 0 only a five axle truck, therefore no data
37 L Axle 9 Variable* LB Left axle 9 weight 0 only a five axle truck, therefore no data
38 R Axle 9 Variable* LB Right axle 9 weight 0 only a five axle truck, therefore no data
39 Total Axle 9 Variable* LB Total axle 9 weight 0 only a five axle truck, therefore no data
40 NS 1 8 N/A Number of axle spaces 4 4 axle spaces
41 NA 1 9 N/A Number of axles 5 5 axles
42 WHLB Variable* FT Wheel base, distance from first to last axle 5174 51 74 ft
(format 99 99 decimal implied)
43 ASP1 Variable* FT Axle Space 1-2 (format 99 99 decimal implied) 1381 13 81 ft
44 ASP2 Variable* FT Axle Space 2-3 (format 99 99 decimal implied) 421 4 21 ft
45 ASP3 Variable* FT Axle Space 3-4 (format 99 99 decimal implied) 2998 29 98 ft
46 ASP4 Variable* FT Axle Space 4-5 (format 99 99 decimal implied) 374 3 74 ft
47 ASP5 Variable* FT Axle Space 5-6 (format 99 99 decimal implied) 0 only four axle spaces, therefore no data
48 ASP6 Variable* FT Axle Space 6-7 (format 99 99 decimal implied) 0 only four axle spaces, therefore no data
49 ASP7 Variable* FT Axle Space 7-8 (format 99 99 decimal plied) 0 only four axle spaces, therefore no data
50 ASP8 Variable* FT Axle Space 8-9 (format 99 99 decimal implied) 0 only four axle spaces, therefore no data
*The values can be found in the Automated Editing of Traffic Data in Florida on pages 12-13.
Conversion of Data
The 25,300 files needed to be arranged properly for the requirements of the project.
A directory structure was created to organize the data. Each file contained one day's
worth of data consisting of hundreds of truck entries. A folder was created for each of
the 37 sites. Within each site's folder, the data were further subdivided into the specific
year that it pertained to.
Preliminary Analysis of WIM Data
After the data were organized into the proper folder system, a preliminary statistical
analysis was initiated. This section presents some of the original schemes applied to
characterize the WIM data in a probabilistic framework. A global perspective was first
used, in which the data from all WIM stations were combined to provide a view of the
overall relative likelihood of heavy vehicle travel in Florida. Extreme value analysis was
then applied to data from specific WIM sites over various time frames. The results of the
analyses presented in this chapter represent a starting point for feedback to the FDOT
project manager. Subsequent meetings narrowed the scope of the analysis to best fit the
intended use of the project results, and are the subject of Chapter 5.
Initial Analysis of Data from All WIM Stations Combined
There were several steps taken that perfected what information needed to be pulled
out of each file. A Visual Basic program was written to extract the minimum and
maximum vehicle classification, the minimum and maximum weight, and the total
number of vehicles for each day of data. The classification of the vehicles comes from
the classification scheme "F" from the FDOT, which can be found in Appendix A. From
the preliminary analysis of the data, it was found that the files consisted of only vehicles
that were classified as trucks (i.e., cars and other non-FDOT-defined-trucks were filtered
out).
The next step was to organize the weight of the vehicles into more precise groups.
Since a permit vehicle is 80,000 lbs or greater, the program only considered trucks
greater that 85,000 lbs. 85,000 lbs was chosen to account for weight measurement error,
thus ensuring that the vehicle needs a permit to operate. On top of the information that
was pulled out of each file by the first version of the Visual Basic program, the total
number of vehicles greater than 85,000 lbs, 90,000 lbs, 105,000 lbs, 120,000 lbs, 135,000
lbs, and 150,000 lbs were also recorded.
The final step was to identify the vehicle classes that were carrying the heaviest
loads. It is more significant if the weight of an extreme load is distributed over, for
example, four axles rather than seven. In addition to the information extracted from each
file in the second version of the program, the final version of the Visual Basic program
identified the classification of any vehicle that was 150,000 lbs or greater.
Table 3-4 presents the summary statistics from the combined WIM records of all
stations and all years. Of all vehicles that were weighed at the WIM stations, 6.12%
exceed 85,000 lbs. 85,000 lbs was the overweight threshold to determine the percent of
overweight vehicles within six ranges shown in Table 3-4. These are calculated as a
percentage among only those vehicles that exceed 85,000 lbs. The highest recorded
vehicle weight in any file was 160,000 lbs. The same information can be seen
graphically in Figure 3-1. Detailed lists of the data broken down by years and site
numbers can be found in Appendix B. The tables found in Appendix B give a better
perspective of the data that were extracted from each site and each year.
This preliminary analysis of all WIM data confirmed the initial presumption that
the WIM data ignores or otherwise filters any vehicle with a gross weight over 160,000
lbs. It was unclear at the start of the project whether this presumption was correct, and
whether it implied the need for additional data sets beyond the WIM site data. The
160,000 lbs maximum confirmed by this preliminary analysis of all WIM data led to the
acquisition of the permit data set that is the subject of Chapter 4.
Table 3-4. Summary of WIM data (all weight in 1000 lbs)
Percentage of Weight within Weight Range
Total Total Percent
Recorded Vehicles Vehicles Out of Vehicles Over 85,000 Ibs only
Vehicles >85 >85 85 90 105- 120- 135- 150-
90 105 120 135 150 160
29,897,981 1,829,854 6.12% 60.49% 33.33% 5.03% 0.77% 0.31% 0.06%
percent out of all vehicles over 85K
S 3.333
S30
20
10
50303
.___,.,^77 0.31 0 .07
85 90 105 120 135 150 160
weight in 1000 lbs.
Figure 3-1. Weight category percentages out of all vehicles over 85,000 lbs
Histograms could now be generated for different years at different sites. The
problem with generating histograms with the data pulled from the WIM files was that it
was very limited. The number of bins and the bin widths were both fixed for the weight
ranges shown in Table 3-4. The histograms that were generated also only apply to
vehicle weights greater than 85,000 lbs, not the whole data set. A broader analysis of the
data was conducted to generate histograms that were more flexible in what they could
present. This involved the development of a companion Visual Basic program for more
generalized processing of the WIM files. The next several sections discuss the analysis
of data at specific WIM sites using an exponential probability model.
Generating Extreme Value Histograms from WIM Data
A Visual Basic program was created to examine all the WIM data files for a
specified time period at a particular site. The program extracted the gross truck weight
for every truck from every truck data file. The program then created a separate text file
for each day, the contents of each consisted of only the gross weight for each truck record
in the file. The program also created a table of contents file that contained a list of the
names of all files that were processed. These files were then input into Mathcad [17] for
analysis. An array of the gross weight data could then be read from a desired file.
For example, the 99320101_1 1.txt file represents the file for January 11, 2001 at
site 9932. Numerous days at a given site (or multiple sites) could be loaded, creating one
large continuous array with all of the data for the files specified. A histogram could be
created by inputting the data source and the number of bins.
An example histogram is provided in Figure 3-2 from the full year of data at a
single WIM station. The WIM station is #9932 which is located on the Florida Turnpike
in Osceola County. The x-axis represents the vehicle weight; the y-axis represents the
number of trucks within each bin at that weight. The general shape of the resulting
histogram is bi-modal with a peak near 20,000 lbs and another near 45,000 lbs. The
lower peak is a distribution of unloaded trucks, while the higher peak is the distribution
of loaded vehicles.
2.5 -104 11111
2 10 -
1.5-10 -
Frequency
-IiL
1.10 4
5000 -
0 I Illll nnnnn-1d----_-_ -
2 104 4.104 6 104 8.104 1 -105 1.2 *10 1.4-10 1.6 -105
Weight (Ib s)
Figure 3-2. WIM station 9932, the full year of data from 2001.
The focus of the project was to model the occurrence of heavy vehicles. Therefore
the dataset was filtered to only look at the heavier vehicles; the vehicles that were to the
right of the second peak of the histogram. The histogram in this range appears to fit an
exponential distribution, defined later in this chapter, as the monotonic decrease in
probability from left to right. The portion of data that this study focuses on was the data
over 80,000 lbs. For the histogram in this example, a cut off of 70,000 lbs was chosen.
Only the samples over this level were kept for further extreme value analysis. Figure 3-3
shows the histogram produced from the full year of data from 2001 for the vehicles over
70,000 lbs.
1 -10 1 1 1 1
SO00
6000
Frequency
J-L
4000
2000
0 -- -lrnnnnnn.,--..- L
7.104 8-104 9-10 1 -105 1.1 105 1.2 -105 1.3 -105 1.4-105 1.5 -105 1.6 105
Weight (Ibs)
Figure 3-3. WIM station 9932 (vehicles greater than 70,000 lbs)
Meaning of the extreme value histogram
To use the histogram to determine probabilities, the data presented in Figure 3-3
needs to first be normalized so the area under the histogram equals one. The normalized
histogram would then represent the probability, out of any vehicle between 70,000 and
160,000 lbs, of a given range of weights passing the given WIM sensor over the time
frame chosen for analysis. An explanation of this process is discussed in the next section.
Modeling the extreme value histogram
It was desired to create an analytical parametric function that represented the
information provided in the normalized extreme value histograms of the data of interest.
A convenient functional form would be flexible enough to represent a variety of WIM
data, from different WIM stations over various time frames. Thus a parametric
probability density function (PDF) was sought that fits the WIM data well. The focus
was again restricted to the extreme values of heavier vehicles.
Fortunately, the monotonic nature of the histogram above 70,000 lbs lends itself
well to a simple PDF known as the exponential PDF. The exponential PDF is
f(x)= Axe -x (1)
where x is the weight, and A is the parameter that is optimized such that the error between
the exponential PDF and the normalized histogram is minimized. The procedure to
identify A involves finding the peak in the 'maximum likelihood function'.
Suppose that Xis a random variable (such as weight) with the probability density
function of f(x, 0), where 0 is a generic single unknown parameter (such as A).
Let xi, x2,..., Xn be the observed values in a random sample of size n (the weights from the
WIM data). Then the likelihood function of the sample is
L(O)= f(xl,,0) f(x,,0)x...x f(x,,,0) (2)
which is the product of the model probability associated with each observed value.
The value of the likelihood function is a function of the unknown parameter 0 and
the data. The maximum likelihood estimator of 0 is the value of 0 that maximizes the
likelihood of the functionL(0). That is, determine the value of 0 that makes the product
of the probabilities of the observations the highest.
In the specific case of the exponential PDF, the likelihood function is
L(A) = (Ax e x)(A 2x x2) ... x (A x e ", ) (3)
The value of likelihood function L(A) was plotted over a range of values of A, and
the value of A that corresponds to the peak value is the best descriptor of the data.
Identifying the peak in the likelihood function was easily done in Mathcad using a built
in optimization function.
It was more convenient to take logarithms and work with the log-likelihood
function. Since the logarithm function is monotonic, the log-likelihood takes its
maximum at the same point as the likelihood function presented in Equation (2). The
likelihood function in this form is now a summation of the natural log of the probability
of each sample (weight) rather than the product. The Mathcad function used to identify
the maximum likelihood value is more reliable in this form:
1(0) = logL()= log/f (x,; 0) (4)
Figure 3-4 illustrates the resulting log maximum likelihood function (Equation 4)
plotted vs. A for the data used to create Figure 3-3. Before calculating A, the data were
first linearly mapped from the 70,000 to 160,000 range into a range of 0 to 1. This was
done since the functional form of the exponential distribution has a lower bound of zero.
The value of A that provides the maximum value in this case was 6.621, calculated using
a Mathcad optimization routine. This A value was used to create the model and
substituted back into the exponential PDF (Equation 1), in this case f(x) = 6.621e-6621x
This analytical function (exponential PDF) now represents the data over the range 0 to 1.
In order to represent the data over the interval of 70,000 to 160,000 lbs, the analytical
function needed to be adjusted to invert the data mapping. Since the interval had
increased from 1 to 90,000, the exponential PDF needed to be divided by 90,000. In
addition, the value of x would become W 70,000 The new exponential PDF
160,000 70,000
equation in terms of the data in its original values Wis
( -Z W-70,000
f (W) 9= 0,00 x e \160,000-70,000 (5)
S90,000 (5)
The exponential PDF in Equation (5) was graphed on top of the normalized
histogram to demonstrate how closely the two curves match in Figure 3-5. Figure 3-5
represents the full year of data from 2001 for all the trucks weighing more than 70,000
lbs. The blue line represents the exponential PDF model identified using maximum
likelihood. This model was superimposed on the normalized histogram of the actual
WIM data. Figure 3-5 denotes the normalized version of Figure 3-3.
5.104 1 1 1I
0
MaxLike
-5 -104
-1-105 I I
0 5 10 15 20
Figure 3-4. Example of a maximum likelihood function for WIM data as a function of A
8 -10 I I I I
Nonnalized Histogram
6.10-5 Exponential PDF
S4.10 -
2.105
6 104 8-104 1 -105 1.2-105 1.4-105 1.6-105
Weight (1bs)
Figure 3-5. Exponential PDF model and normalized histogram (WIM station 9932)
Application of the extreme value model
An exponential PDF model of extreme vehicle weights was developed for many of
the WIM stations over varying periods of time. This produced a view of the relative
likelihood of heavy vehicles in various parts of Florida. Since the locations of the WIM
stations were available, these distributions can be tied to bridges of interest. For
example, the distribution fit to data from a WIM station along 1-95 may vary
considerably from a different station along 1-10. The difference may show a much higher
probability that heavier vehicles will approach a particular bridge on the east coast
compared to a bridge in the panhandle. These studies may also show a change in the
weight distributions at the same station during different seasons.
Two additional examples are presented. The first looks again at WIM station 9932,
but only uses the data for the first three months of the year rather than the complete year.
Figure 3-6 presents the full histogram of data from the first three months of 2001 from
WIM station 9932. Figure 3-7 presents the resultant exponential PDF fit using maximum
likelihood on the normalized extreme value histogram. From the full year to the first
three months the A parameter changed from 6.621 to 8.069.
1.5 -104
1.104 k
Frequency
IL
Figure 3-6.
6-10-5
.o
o -.5
4- 410
2-105
5000 -
2.104 4.104 6 .104 8 104 1 -105 1.2 *105 1.4-105 1.6-105
Weight (b s)
First three months of data for 2001 from WIM station 9932
IllllII
Normalized Histogram
.IL
Exponential PDF
I
7-104 s-104 9.104 1 105 1.1 -10 1.2-105 1.3-105 1.4-105 1.5-105 1.6-105
Weight (bs)
Figure 3-7. Exponential PDF model and normalized histogram (first three months from
WIM station 9932)
The second example uses the entire year of 1998 from WIM station 9901, located
on 1-10 near Monticello in Jefferson County. Figure 3-8 presents the full histogram of
data from WIM station 9901. Figure 3-9 presents the resultant exponential PDF fit using
maximum likelihood on the normalized extreme value histogram. The cutoff point for
the data from WIM station 9901 was 75,000 lbs instead of 70,000 lbs which was used for
the previous two examples. The point where the exponential curve starts to develop
differs from station to station; therefore the cutoff point was adjusted. From the full year
(2001) at station 9932 to the full year (1998) at station 9901 the A parameter changed
from 6.621 to 20.323.
6 .104
4.104 F
Frequency
nL
2.104 -
2 -10 4 104 6.104 -104 1 105
Weight (Obs)
Figure 3-8. WIM station 9901, the full year of data from 1998
1.2-105 1.4.105 1.6-105
I I I
1.5-10 -
0
1 -10-4 -
5.10-5 -
0 --
7 .104 S-104 9.104 1 .105 1.1 105 1.2-105 1.3-105 1.4-105 1.5-105 1.6-105
Weight (ibs)
Figure 3-9. Exponential PDF model and normalized histogram (WIM station 9901)
A higher 2A value indicates that the right tail of the distribution (the heaviest vehicle
weights) were less probable when compared to low values of A. That is, the higher the A,
the less likely heavier vehicles will be observed. Coupling such relative probability
information with the frequency of observations of all trucks at a given WIM station
provides a quantification of heavy vehicles traveling along that WIM route.
Extensions of the extreme value model
Thus far the extreme value modeling of heavy vehicles did not include information
regarding the likelihood of multiple heavy vehicles on a bridge. The histograms that
were produced (e.g., Figures 3-2 and 3-3) do not use the time between individual WIM
records as an input. However, the methodology presented above can be adjusted to take
advantage of the time stamp of each record, which was provided in the WIM records.
The modeling discussed above may be extended to include additional independent
variables, such as time between WIM records. This extension will be useful for
identifying the likelihood of multiple heavy vehicles approaching bridges. For example,
similar modeling techniques can be used to identify probabilities for the total weight to
pass a WIM station over a chosen time frame, say five minutes. Another distribution can
be developed to describe the average headway between adjacent weighted vehicles.
Total weights could potentially exceed 160,000 lbs if several heavy vehicles are traveling
close together. Short of placing WIM sensors immediately before a bridge of interest,
this modeling method is valid for helping determine the probability of simultaneous
heavy vehicle loads on a bridge.
The consideration of headway information in probability modeling was a subject
that was pursued more rigorously in Chapter 5, when the analysis was shifted to target the
likelihood of multiple heavy vehicles occurring within a specified length of road. This
includes multiple vehicles traveling together, and vehicles traveling opposite directions
which cross the same WIM sensor within a short time frame.
The next section discusses in detail irregularities identified within the WIM data
provided by the FDOT during the course of the preliminary analyses discussed thus far.
The forms, sources and significance of these irregularities were investigated to determine
whether they were likely to have a significant impact on subsequent data analysis.
Difficulties with the WIM Datasets
In the development of the Visual Basic programs and the preliminary analysis of
the WIM data, numerous irregularities and difficulties were encountered. The next
section will discuss some of the difficulties that have been observed with the contents of
the WIM records. The next chapter moves from the WIM datasets to the permit vehicle
records that contain information for vehicles over 160,000 lbs.
There were six complications that were encountered when analyzing the WIM
datasets. The first two complications were resolved, while the last four remain
unresolved. The next six subsections discuss these issues.
Inconsistent Formatting in WIM Data Files
The majority of the WIM data were set up so that each line of data represented all
of the statistics for a single truck. Each new line represented a new truck that passed the
sensor. Data at a few of the WIM stations were not broken up line by line for each truck
that passed over the sensor; instead they were one continuous line of data. The site
numbers and years of data that had the problem are listed in Table 3-5.
A solution was reached using a Visual Basic program. A rectangular box character,
similar to the character shown in parentheses ( ), separated adjacent entries on the same
line. The Visual Basic program produced an identical file in the correct format. Each
time a box was encountered, a new line of text was created below the previous line. This
process eliminated the continuous text string and organized the file in a line by line basis.
Table 3-5. WIM stations with an inconsistent file format
Site Number Years
9901 1998, 1999
9908 1998, 1999, 2000
9921 1998, 1999, 2000
9935 1998, 1999, 2000
9936 1998, 1999, 2000
Blank Data Files
Any single data file contained the data collected during a 24-hour period at a
particular WIM station. Some data files contained no data for a given day. Ordinarily, if
there were no data for a given day, there was no file for that day. The assumption was
made that there must have been some complication in sending the data from the site back
to the DOT. These files were omitted from the data files used for analysis. The site
numbers and years of data that contained blank files are listed in Table 3-6. The table
does not indicate that an entire year of data was missing, only that one or more days in
that year were blank.
Table 3-6. WIM stations and years that contain blank files
Site Number Year(s) Site Number Year(s)
9901 2001 9935 1999,2000,2003
9906 2001 9936 2001
9907 2002 9937 1998
9909 2001 9938 2000
9914 2001 9939 1998, 1999, 2000, 2003
9917 2001 9940 2003
9919 2001,2002 9942 2000, 2001,2002, 2003
9921 2000 9943 1999,2003
9925 2002,2003 9944 1998,1999,2001,2003
9929 2003 9946 2000,2003
9931 2001
Same Vehicle Entry Recorded More than Once
Some data files contained many more entries than other files around the same time
period (each file should be a single day). It was found that the large files were combining
multiple records of days into one large file. This was not a big problem if any vehicle
was simply recorded once, but stored in the wrong file (a different day). There was a
time and date stamp associated with each record. However, in some cases one or more of
the days that were contained within the large file would also have its own VTR (vehicle
truck record) file. This means that some days of data were represented twice in a dataset.
There were two different situations, the first was when a day in the large file was
identical to its VTR file, and the second situation was when it was not identical.
An example of files with the first problem was found in records
99320209.041_VTR and 99320209.051_VTR. The first file represents the day
September 4, 2002 and is 508 KB; the second file represents September 5, 2002 and is
991 KB. The September 5th file contains data from both days. When splitting the
September 5th file into two files, a 508 KB file and a 483 KB file were created which
represent September 4th and 5th respectively. The two September 4th files were identical,
therefore recording all the data from September 4th twice.
An example of files with the second problem was found in the files
99130202.111_VTR and 9932130202.121_VTR. The first file represents the day
February 11, 2002 and is 166 KB; the second file represents the day February 12, 2002
and is 816 KB. The February 12th file contains data from both days. When separating the
February 12th file into two files a 390 KB file and a 426 KB file were created which
represent the complete files for both days. The reason the February 11th file increased
from 166 KB to 390 KB was that the 166 KB file only had the first 11 hours of the day,
whereas the 390 KB file contained all 24 hours. This meant that a portion of February
11th was recorded twice.
End of Month Carryover into the Subsequent Month
This problem was an extension of the previous problem. The issue was still
multiple days of data being combined into one data file. In some cases the day or days at
the end of a given month were combined with the beginning days in the subsequent
month. When multiple data files were combined into one they were arranged in
ascending order, adding the next day to the end of the previous day. The particular
problem in this case was that when the data switched from one month to the next, the data
from the prior month did not have the proper month number in its date stamp, but rather
has the month subsequent to it.
An example of a file that has this problem was found in the file 99469812.021.
This file should only contain the data from December 2, 1998. Instead it contained the
data from November 30th, December 1st, and December 2nd. The day of data from
November 30th had been improperly date stamped as December 30th, thus the file appears
to contain December 30th, December lst, and December 2nd. At this WIM station there
was no November 30th file, but there was a separate December 30th file. The actual
December 30th file and the part of the December 2nd file that contained data improperly
stamped as December 30th have nothing in common (no repeats of specific vehicle
weights or times). Thus, the conclusion was that November 30th was a part of the
December 2nd record with an improper date stamp.
Multiple Days of Data in a File with No Reset of the Vehicle Count
This problem was similar to the previous two problems. It deals with multiple days
of data being combined into one file. The end of any given day should result in a
resetting of the time to midnight (00:00:00) and vehicle number to 1, thus providing a
count of vehicles per day. The issue was that when the combined file switched from one
day to the next, the survey hour, minute, second, and vehicle number did not reset for the
new day. A file with this problem was 99350110.021_VTR. This file was supposed to
contain October 2, 2001 data. The records within jumped dates from September 21st to
October 21st to October 1st before a 24-hour period was completed and the time and
vehicle number were reset. However, when it went from October 1st to October 2nd, it did
not encounter this problem. Table 3-7 presents an example from portions of WIM station
9935 on October 2, 2001. This site contained more than one day of data without resetting
the time stamp or vehicle number. The light grey highlight represents when the time
stamp and vehicle number do not reset. The dark grey highlight represents the correct
reset of the time stamp and vehicle number.
Table 3-7. WIM file 99350110.021 VTR
File County Station Date Hour Minute Second Vehicle
Type Number Number Number
VTR 93 9935 9/21/2001 1 55 40 146
VTR 93 9935 9/21/2001 1 55 46 147
VTR 93 9935 10/21/2001 1 57 42 151
VTR 93 9935 10/21/2001 1 59 9 152
VTR 93 9935 10/21/2001 14 24 59 4241
VTR 93 9935 10/1/2001 14 33 26 4281
VTR 93 9935 10/1/2001 14 33 50 4283
VTR 93 9935 10/1/2001 23 58 19 3274
VTR 93 9935 10/1/2001 23 58 25 3275
VTR 93 9935 10/2/2001 0 8 27 10
Naming of Combined Files by the Last Day
The last problem identified in the WIM files again deals with multiple days of data
being combined into one file. Whenever multiple days of data were combined into one
file, the file was named for the last day of recorded data in the combined file. Looking at
the file 99350110.021_VTR again, the file was supposed to represent October 2, 2001.
This means that the last day in the file should be October 2, 2001. Instead the file
continues to record days up to October 13th
Resolving Problems with WIM Files
The underlying issue in the four unresolved problems was that they all were
combining multiple days of data into a single file. Each identified problem was slightly
different, but inevitably came down to multiple days of data being recorded as a single
day. To figure out how widespread of a problem this was, an evaluation of the data
needed to be done to see how many files combined data. A Visual Basic program was
created to open each file and look for a change in the date. If the program came across a
file with more than one date it would record the file name, the dates that it had combined
in the file and the starting and ending hours for each of the dates. The starting and ending
hours were recorded to check to see if an entire day of data was recorded. A text file was
created for each year at each of the 37 WIM stations summarizing all the files that were
combining days of data. The text output from 2001 for site 9921 is shown in Table 3-8.
Table 3-8. List of the files with multiple days of data for the site 9921, year 2001
File Date Start Time End Time
File Name File Date
Number Hr. Min. Sec. Hr. Min. Sec.
165 99210106.151_VTR 6/14/2001 2 45 22 22 46 11
165 99210106.151_VTR 6/15/2001 0 40 3 23 45 16
176 99210106.271_VTR 6/26/2001 14 45 6 21 18 17
176 99210106.271 VTR 6/27/2001 0 18 43 19 18 35
212 99210108.021_VTR 8/1/2001 2 47 31 22 29 46
212 99210108.021_VTR 8/2/2001 0 32 32 22 22 24
219 99210108.161_VTR 8/15/2001 13 57 0 20 10 36
219 99210108.161 _VTR 8/16/2001 3 18 3 18 52 0
285 99210110.211_VTR 10/20/2001 1 46 55 23 46 17
285 99210110.211 VTR 10/21/2001 1 48 46 22 52 42
294 99210110.301 VTR 10/29/2001 0 29 13 22 18 54
294 99210110.301 VTR 10/30/2001 3 13 50 18 40 1
Once the evaluation of the dataset was complete, it was found that out of 25,300
files, 1,284 files recorded multiple days of data into one day. This is roughly 5% of the
data files. Given the complexities involved in untangling files that suffered from one or
more of the above identified problems, there was not enough confidence that any one
solution (algorithm) could be created to solve these issues within a reasonable time
frame. Further, there was the possibility that there were additional problems with these
files that had not been identified. Thus, fixing the identified problems would not
guarantee that the data now offered a clean representation of the actual vehicle travel at
35
those WIM stations and days. It was important to make an effort to remove data that may
contaminate the results of the statistical analyses. For this project, the files with multiple
days of data were omitted from the analysis. A summary of all the files with multiple
days of data can be found in Appendix C.
CHAPTER 4
PERMIT VEHICLE ANALYSIS:
REGIONAL VEHICLE MODELING
The vehicle truck records that were obtained from the Florida Department of
Transportation's WIM sensors did not include records for trucks that weighed in excess
of 160,000 lbs or had more than nine axles. Another source of data was required to
account for vehicles that fit this description. As discussed in Chapter 1, the FDOT issued
permits to vehicles that exceed standard size and/or 80,000 lbs. Each permit was
recorded, and therefore served as a potential source of information for vehicles over
160,000 lbs. The permitting office supplied a hard copy of the permits issued to trucking
companies in Florida from January 2002 to April 2004. Processing and analysis of these
permit records is addressed in this chapter.
Formatting and Processing
The data supplied in the permit records consisted of: permit vehicle weight, vehicle
width, permit number, the date the permit was issued, company name, permit type, permit
class ID, vehicle route, and route restrictions. The categories with the most significance
to the project were the vehicle weight, permit date, permit type, and route/restrictions.
The hard copy of the permit listing obtained from FDOT was scanned into
electronic format using optical character recognition software. An example of one of the
scanned sheets is shown in Figure 4-1. The hundreds of pages of scanned data were
carefully reviewed to find errors created during the scanning process. After the
identifiable errors in the data had been fixed, a categorization of where the trucks were
traveling throughout the state was needed.
OVERWEIGHT PERMITS ISSUED 160K- 200K 10 33 Monday, April 19, 2004 21
FROM 01A)1/2003 TO 12131P2003
----TYPEPERM=T PRMT CLS ID=S ---
(contnmud)
PERMIT PERMIT
Obs WEIGHT WIDTH NUMBER PERMDATE NAME ROUTE
980 160000 14 12337 21AUG03 DAILY EXPRESS, INC US-27, SR-80, US-441, US-98, SR-809, SR-
981 160000 14 12430 22AUG03 COMBINED TRANSPORT, INC. I-10,1295,1-95,1-595
982 160000 14 12596 22AUG03 LEE MAR BUILDING& CONSTRUCTION CORP 1-75, SR-78
983 160000 14 12682 23AUG03 ADMIRAL MERCHANTS MOTOR FREIGHT US231 SR20 SR267 US98 USALT27 175 SR44 U
984 160000 14 12721 25AUG03 DAILY EXPRESS, INC US-27, SR-80, US-441, US-98, SR-809, SR-
985 160000 14 13003 25AUG03 SOUTHWEST UTILITY SYSTEMS US-41
986 160000 12 13048 25AUG03 RINGPOWER CORP SR-263, I-10, 1-75, SR-64, US-27, US-98
987 160000 16 13089 26AUG03 COUNTS CONST. US-441, SR-326
988 160000 16 13147 26AUG03 INTERNATIONAL TRUCKING & RIGGING CO INC SR-826, US-27
989 160000 14 13161 26AUG03 LEE MAR BUILDING& CONSTRUCTION CORP SR884, 175
990 160000 14 13371 26AUG03 HUBBARD CONSTRUCTION COMPANY SR-436, SR-434
991 160000 12 13500 26AUG03 UNITED ROAD SERVICE I-10
992 160000 12 13566 27AUG03 RINGPOWER CORP 1-95, US-1
993 160000 14 13621 27AUG03 AMERICAN ENG. & DEY. CORP. US-441, SR-848, 1-95, SR-858, US-1, SR-8
994 160000 12 13899 27AUG03 HYDRO ROCK COMPANY, INC 1-75
995 160000 14 13935 27AUG03 SOUTHWEST UTILITY SYSTEMS 175
996 160000 14 13939 27AUG03 HUBBARD CONSTRUCTION COMPANY SR482, SR436 SR426, & RETURN
997 160000 14 14041 28AUG03 LEE MAR BUILDING& CONSTRUCTION CORP SR-78, 1-75
998 160000 14 14198 28AUG03 RINGPOWER CORP US 90, SR 115, SR 202, US 1
999 160000 12 14463 29AUG03 VESCO SPECIALIZED CARRIERS US-319, SR-61,1-10, SR-263
1000 160000 14 14469 29AUG03 MCTYRE TRUCKING CO INC US-17, 1-4, SR-423
1001 160000 14 14470 29AUG03 MCTYRE TRUCKING CO INC SR-423,1-4, US-17
1002 160000 14 14620 02SEP03 ADMIRAL MERCHANTS MOTOR FREIGHT US231 SR20 SR267 US98 USALT27 175 SR44 U
1003 160000 12 14743 02SEP03 LEWARE CONSTRUCTION COMPANY US-27, FTP, I-4, US-441
1004 160000 14 14916 03SEP03 KAUFF'S OF MIAMI SR 704, SRSO09, 1-95, SR 60
1005 160000 12 15097 03SEP03 RINGPOWER CORP US-17, SR-100, SR-21,1-295, SR-13, SR-1
1006 160000 14 15194 03SEP03 RINGPOWER CORP SR-16,1-95, US-1
1007 160000 12 15195 03SEP03 MCTYRE TRUCKING CO INC SR-44, 1-75,1-275 S, SR-60
1008 160000 12 15277 04SEP03 RING POWER CORP SR-263, 1-10, US-129, US-41
1009 160000 12 15278 04SEP03 RING POWER CORP US-41, US-129, 1-75, SR-326, US-301
1010 160000 14 15282 04SEP03 AMERICAN ENG & DEV CORP US-441
1011 160000 14 15320 04SEP03 RINGPOWER CORP. SR-206, 1-95, US-1
1012 160000 14 15442 04SEP03 KEARNEY DEVELOPMENT CO INC SR-60, US-301
1013 160000 14 15449 04SEP03 JOHNSON BROTHERS CORP US 192 W, US 27, 1-4 W, US 98 S, SR 60 W
1014 160000 14 15467 04SEP03 AMERICAN ENG & DEV CORP US-1, SR-858, 1-95, SR-848
1015 160000 14 15593 05SEP03 HUBBARD CONSTRUCTION COMPANY SR-426 SR-436, 1-4, SR-423, SR-438
1016 160000 14 15595 05SEP03 HUBBARD CONSTRUCTION COMPANY US-1, 195, 1-295
1017 160000 14 15604 05SEP03 HUBBARD CONSTRUCTION COMPANY I-4, SR-435
1018 160000 12 15608 05SEP03 C D S SITEWORK & TRUCKING, INC US-192, I-4, US-27
1019 160000 14 15865 05SEP03 KEARNEY DEVELOPMENT US-301,1-4,1-275, SR-60, US-19A, SR-58
1020 160000 14 15998 05SEP03 C D S SITEWORK & TRUCKING, INC US-192, US-27, SR-60
1021 160000 14 16322 08SEP03 SOUTHWEST UTILITY SYSTEMS I-75
1022 160000 12 16324 08SEP03 KEARNEY DEVELOPMENT CO, INC SR-686,1-275, I-4, 1-75, SR-60
1023 160000 12 16341 08SEP03 RING POWER CORPORATION SR-482, US-441, I-4, 1-95, US-1
1024 160000 14 16379 08SEP03 JOHNSON BROTHERS CORP. US-192, US-27, I-4, US-98, SR-60
1025 160000 12 16504 09SEP03 PATCO CONTRACTORS INC US-41, SR-50, 1-75, SR-44, US-27/441, SR
1026 160000 16 16639 09SEP03 COUNTS CONST. SR-200
1027 160000 14 16764 10SEP03 AMERICAN ENG & DEV CORP US-441, SR-820
1028 160000 14 16817 10SEP03 HUBBARD CONSTRUCTION COMPANY US-441, I-4, SR-434, SR-419
1029 160000 14 17075 10SEP03 ADMIRAL MERCHANTS MOTOR FREIGHT US231, SR20, SR267, US98, US27 SR75, SR
1030 160000 12 17157 11SEP03 MCTYRE TRUCKING CO INC I-10, 1-75, FTP, US-27
Figure 4-1. FDOT permit listing sheet scanned using optical recognition software
Several of the companies on the list that had a large number of vehicles permitted
were contacted for further information regarding vehicle weight, permit date, and route.
Many company representatives were hesitant to talk to someone inquiring about the
movements of their permit vehicles, but several were forthcoming and cooperative.
It was found through these phone interviews that the weight on the FDOT permit
was typically within 5% of the actual truck weight. The permit date and permit type
provided a window of time for the permit use. A blanket (B) permit is valid for one year,
thus a single blanket permit may be used over the same route by the same vehicle
multiple times. Blanket permits are used for vehicles that do not exceed 200,000 lbs. A
trip (T) permit is valid for a single use to or from a destination. The trip permit allows
the truck a five day travel window for its single use. Finally, the provided routes consist
only of major roads. These major roads had restrictions listing specific locations off
limits. Each company's representative claimed strict adherence to the permissions
granted in the permit. The penalty of violation can severely damage the company's
ability to conduct business.
Zones for Permit Vehicle Travel
A goal of this project was to develop likelihood functions that describe the
probability of excessive weight occurring along Florida bridges due to heavy vehicle
traffic. Precise data records of vehicle weight, location and time of travel were most
useful for developing these functions. In the case of the permit records for vehicles over
160,000 lbs, the specific origin, destination, and route were not provided in the permit
records. For example, a route may be listed simply as 1-95, or SR-823, or some
combination of roads. From the perspective of this project, a single permitted vehicle
may travel numerous times over a year (blanket type), or a single time (trip type)
anywhere along the listed routess.
The lack of specificity in vehicle location, time and frequency of travel necessitates
a procedure to identify the most likely regions of travel within Florida for a given permit.
The roads in the state needed to be divided into regions to better determine what parts)
of Florida a given permit allowed travel.
The determination of regions was conducted using ArcMap, a Geographic
Information System (GIS) based software tool that is part of a larger software package
called ArcGIS [18]. ArcMap can overlay user selected layers of data called shape files
onto a map. Using the Florida Geographic Data Library (FGDL) [19], an image of all the
counties in the state of Florida was loaded. Once the shape file was loaded, the state was
divided into regions to better determine what parts) of Florida the permitted vehicles
were traveling in. Five regions were chosen, each region having at least one major
metropolitan area, and a major interstate. Once the regions were determined, they could
be used to designate which roads should be assigned to which region. Figure 4-2 shows
the regional breakdown of Florida developed for this study.
The list of roads came from two different sources. The first list of roads came from
the major roads shape file in the FGDL. The second list came from the FDOT website
[20], from which a U.S. highways shape file and state highways shape file were
downloaded. The two lists were loaded into ArcMap, and the roads were broken down
into the five regions.
A Visual Basic program was written to compare the roads that each truck used (as
provided in the scanned, processed permit records) to the roads in each region defined in
Figure 4-2. An analysis of where the trucks were traveling within Florida (by region)
was then determined. Many of the permit records had routes that spanned more than one
region. For example, permits that included 1-95 as a route were in at least regions 2, 4,
and 5. A random sample of five permit records were pulled from the database to show
what the records look like after the zone classification was done. These permit records
are provided in Table 4-1.
Regional Breakdown of Florida
PE A A L -
PEN S A.' j.;. ;, TA LLA$iA Ss
**;-- -..f-o-
a
0 45 90
Miles
Figure 4-2. Regional partitioning of Florida for classification of travel for permitted
vehicles greater than 160,000 lbs
NLLE I
L,
ST PE
180
270
360
Table 4-1. Examples of processed permit vehicle records
PERMIT PERMIT PERMIT
WEIGHT PERMIT PERMIT COMPANY ROUTE PERMIT REGION
NUMBER DATE TYPE
160000 53437 5-Feb-02 COMPANY A US-27, 14, T 1 2 3 4 5
US-17, US-92
160000 87912 19-Jun-02 COMPANY B 1-95 T 2 4 5
160000 67493 26-Mar-02 COMPANY C SR-823 T 5
180500 53555 5-Feb-02 COMPANY D 1-75, 1-10, U- T 1 2 3 5
221, US-90
197000 60278 28-Feb-02 COMPANY E SR-37 SR-60 T 3 4
I-4
Difficulties with the Permit Vehicle Datasets
Overall, the issues and complications with the data within the permit vehicle
listings were minimal. However, the detail within the permit vehicle datasets was fairly
limited, and therefore the detail of what could be extracted was limited. The most
significant example was a lack of specific time and location of travel for any given
vehicle.
Unknown Routes
Some of the routes that were scanned into the database did not appear in the list of
roads in either the FGDL shape file or the FDOT website. To ensure that no roads were
left out, a third source, the Florida Traffic Information (FTI) 2002 CD [21] was used.
Even after including this third source, there remained roads listed in the permit records
that were still not accounted for. Every road that did not appear in any of the three
sources was compared to the resulting hard copy entry to ensure there was no error in the
route entry due to the scanning process. One possible error source was a data input error
in the hard copy of permit records supplied to the project by the FDOT.
42
A list of the roads that did not show up in any of the three different sources were
sorted by year and shown in Table 4-2. Inspection was done to see whether an incorrect
prefix explained the error. For example, since SR-27 could not be found, US-27 was
checked. However, if US-27 had not existed or fit into the travel pattern of the vehicle
given its other listed routes, the number rather than the prefix may have been incorrectly
entered.
It was not anticipated that the presence of these unaccounted for routes would
substantially alter the results of the analysis of the permit vehicle datasets. Routes that
could not be accounted for would simply be ignored when assigning the regions) to that
permit record. This represented a small fraction of the total records available.
Table 4-2. Routes not accounted for in the permit records
2002 2003 2004
SR-27 SR-648 SR-28 SR-484 SR-1 SR-532
SR-36 SR-672 SR-32 SR-532 SR-33A SR-540A
SR-58 SR-675 SR-58 SR-588 SR-42 SR-587
SR-98 SR-689 SR-67 SR-672 SR-99 SR-640
SR-99 SR-702 SR-86 SR-782 SR-110 SR-672
SR-131 SR-788 SR-135 SR-828 SR-210 SR-709
SR-169 SR-812 SR-182 SR-846 SR-283 SR-778
SR-197 SR-828 SR-204 SR-864 SR-288 SR-854
SR-198 SR-846 SR-236 SR-896 SR-395 SR-866
SR-210 SR-896 SR-269 US-42 SR-455 US-21
SR-221 SR-957 SR-306 US-50 SR-466 US-24
SR-236 US-33 SR-460 US-94 SR-470 US-47
SR-280 US-39 SR-462 US-482 SR-475A US-701
SR-284 US-39 SR-466 US-92-BUS SR-512
SR-286 US-44 SR-466A 1-575
SR-319 US-111 SR-470 1-594
SR-325 US-175
SR-328 US-275
SR-379 US-279
SR-395 1-45
SR-448 1-85
SR-485 1-294
SR-532 1-785
SR-587 1-810
Routes through Non-Contiguous Regions
When the permit vehicle records were assigned to regions, it was assumed that
when a vehicle travels through multiple regions, the regions would be adjacent to each
other. When examining the permit records it was found that in some circumstances a
vehicle would travel through two regions that were not contiguous. An example of this
was a truck permitted to use SR-80 and SR-104. SR-80 runs through Lee, Hendry, and
Palm Beach counties in south Florida (region 5). SR-104 is located outside Jacksonville
in Duval County (region 2). The permit records were double checked to guarantee there
was not an error in the scanning process. Possible explanations for this could be that one
or more routes were left off the FDOT permit records, or that one of the routes listed in
the description are incorrect.
Determination of Multiple Vehicles on a Bridge
The major point of interest for this project was modeling the probability of the
occurrence of more than one heavy vehicle on a bridge at the same time. The permit data
did not provide this data directly. The specific time or date of travel was not given, nor
was the specific path from origin to destination provided. Without this information a
concurrency evaluation could not be done for the vehicles over 160,000 lbs.
Blanket and Trip Permit Implications
Another significant consideration was contained within the legal travel conditions
associated with each of the two permit types. In addition to the lack of specification of
date and time of travel, blanket permits may be re-used over a one year period as often as
needed. Thus, a single permit may represent hundreds of individual occurrences of a
vehicle of that permitted weight traveling anywhere within its identified regions. Trip
permits represent a single occurrence any time within a five-day period within its regions.
Accounting for the multiple trips per permit, for blanket-type permits, could be
accomplished by simply weighting the number of individual blanket permits by a factor
that represents an average number of trips per permit. However, such a factor was not
easily determined, and would be better represented by a discrete random variable. The
characterization of this random variable could be the topic of a subsequent study, but was
beyond the scope of this study.
The probabilistic modeling presented in the next section did not account for this
issue, and simply treats each permit entry as an individual occurrence of a weight within
a region or regions. It was known that this approach would produce skewed results in the
modeled probability density functions. Most likely this would manifest as an
underestimation of the relative probability of weights closer to the low end of 160,000 lbs
compared to the high end of 1,000,000 lbs. This was because the blanket permits were
clustered between the 160,000 and 200,000 lb end of the weight range. Heavier vehicles
were required to have trip permits (single occurrence only) rather than blanket (multi-trip
potential).
Within the context of the exponential distribution that was applied in the next
section, this skewing of the data caused by counting blanket permits as a single
occurrence will produce X values that are too low. Recall from Chapter 3 that a larger X
value indicates a higher relative probability at the lower range of possible values for
weight (the random variable). Thus, if lower weight vehicles were multi-counted due to
blanket permit travel, a lower X value would be expected corresponding to a steeper
distribution that attenuates more quickly as it approaches higher weights.
Probabilistic Modeling of the Permit Vehicle Data
Rather than providing a model at individual WIM stations, the format of the permit
vehicle data required that models represent travel within the five regions in Figure 4-2.
This would make it more difficult to extrapolate the models to individual bridges, but the
route restriction data helped to narrow down the possibilities.
The weights from all the permit vehicle data were input into Mathcad for analysis.
There were 8,968 permit vehicle records. Of the 8,968 records, nineteen were over
1,000,000 lbs. The highest weight that was found in the printouts was 8,300,000 lbs.
They represent special cases where travel was closely monitored to guarantee precise
route and speed restriction adherence. Any bridges en route for these cases were
specifically analyzed for the presence of this vehicle, and no other vehicle was permitted
on the bridge at the same time. Therefore, they do not represent a 'random occurrence'
of a heavy vehicle, and were left out of the analysis.
A histogram was generated in the same manner as was used for the WIM data in
Chapter 3. Figure 4-3 shows the histogram of all permit data (between the weights of
160,000 lbs and 1,000,000 lbs). The x-axis represents the vehicle weight and they-axis
represents the number of trucks within each weight category. The histogram is not nearly
as smooth as the histograms generated for the WIM data. The reasons for this were that
there was not as much data for vehicles over 160,000 lbs and the fact that the data were
bunched into weight groups and do not represent the exact weight of the vehicle. This
was more evident as the weight got higher. Figure 4-4 shows the resultant exponential
PDF fit using maximum likelihood on the normalized histogram.
4000 -
3000
Frequency
J.L
2000
1000 V
Figure 4-3
2.5 -10-5
2 10-5
1 .10-5
50.0-
5.106
2.105 3.105 4.10 5 105 6.105 7. 10 8.105 9.105 1 .10
Weight (Ibs)
. Histogram of all permit vehicle data excluding weight over 1,000,000 lbs
I0 II i lIIlI I
1 -105 2 105 3 105 4-10 -0 510 6 10 7105 8105 9-105 1 -10
Weight (lbs)
Figure 4-4. The exponential PDF model on the normalized extreme value histogram
Regional Probabilistic Modeling of the Permit Vehicle Data
When these records were divided into the regions of travel (Figure 4-2) the number
of records became limited. Region 5 had the most permit vehicle records for one region
with 236. The other four regions all had less than 80 vehicles that only passed through
their region. With such a small number of vehicles it was hard to generate a histogram
I I I I I I I I
I I I
Nonnalized Histogram
Exponential PDF
47
that has any statistical significance. However, the benefit of having the five regions was
the ability to look at truck travel throughout different parts of the state that encompass
multiple regions.
Using the regional partitioning of the state, an exponential PDF was generated for
different parts of Florida. The four areas were the east coast of Florida (regions 2, 4, and
5), the Florida panhandle (regions 1 and 2), central Florida (regions 3 and 4), and south
Florida (region 5). Each area was analyzed for vehicles between the weights of 160,000
lbs and 1,000,000 lbs. Figure 4-5 shows the exponential PDF models using the
maximum likelihood function for the permit vehicle data from different areas of Florida.
I I I- 4. 10-5----- -
A B
Normnnalized Histogram Nonalied Histogram
Exponential PDF 3 10 Exponential PDF
2 10 -
0o i 2 10-
1 10- I
0 1 10 -
0 2-105 4-105 6-10 -8 105 1 106 0 2 105 4 105 6 10 8 10 1 10
Weight (1bs) Weight (Obs)
4 ,10-j I I I I I I
C D
Nonnalized Histogram | Normalized Histogram
3 10 Exponential PDF Exponential PDF
2 10
22 10-5
1 I0-5 1
0 0
0 2-105 4-105 6-105 8 105 1 106 1 105 2-105 3-105 4-105 5-105 6 10j
Weight (bs) Weight (Ibs)
Figure 4-5. Exponential PDF models on the normalized extreme histogram. A) East
coast of Florida. B) Florida's panhandle. C) Central Florida. D) South
Florida
The X parameter was different for each area. The east coast of Florida had a A
parameter of 23.278, the Florida panhandle had a A parameter of 25.373, central Florida
had a A parameter of 27.255, and south Florida had a A parameter of 10.27. If the
numbers of occurrences of blanket permit weights were multi-counted as suggested in the
previous section, these A values would increase. Thus, the distributions in Figure 4-5
would become steeper, with a higher relative probability of the lower range of weights.
Conclusions
This information was presented to the FDOT project manager. After discussion of
the limits of the permit data precision, it was concluded that only the WIM data would be
used for subsequent analysis. Even with the ability to separate the permit data into
regions, the inability of the permit data to give specific times and locations of truck travel
did not allow for an exact analysis of multiple vehicles on a bridge. The gap of
information between the WIM data and the permit data prevented analysis of both at this
time. Further modeling and analysis of the permit vehicle data is left as a subject for a
possible future project.
CHAPTER 5
ANALYSIS OF WEIGH-IN-MOTION HEADWAY DATA:
CONCURRENT VEHICLE MODELING
The previous chapter presented the datasets provided by the FDOT. Some
preliminary statistical analyses and problems were identified within the datasets. This
chapter discusses the methods developed to evaluate concurrent vehicles on a bridge at
the same time. This final course of analysis was determined after consultation with the
FDOT project manager.
The fundamental approach was to model the measured headway between vehicles
in order to evaluate the probability of concurrent vehicles appearing at a given WIM
station. Several WIM stations had more than one bridge within close proximity. Thus,
the evaluation of multiple heavy vehicles at a WIM station could be extrapolated to the
nearby bridges. An examination of all the WIM sites was conducted to find a small
sample of sites that had the combination of a high percentage of trucks over 80,000 lbs, a
high number of bridges close to the site, and a high volume of truck traffic. These WIM
sites were then used for the remainder of the analyses.
Headway Analysis
Headway is defined by the Highway Capacity Manual as the time, in seconds,
between two successive vehicles as they pass a point on the roadway, measured from the
same common feature of both vehicles (for example, the front axle or the front bumper)
[20]. A Visual Basic program was created to load each WIM file and obtain the headway
between pairs of vehicles. The program created a new file (per station, per day) that
contained the list of the headways for all the vehicles for each day of data. A master file
with a list of all files produced was also created. A sample of the headways at each site
was taken to get an initial view of the distribution. This sample excluded all files that
had any of the problems identified in Chapter 3. Only the headway values that were
between zero and thirty minutes were examined. This eliminated any other irregularities
in the WIM files. These processed headway files were then loaded into Mathcad for
analysis. After analyzing the headway data it was found that the distribution of the
headway data followed an exponential curve. The histograms of headway data differed
from site to site, but always followed an exponential curve. A summary of the critical
statistics for the headway data from all WIM sites is presented in Table 5-1. The total
number of vehicles sampled were the vehicles that were within the zero to thirty minute
headway range. The information presented in Table 5-1 represents a one or two year
sample of data from each WIM station depending on the number of years of data that
were collected.
Examples of the headway histograms are shown in Figure 5-1. Two histograms are
displayed in Figure 5-1 showing WIM stations 9908 and 9940. WIM station 9908 is
located on US-319 in Tallahassee and WIM station 9940 is located on SR-287 in Quincy.
The two WIM stations are located in Leon and Gadsden counties, respectively.
Table 5-1. Headway data statistics
Number of Headway Statistics (in seconds)
Station Vehicles Standard
Mean Median Mode
Sampled Deviation
9901 1,466,370 27.83 35.19 *
9904 939,314 20.52 30.76 12 *
9905 874,402 17.43 27.85 9 *
9906 537,499 37.53 102.33 13 2
9907 106,634 90.03 150.17 42 2
9908 190,069 131.69 222.93 60 3
9909 54,652 247.57 311.56 132 2
9913 594,678 53.72 77.12 30 2
9914 1,393,713 14.46 23.22 *
9916 88,813 154.09 226.37 78 3
9917 37,587 252.80 312.24 141 3
9918 297,304 38.09 63.20 19 2
9919 902,377 16.05 21.57 9 *
9920 227,855 16.32 22.36 9 1
9921 77,563 247.86 305.53 139 0
9922 84,511 34.71 51.83 18 2
9924 127,763 103.25 181.26 44 2
9925 46,747 203.71 275.88 108 2
9926 1,114,120 20.02 34.36 10 *
9927 105,252 102.84 161.06 50 3
9928 511,397 24.89 31.79 15 1
9929 8,613 364.69 362.13 249 2
9930 31,330 310.81 342.85 193 3
9931 547,775 23.85 30.88 14 2
9932 751,230 48.26 63.43 29 *
9934 456,940 39.01 93.00 15 2
9935 672,615 38.85 64.16 18 *
9936 1,445,407 21.07 29.08 *
9937 94,690 204.42 280.75 106 3
9938 105,565 192.17 170.61 99 2
9939 35,968 425.45 418.16 285 3
9940 132,696 226.23 295.32 120 3
9942 66,204 366.83 379.85 238 2
9943 105,655 270.49 325.50 154 2
9944 47,783 349.01 365.55 225 3
9946 78,319 413.74 397.56 284 3
*The values could not be calculated by Mathcad because the dataset was too large.
5.104
4-104
3-104
Frequency
2.104
1.104
2.104
1.5-104
Frequency
nU
1 .104
500 1000 1500
Time (seconds)
0 500 1000 1500
Time (seconds)
Figure 5-1. Headway frequency histograms. A) Represents site 9908. B) Represents site
9940
Identification of WIM Sites to Conduct Headway Analysis
The ultimate goal of this project was to determine the probability of the existence
of concurrent permit vehicles on a bridge. Since the headway data were coming from the
WIM stations and not bridges, it was difficult to predict when exactly these vehicles
would be on nearby bridges. A determination of which sites were in close proximity to
bridges was conducted. The assumption was that the occurrence of concurrent permit
vehicle at a given WIM site was as likely to have occurred at a nearby bridge. Thus, the
concurrence study at a given WIM station was extrapolated to nearby bridges.
Two shape files were downloaded from the FDOT website [18] to provide input to
the GIS platform used in this study. The first one contained the location of the WIM
sensors along Florida's roadways. The second contained bridge locations in the state of
Florida. Using ArcMap, the layers were loaded along with the major roads and the
county boundaries shape files from the Florida Geographic Data Library (FGDL) [17]. A
15-mile radius was created around each of the WIM sites. Bridges within this 15-mile
radius were pulled from the original shape file and assigned to the WIM station they
pertained to. Four new shape files were created, each containing only the bridges that
related to their respective WIM stations. Once the bridges were assigned to each WIM
station, only the bridges that were located along the WIM route were extracted. For
example, bridges that were on other major roads within the 15-mile radius were
eliminated.
Only a sample of the WIM sites had this analysis conducted for them. From
previous analyses (found in Appendix B), only the sites with a high number of passing
trucks and a high percentage of trucks over 85,000 lbs were considered. The WIM shape
file did not contain the locations of WIM station 9914 or 9916. Since the WIM stations
were not in the WIM shape file, they were also omitted from the analysis. Table 5-2
shows the results from the ArcMap analysis of the bridges within the 15-mile radius of
the WIM sites. The grey entries were the sites that were not evaluated in ArcMap; the
four highlighted entries were the sites for which the detailed headway analysis was
conducted. The four sites highlighted in Table 5-2 were chosen because they contained a
high volume of trucks passing over the sensor, numerous trucks over 85,000 lbs, and
several bridges within the 15-mile radius. Additionally, this selection of sites provided
some variance in regional location. Figure 5-2 shows the locations of the four selected
WIM sites, as well as the regional partitioning of the state.
Table 5-2. Results from the ArcMap analysis of bridges
Years % of Trucks
Site Bridges Region Trucks o at
of Data >85,000
9901 16 1 3,590,583 4 0.36
9904 30 2 943,096 2 4.44
9905 2 1,064,202 2 2.08
9906 26 4 540,931 2 4.71
9907 17 1 468,160 3 3.22
9908 8 1 869,124 6 1.08
9909 4 2 208,210 3 6.76
9913 29 4 1,121,712 3 4.31
9914 2 1,525,164 2 4.08
9916 1 391,967 3 5.04
9917 3 83,960 2 1.17
9918 3 5 1,533,122 3 10.07
9919 4 1,692,297 3 0.96
9920 3 227,899 1 3.89
9921 10 5 361,043 6 0.35
9922 3 84,545 1 1.80
9923 2 0 0 0
9924 15 1 194,583 1 0.74
9925 7 4 120,248 2 3.93
9926 78 3 1,153,455 2 4.32
9927 3 370,861 2 0.28
9928 9 1 846,732 2 1.97
9929 4 15,195 2 0.17
9930 5 118,513 2 0.74
9931 19 3 1,390,339 3 4.72
9932 17 4 901,222 3 6.11
9934 5 698,562 3 4.82
9935 4 5 2,872,418 6 6.01
9936 16 2 4,352,192 6 3.22
9937 3 1 357,374 5 3.65
9938 9 1 274,550 3 4.33
9939 9 1 136,363 6 3.14
9940 7 1 453,541 6 2.02
9942 1 187,081 6 4.26
9943 4 1 323,456 6 9.60
9944 2 1 149,946 6 9.09
9946 0 1 245,335 6 7.40
WIM Sites Used for Analysis
Region 2
Legend
0 9936
9932
o 9926
o 9913
15 Mile Radius
Region 5
Region 4
Region 3
Region 2
Region 1
0 37.5 75 150 225 300
Miles
Figure 5-2. Locations of the four WIM sites selected for headway analysis
Analysis of the Four Chosen WIM Sites
The four chosen WIM stations were 9913, 9926, 9932, and 9936 (indicated in
Figure 5-2). These WIM stations were looked at closely in ArcMap to include only the
bridges along the route and to exclude any overpasses or exit ramps. After looking at the
bridges a second time, the number of bridges was reduced to 11 bridges at WIM station
9913, 56 bridges at WIM station 9926, 15 bridges at WIM station 9932, and 10 bridges at
WIM station 9936. Figure 5-3 shows a close up view of each of the four WIM stations,
the 15-mile radius, the WIM sensor, the route the WIM sensors are located on, the major
roads in the area, and the bridges along the WIM route.
9913
9932
9926
9936
Legend
c Sites
- Bridges
15 Mile Radius
-- Route with WIM sensor
--- Major Roads
0 2.5 5 10 15 20
Miles
Figure 5-3. Detailed view of the four WIM sites selected for headway analysis
Bridge Length Determination
Once the sites with multiple bridges were selected and documented, the length of
the bridges around each of the four sites was determined. Each of the bridges contained
in the bridges shape file had attributes associated with them. One of those attributes was
length. The length was pulled from the attributes table for each of the bridges. From
these, the average bridge length was calculated for all the bridges within the 15-mile
radius and used for each individual site's headway analysis.
Speed Determination
To ascertain an average speed that the trucks were traveling over the WIM sensor, a
Visual Basic program was created to pull out the minimum, maximum, and average
vehicle speeds for each WIM file. Once the average speed for vehicles in each WIM file
was determined, yearly and overall speed averages were calculated. Table 5-3 shows the
average vehicle speeds and the average bridge lengths for the four sites. Total trucks
refers to all trucks registered by the WIM station, not just those over 85,000 lbs.
Table 5-3. Average speeds and bridge lengths
Total Avg. Site Avg. Avg. Bridge
Trucks Speed Speed (mph) Length (ft)
2001 442627 67.38
9913 2002 326560 66.61 67.14 314.08
2003 266681 67.39
9926 2002 532940 63.25 63.23 317.84
2003 581476 63.21
2001 383310 66.31
9932 2002 368393 68.08 67.17 186.53
2003 6942 66.66
1998 413997 67.20
1999 583801 67.79
9936 2000 783286 67.73 68.09 229.58
2001 536465 67.65
2002 1031798 68.50
2003 433397 69.52
Headway Determination at the Four WIM Sites
Another Visual Basic program was written to give a more detailed evaluation of the
headway of vehicles passing the four selected WIM sites. The program extracted any
vehicles that were within a user-specified headway time interval for each of the four sites.
Using the average speed and average bridge length for each site (see Table 5-3), a
specific headway time interval was calculated for each site that would capture when
multiple vehicles would be around each WIM station. This represents their potential
concurrent occurrence on a bridge within the 15-mile radius area. The appropriate
headway interval calculated for the four WIM stations were as follows
* WIM Station 9913: 3 seconds
* WIM Station 9926: 3 seconds
* WIM Station 9932: 2 seconds
* WIM Station 9936: 2 seconds
These headway intervals were rounded to the nearest second because the precision of the
timestamp from the WIM files was integer seconds. The headway interval represents a
period of time that captures any number of vehicles that cross the WIM station, not just
the time between two consecutive vehicles.
The headways mentioned in the previous paragraph were calculated for vehicles
that were traveling in the same direction. However, for vehicles traveling in opposing
directions, the headway time was divided in half. Since the vehicles were traveling in
opposite directions, their speeds were additive. A vehicle traveling 60 mph one way and
another traveling 60 mph the other way equaled a total of 120 mph. This was twice the
speed for the same distance (i.e. bridge length), therefore, it equaled half the time.
The Visual Basic program grouped vehicles into different headway groups based
on the aforementioned headway input for the different sites. The time stamp, lane of
travel, and vehicle classification were also recorded. The lane of travel was useful in the
determination of what direction the vehicles were traveling when they appeared on the
bridge, that is, whether the vehicles were traveling in the same direction or opposing
directions. The program created a text file for each individual day of data. A summary
file was also produced listing the total number of vehicles, the groups of two vehicles on
the bridge, the groups of three vehicles on the bridge, the groups of four vehicles on the
bridge, the groups of five vehicles on the bridge, the number of groups containing at least
two vehicles 80,000 lbs or greater, and whether the 80,000 lb vehicles were traveling in
the same direction or opposing directions.
In addition to the output described in the previous paragraph, the Visual Basic
program created another file for each individual day of data containing the summation of
the weights of vehicles in each headway group for that day. Along with the weight
summation, the program also created a table of contents file that contained a list of all the
filenames that had the summation of headway weight extracted from them. These files
were then input into Mathcad for analysis.
In total, the Visual Basic program created four new files. For each individual day
of data the program created two files, one containing the headway groups, and one
containing the summation of weight from each headway group. For example, when the
file 99130202.011_VTR was processed, the files 99130202.01 l_VTR.txt and
99130202.011_VTRWT.txt were created. For each year of data that were processed, a
stat.txt and a toc.txt file were created. The stat.txt file contains the summary information
from all the VTR.txt files and the toc.txt file was the file that was read into Mathcad
containing all the names of the VTRWT.txt files.
Results
The occurrence of concurrent vehicles each 80,000 lbs or greater was a rare event
when compared to the amount of trucks traveling Florida's roads. Site 9926 had the
highest percentage of concurrent 80,000+ lb vehicles on a bridge for a single year with
0.26%. This was relative to the total trucks passing over the WIM station. Even though
the rate was relatively small, the frequency of this event occurring was not negligible.
For example, in 2002 at site 9936 there were 789 instances where at least two 80,000 lb
vehicles were within two seconds of each other at the location of the WIM sensor. That
translates to an average of just over two times every day for the entire year. In the case of
site 9926, the phenomenon of two 80,000 lb vehicles occurred four times a day for the
year of 2002.
Table 5-4 shows the results from the headway analysis. The table shows the total
trucks passing the WIM site, the groups of two, three, four, and five vehicles on a bridge
(i.e., within the calculated headway for that WIM site as defined earlier), and the percent
of the total vehicles in each of those groups relative to the total number of trucks passing
the given WIM station that year. The last four columns show the frequency of two
concurrent vehicles over 80,000 lbs, the percent of those vehicles out of the total truck
population passing the WIM station, the frequency of three concurrent vehicles over
80,000 lbs, and the percent of those vehicles out of the total truck population passing the
WIM station, respectively.
Table 5-4. Summary of headway results
Total
Trucks
Groups of 2
Sum
Percent
Groups of 3
Sum
Percent
Groups of 4
Sum
Groups of 5
Percent
2001 442627 25335 5.72% 758 0.17% 15 0.003%
9913 2002 326560 17562 5.38% 475 0.15% 3 0.001%
_ 2003 266681 14429 5.41% 327 0.12% 3 0.001%
532940
581476
383310
368393
6942
413997
63200
85833
6931
7527
19283
11.86%
14.76%
1.81%
2.04%
1.92%
4.66%
3753
6311
0.70%
1.09%
0.026% 6 0.001%
0.052% 10 0.002%
2 Vehicles >
80,000 Ibs
Sum
112
147
309
1395
743
61
1999 583801 30197 5.17% 438 0.08%
2000 783286 41364 5.28% 614 0.08%
2001 536465 29065 5.42% 471 0.09%
1031798
433397
53546
13826
5.19%
3.19%
3 Vehicles >
80,000 Ibs
Percent
0.03%
0.05%
0.12%
0.26%
0.13%
0.02%
4 ^^
1 0.0004%
5 0.0009%
6 0.0010%
Site
Year
2002
2003
2001
2002
2003
1998
9926
9932
9936
2002
2003
mm ,
Of the vehicles over 80,000 lbs that arrived within the given headway interval for
each of the four WIM stations, the majority (at least 70%) of these vehicles were
traveling in the same direction. Table 5-5 shows the results for the case of only two
concurrent vehicles near the WIM station. The fifteen instances when there were three
permit vehicles occurring near the WIM station, twelve times (80%) two of the three
vehicles were traveling in the same direction. Three times (20%) all three vehicles were
traveling in the same direction.
Table 5-5. Summary of the travel direction of 80,000+ lb vehicles
Traveling in the Traveling in
Site 2 Vehicles> Same Direction Opposing Directions
80,000 Ibs
Vehicles Percent Vehicles Percent
9913 568 486 85.56% 82 14.44%
9926 2138 1516 70.91% 622 29.09%
9932 148 125 84.46% 23 15.54%
9936 1541 1382 89.68% 159 10.32%
Table 5-6 presents a comparison of the number of vehicles appearing concurrently
at the WIM station that were 80,000 lbs or greater traveling in the same direction to the
total number of vehicles 80,000 lbs or greater passing the WIM station. Table 5-5 and 5-
6 together show that, although concurrent permit vehicles travel the same direction 70%
of the time, this concurrence occurs as only a small percentage of total permit vehicle
traffic. This suggests that permit vehicles traveling in convoys close enough to allow
concurrent bridge loading was the exception rather than the trend or rule.
Table 5-6. Summary of same direction concurrent permit vehicles compared to all
80,000+ lb vehicles
Total Permit Vehicles within Headway Interval
Site Permit Traveling in the Same Direction
Vehicles Frequency Percentage
9913 45,990 487 1.06%
9926 46,754 1518 3.25%
9932 45,083 125 0.28%
9936 127,818 1382 1.08%
Generating Concurrent Vehicle Histograms from Headway WIM Data
Using Mathcad to analyze the total concurrent weight information that was
provided by the Visual Basic program, an idea of the weight distribution over the given
headway interval for each WIM station could be determined. In the same manner that the
data were input to generate histograms in Chapter 3, an array of the total weight data over
the headway interval was read from a desired file. All the data from each year were input
into Mathcad for each WIM station. The next four figures show the resultant histogram
of the summation of the total weight passing the WIM station within the assigned
headway interval from the Mathcad analysis of the four WIM stations. Figure 5-4 shows
the histogram for WIM station 9913, Figure 5-5 shows the histogram for WIM station
9926, Figure 5-6 shows the histogram for WIM station 9932, and Figure 5-7 shows the
histogram for WIM station 9936.
4000
3000
Frequency
2000
1000 -
o0 n -lnnnh -- -_____
5 .104 1 -105 1.5 .-10 2 .105 2.5 .-10 3 10
Weight (1bs)
Figure 5-4. Histogram of total weight passing WIM station 9913 in a 3-second interval
1 -104 1 I 1 1 1
00
6000
Frequency
4000
H H Innhn.------ _
5-104 1 .10 1.5 10 2.105 2.5-105 3.105 3.5-105
Weight (Ibs)
Figure 5-5. Histogram of total weight passing WIM station 9926 in a 3-second interval
S00 -
600 -
Frequency
S 400
200
5 104 1 -105 1.5 105 2.105 2.5 105
Weight (ibs)
Figure 5-6. Histogram of total weight passing WIM station 9932 in a 2-second interval
1 -10 -
Frequency
.IL
5000 -
0 nnd .flnnL 1
5 104 1 -105 1.5 -105 2 105 2.5 -105 3 105
Weight (1bs)
Figure 5-7. Histogram of total weight passing WIM station 9936 in a 2-second interval
Modeling the Extreme Value Histogram Concurrent Permit Vehicles
The minimum total weight that two concurrent permit vehicles should weigh is
160,000 lbs (assuming they are loaded-i.e., not empty on a return trip). Thus the
modeling of an extreme value histogram evaluated weights above this threshold. All
weights above this threshold were not necessarily combinations of permit vehicles; but
combinations of any trucks that were captured within the headway interval. The lower
limit of 160,000 lbs represents the minimum combined weight of two permit vehicles.
This study assumes that the weight of four 40,000 lb vehicles was as significant as two
80,000 lb vehicles. The upper limit used differed from site to site. The maximum weight
of a group of vehicles within the assigned headway at WIM station 9913 was 290,190
lbs, at WIM station 9926 it was 319,880, at WIM station 9932 it was 250,930, and at
WIM station 9936 it was 276,940.
It was desired to create an analytical parametric function that represented the
information provided in the normalized extreme value histograms of the data of interest.
A convenient functional form would be flexible enough to represent WIM data from the
four different WIM stations. Thus a parametric probability density function (PDF) was
sought that fits the WIM data well. The focus was restricted to the extreme values of
total vehicle weights heavier than 160,000 lbs.
The exponential PDF model was used to fit the extreme value histograms. The
same process used to fit the extreme value histograms in Chapter 3 was used for this
analysis, using a different range of W. Equations (1) through (4) (see Chapter 3) apply to
the extreme value modeling conducted in this chapter. Substituting the exponential PDF
equation (f(x) = A *e-",x) into the log maximum likelihood function, defined as
1(0) = log L(0) = log f(x,; 0), enables an optimization routine to be run in Mathcad
1=1
to calculate the A values.
Since this chapter had a different range of weight data, Equation (5), found in
Chapter 3, would change. Before calculating A, the data were linearly mapped from the
160,000 to 290,190 range (WIM station 9913) into a range of 0 to 1. The upper limit of
the range changed for each of the four WIM stations depending on the maximum weight.
This A value was used to create the model and substituted back into the exponential PDF
(Equation 1). In the case of WIM station 9913 it would be f(x) = 6.638e -6638x This
analytical function (exponential PDF) now represents the data over the range 0 to 1. In
order to represent the data over the interval of 160,000 to 290,190 lbs, the analytical
function needed to be adjusted to invert the data mapping. Since the interval had
increased from 1 to 130,190, the exponential PDF needed to be divided by 130,190. In
addition, the value of x would become W-16-,000 The new exponential PDF
290,190 160,000).
equation in terms of the data in its original values Wis
A W 160,000
f(W) = Ae 290,190 160,000 (6)
130,190
The A parameter for WIM station 9913 that provided the maximum value was
6.638. The exponential PDF for WIM station 9913 now takes the form of
f(x) = 6.638e-6 638 The A parameters for the other three WIM stations were 8.933,
5.850, and 8.281 for WIM stations 9926, 9932, and 9936, respectively.
Figures 5-8, 5-9, 5-10, and 5-11 show the exponential PDF model and the
normalized histogram of the summation of the total weight equaling at least 160,000 lbs
passing the WIM station in the headway interval from the Mathcad analysis of WIM
stations 9913, 9926, 9932, and 9936, respectively.
5 -10.5 111111
Nonnalized Histogram
4.10-5
Exponential PDF
P -, -5
2 -10
1.6 -105 1.8 105 2105 2.2 105 2.4-105 2.6-105 2.8-105 3.105
Weight (lbs)
Figure 5-8. Exponential PDF model and normalized histogram (WIM station 9913)
6.10-5
S4.10-5
- 10
2-10-
1.6 *105 1.8 -105 2.105 2.2-105 2.4-105 2.6-105 2.8-105 3.105 3.2 *105
Weight (ibs)
Figure 5-9. Exponential PDF model and normalized histogram (WIM station 9926)
S.10-5
6 .10-
4.10-5
2 .10-
1.6 *105 1. -105 2-105 2.2 *105 2.4-105 2.6 *105
Weight (Ibs)
Figure 5-10. Exponential PDF model and normalized histogram (WIM station 9932)
Normalized Histogram
IJL
Exponential PDF
W ~fl.nnnnI I
f LLLLU
.
8-10^ 1I-----
Normalized Histogram
6 "10- Exponential PDF
4.10-5
2 .0-5
S410
1.6 105 12. 10i 2 105 2.2 10 2.4.105 2.6 .10 2. .10
Weight (lbs)
Figure 5-11. Exponential PDF model and normalized histogram (WIM station 9936)
Interpretation of the Extreme Value Histogram
Figures 5-8 through 5-11 represent conditional probabilities. They provide
probabilities of the total combined weight of vehicles given that the total combined
weight of the vehicles at the WIM sensor was at least 160,000 lbs, which was equivalent
to two permit vehicles. The conditional probability is represented asP(w p), where w is
any weight combination of vehicles andp is the event that a combination of vehicles is
160,000 lbs or greater. If the conditional probability is multiplied by the probability that
a weight of at least 160,000 lbs shows up at the WIM sensor, the probability of that
particular load combination can be found. This is represented as
P(w) =P(w p)x P(p) (7)
Referring to Table 5-4, two permit vehicles of at least 80,000 lbs (giving a total
weight of at least 160,000 lbs) occur at any of the evaluated WIM stations at least once in
the time span analyzed. This means that the probability of at least one weight
combination of at least 160,000 lbs per WIM station in a given year was reasonably
estimated at 100%. This simplifies Equation (7) above to
P(w p)= P(w) (8)
Thus Figures 5-8 through 5-11 can be viewed directly as the probability of the
likelihood of total concurrent weight Wwithin several years (number of years varies
among stations, see Table 5-4).
The histograms generated at the four WIM stations could not be used directly to
represent the probability of total weight of concurrent permit vehicles at other locations
around the state. The lambda values were customized to the individual WIM stations
using specific information of vehicle travel speed at the WIM station and average bridge
length in the area. The WIM station was then used as a hypothetical bridge that would
experience concurrent vehicle occurrence and reasonably be extrapolated to other bridges
in the vicinity of and along the same route as the WIM station.
This same method of analysis could be conducted at any of the other 33 WIM
stations. An analysis of the surrounding bridges within a specified radius from the WIM
station and an analysis of the speed of the vehicles passing the WIM station would first
be conducted to accurately represent the conditions at each of the WIM stations. Once
that information was evaluated, an extreme value histogram and an exponential PDF fit
could be determined at any other WIM station around the state.
Applications of Extreme Value Concurrent Weight Models
'Concurrent' is defined as the occurrence of more than one vehicle within an
interval that is within the average length of nearby bridges on same route. Here are three
examples of how the extreme value concurrent weight models (Figures 5-8 through 5-11)
can be used.
Given that multiple vehicles occurred concurrently at WIM station 9913, what is
the probability that the total weight is between 200,000 and 250,000 lbs? The solution
would be to integrate the normalized histogram or fitted exponential PDF model between
200,000 and 250,000 lbs. The area is the probability in decimal form.
Given that multiple vehicles occurred concurrently at WIM station 9926, what is
the probability that the total weight will exceed 280,000 lbs? The solution would be to
integrate the normalized histogram or fitted exponential PDF model from 280,000 lbs to
the upper limit (319,880 lbs).
Given that multiple vehicles occurred concurrently at WIM station 9936, what is
the probability that the total weight is at most 230,000 lbs? The solution would be to
integrate the normalized histogram or fitted exponential PDF model from the lower limit
of 160,000 lbs to 230,000 lbs.
These data are bounded between a lower limit of 160,000 lbs and an upper limit
that ranges from 250,930 to 319,880 lbs depending on what site was being analyzed. The
PDF model will not provide probabilities of concurrent vehicles over the upper limit or
under 160,000 lbs. That is, direct extrapolation of the PDF model beyond its defined
range is not valid. However, more data provided over a larger range of weights could be
used to develop a similar model that covers the range of interest.
CHAPTER 6
SUMMARY AND RECOMMENDATIONS
This thesis documents a study on overweight vehicle travel, specifically the
characterization of concurrent permit vehicles on bridges at four different WIM stations
located in the state of Florida. The following sections summarize contributions to and
conclusions about, the research found in this document and present recommendations for
future research.
Summary
Chapter 3 discussed the preliminary analysis of the WIM data. An initial extreme
value model was created along with the identification of numerous irregularities in the
data. Out of the 25,300 files, approximately 5% of the data files were not used due to
these irregularities. The analysis of the data found that no WIM data file contained a
weight greater than 160,000 lbs. This was due to a filter that was set to discard any data
above that threshold. This filter was beyond the control of the investigators, and filtered
data was deemed irretrievable.
A second source of data was needed to evaluate the vehicles over 160,000 lbs.
Chapter 4 discussed the use and limitations of the permit data. The permit data were
scanned into electronic format and placed into one of five partitioned regions of Florida.
The permit data were then examined on a regional basis. It was concluded that only the
WIM data would be used for subsequent analysis. Even with the ability to categorize the
travel patterns of heavy vehicles from the permit data into regions, the inability of the
permit data to give specific times and locations of truck travel does not allow for
quantitative analysis of multiple vehicles on a bridge.
Chapter 5 discussed the development of a probabilistic model of concurrent vehicle
weights at a WIM station using measured headway intervals determined by average speed
and average length of bridges local to the given WIM station. The results represent the
likelihood of various levels of combined total weight from concurrent permit vehicles at
the WIM station. A more specific (accurate) probability model would require the
installation of WIM sensors on or next to bridges of interest.
In the evaluation of the headway data, this study observed an appreciable likelihood
of permit vehicles (vehicles over 80,000 lbs) appearing concurrently on each of the four
analyzed WIM stations (Table 5-4). Thus, the resultant probability models of combined
weight of concurrent vehicles directly represent the likelihood of an extreme loading
condition.
Permit vehicles were traveling in the same direction in 70% of the observed
concurrent cases. Although same direction concurrent permit vehicles account for a total
of about 1% of the total number of observed permit vehicles among the four WIM
stations, this still represents hundreds of concurrent vehicle loading events per year per
analyzed WIM station. Thus, this was more than a negligible occurrence.
The exponential PDFs generated from the four WIM stations (Figures 5-8 through
5-11) can be used to predict the probability of occurrence of the combined weight of
concurrent vehicles around the given WIM station. An assumption was made that this
analysis data can be extrapolated to the nearby bridges on the same route as, and within
15 miles of, the WIM station. That is, it was reasonable to expect that the observed
occurrences of concurrent permit vehicles could have as likely occurred at a nearby
bridge, and thus Figures 5-8 through 5-11 can be applied directly to the bridges.
The histograms generated at the four WIM stations cannot be used to give the
probability of occurrence of concurrent permit vehicles at other locations around the
state. They can only be used to predict concurrent permit vehicle weights at or around
the four WIM stations. Each of the four WIM stations used specific information of
vehicle travel speed at the WIM station and average bridge length in the area. However,
this same method of analysis could be conducted at any of the other 33 WIM stations.
An analysis of the surrounding bridges within a specified radius from the WIM station
and an analysis of the speed of the vehicles passing the WIM station would first be
needed to accurately represent the conditions at each of the WIM stations. Once that
information is evaluated, an extreme value histogram and an exponential PDF fit could be
determined at any other WIM station around the state.
It needs to be reemphasized that the probability models of concurrent permit
vehicle weight did not include weights from individual vehicles that exceed 160,000 lbs.
Although such vehicles were generally rare, it was reasonable to assume that the
probability models developed without these data were skewed in a non-conservative way
toward a higher probability of lower concurrent weights. Additional data collection
would be needed at WIM stations that retain 160,000+ lb vehicles to ascertain the impact
of this unaccounted for data.
Recommendations
There is a need for the WIM data that is being processed to incorporate the weights
of all vehicles that pass the sites. The inability for the WIM sensors to record weight
over 160,000 lbs severely limits the ability to perform a realistic analysis of the most
extreme weights. In addition, the difficulties with the WIM data files, like combining
multiple days of data into one file, need to be addressed and corrected. An overhaul of
the WIM sensors and collection process is recommended to better reflect the increasingly
likely occurrence of heavier vehicles.
The project did not focus on individual vehicles with specific axle configurations.
The next step would be to look at individual vehicles with specific axle configurations
that the FDOT has a special interest in. Weight by itself is only one factor, the axle
configuration at any given weight can be another significant factor. A study that predicts
the probability of these special interest vehicles and the occurrence of concurrent
combinations of special interest vehicles on bridges is recommended.
The project evaluated the permit vehicle records (vehicles over 160,000 lbs), but
did not do an in-depth analysis of the data. One major obstacle was the inability to know
how many trips a vehicle with a blanket permit makes within a year. Determining a
system to weight blanket permits (how many trips per blanket) is recommended and
would be the first step in the process to further analyze the permit vehicle records
collected through 2004. However, future collection of such vehicles at the WIM stations
directly would be most beneficial.
APPENDIX A
FDOT CLASSIFICATION SCHEME "F"
CLASSIFICATION SCHEME "F"
DESCRIPTION
NO. OF
AXLES
1 MOTORCYCLES 2
ALL CARS 2
2 CARS W/ 1-AXLE TRLR 3
CARS W/2-AXLE TRLR 4
PICK-UPS &VANS
I & 2 AXLE TRLRS
2.,3. & 4
BUSES 2 & 3
2-AXLE, SINGLE UNIT 2
p 3-AXLE, SINGLE UNIT 3
Ef 4-AXLE. SINGLE UNIT 4
2-AXLE TRACTOR.
I -AXLE TRLR(2S1) 3
2-AXLE TRACTOR, 4
2-AXLE TRLR(2S2)
3-AXLE TRACTOR, 4
1 -AXLE TRLR(3S I)
S3-AXLE TRACTOR,
2-AXLE TRLRF3S2) 5
3-AILE TRUCK,
W/2-AXLE TRLR 5
TRACTOR W/ SINGLE
TRLR
6&7
5-AXLE MULTI- 5
TRLR
6-AILE MULTI-
TRLR 6
CLASS.
GROUP
3
4
5
6
7
8
9
10
11
12
ANY 7 OR MORE AXLE 7 or more
System Usage Data 1/9/90
r r T -::171HI^
APPENDIX B
WIM DATA SUMMARY
The content of this appendix summarizes the preliminary analysis of the WIM data
obtained from the FDOT. The data summarized here contains data from every file
acquired from the FDOT including files that contain multiple days of data. The
subsequent pages present the name and location of every site and are broken down in a
yearly basis. Within each year are the number of days of data, the total vehicles, the
number of vehicles 85,000 lbs or greater, the number of vehicles 90,000 lbs or greater,
the number of vehicles 105,000 lbs or greater, the number of vehicles 120,000 lbs or
greater, the number of vehicles 135,000 lbs or greater, and the number of vehicles
150,000 lbs or greater.
9901: 1-10, Monticello
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 309 824570 4472 1134 258 100 34 10
1999 295 783805 1612 635 191 81 34 7
2002 268 1256199 3287 1652 653 228 79 13
2003 179 726009 3490 1241 428 175 60 21
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 309 824570 0.542 0.138 0.031 0.012 0.004 0.0012
1999 295 783805 0.206 0.081 0.024 0.010 0.004 0.0009
2002 268 1256199 0.262 0.132 0.052 0.018 0.006 0.0010
2003 179 726009 0.481 0.171 0.059 0.024 0.008 0.0029
9908: US-319, Tallahassee
YEAR #OF WT >
DAYS VEHICLES 85,000
1998 345 182175 2582
1999 217 128603 1606
2000 185 109917 617
2001 348 190605 716
2002 319 169719 632
2003 184 88105 3244
YEAR #OF
DAYS VEHICLES 85,000
1998 345 182175 1.417
1999 217 128603 1.249
2000 185 109917 0.561
2001 348 190605 0.376
2002 319 169719 0.372
2003 184 88105 3.682
WT >
90.000
508
273
204
368
293
1192
%>
90,000
0.279
0.212
0.186
0.193
0.173
1.353
WT > WT > WT > WT >
105,000 120,000 135,000 150,000
49 6 2 0
32 6 4 0
45 7 0 0
74 9 3 0
51 6 0 0
45 4 1 0
%> %> %> %>
105,000 120,000 135,000 150,000
0.027 0.003 0.001
0.025 0.005 0.003
0.041 0.006
0.039 0.005 0.002
0.030 0.004
0.051 0.005 0.001
9904: 1-75, Micanopy
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 72 234387 14426 10041 1834 10 4 0
2003 163 708709 27461 8196 338 79 26 5
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 72 234387 6.155 4.284 0.782 0.004 0.002
2003 163 708709 3.875 1.156 0.048 0.011 0.004 0.0007
9905: SR-9/I-95, Jacksonville
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 145 914464 17635 7846 546 68 17 5
2003 43 149738 4483 2042 82 16 3 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 145 914464 1.928 0.858 0.060 0.007 0.002 0.0005
2003 43 149738 2.994 1.364 0.055 0.011 0.002
9906: 1-4, Deltona
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 245 545530 24263 13018 1317 42 3 0
2002 53 25401 2652 1840 324 4 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 245 545530 4.448 2.386 0.241 0.008 0.001
2002 53 25401 10.441 7.244 1.276 0.016
9907: US-231, Youngstown
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 200 163858 3706 2406 363 3 1 0
2002 200 194693 6369 4131 673 7 0 0
2003 125 109609 4977 3164 583 3 1 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 200 163858 2.262 1.468 0.222 0.002 0.001
2002 200 194693 3.271 2.122 0.346 0.004
2003 125 109609 4.541 2.887 0.532 0.003 0.001
9909: US-19, Chiefland
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 61 20204 467 252 13 0 0 0
2002 246 131818 13354 8365 1107 5 2 1
2003 211 56188 261 72 3 1 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 61 20204 2.311 1.247 0.064
2002 246 131818 10.131 6.346 0.840 0.004 0.002 0.0008
2003 211 56188 0.465 0.128 0.005 0.002
9913: Turnpike, St.Lucie Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 270 481322 11923 8697 4859 2521 964 103
2002 214 364043 12827 9552 4789 2529 1040 115
2003 163 276347 23595 15745 4670 2173 1152 329
#OF %> %> %> %> %> %>
YEAR85,000 90,000 105,000 120,000 135,000 150,000
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 270 481322
2002 214 364043
2003 163 276347
2.477
3.523
8.538
1.807
2.624
5.698
1.010
1.316
1.690
0.524
0.695
0.786
0.200
0.286
0.417
0.0214
0.0316
0.1191
9914: SR-9A/I-295, Duval Co.
#OF
YEAR #OF
DAYS
2001 265
2002 21
#OF
YEAR #OF
DAYS
2001 265
2002 21
WT >
VEHICLES 85,000
1419714 57701
105450 4555
%>
VEHICLES 85,000
1419714 4.064
105450 4.320
WT >
90,000
30506
2424
%>
90,000
2.149
2.299
WT >
105,000
2785
201
%>
105,000
0.196
0.191
WT >
120,000
60
1
%>
120,000
0.004
0.001
WT >
135,000
2
0
%>
135,000
0.0001
WT >
150,000
0
0
%>
150.000
9916: US-29, Pensacola
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 241 176376 7673 4858 802 5 0 0
2002 254 125943 6086 3795 597 3 0 0
2003 185 89648 5984 4452 1252 5 2 1
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 241 176376 4.350 2.754 0.455 0.003
2002 254 125943 4.832 3.013 0.474 0.002
2003 185 89648 6.675 4.966 1.397 0.006 0.002 0.0011
9917: US-41, Punta Gorda
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 234 44385 876 456 29 3 0 0
2003 167 39575 108 39 6 5 1 0
#OF %> %> %> %> %> %>
YEAR85,000 90,000 105,000 120,000 135,000 150,000
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 234 44385 1.974 1.027 0.065
2003 167 39575 0.273 0.099 0.015
0.007
0.013
0.003
f
9918: US-27, Clewiston
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 310 657107 68711 44619 6717 55 6 1
2002 277 573517 64732 44787 7689 26 4 0
2003 138 302498 20938 14084 2760 28 7 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 310 657107 10.457 6.790 1.022 0.008 0.001 0.0002
2002 277
2003 138
9919: 1-95, Malabar
#OF
YEAR #OF
DAYS
2001 172
2002 153
2003 2
#OF
YEAR #OF
DAYS
2001 172
2002 153
2003 2
9920: 1-75, Sumter Co.
YEAR #OF WT > WT >
DAYS VEHICLES 85.000 90,000
2003 44 227899 8869 695 99 45 16 8
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2003 44 227899 3.892 0.305 0.043 0.020 0.007 0.0035
573517
302498
11.287
6.922
7.809
4.656
1.341
0.912
0.005
0.009
0.001
0.002
VEHICLES
932345
754340
5612
VEHICLES
932345
754340
5612
WT >
85,000
8136
6917
1197
%>
85,000
0.873
0.917
21.329
WT >
90,000
3985
3099
861
%>
90.000
0.427
0.411
15.342
WT >
105,000
554
304
163
%>
105,000
0.059
0.040
2.904
WT >
105,000
WT >
120,000
98
59
0
%>
120,000
0.011
0.008
WT >
120,000
WT >
135,000
26
11
0
%>
135,000
0.003
0.001
WT >
135,000
WT >
150,000
3
2
0
%>
150.0003
0.0003
0.0003
WT >
150,000
9921: SR-5, Martin Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 341 75433 229 131 13 0 0 0
1999 329 73589 157 84 11 0 0 0
2000 353 87598 169 84 4 0 0 0
2001 356 59830 449 300 53 0 0 0
2002 298 41157 210 149 23 0 0 0
2003 136 23436 45 26 1 1 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 341 75433 0.304 0.174 0.017
1999 329 73589 0.213 0.114 0.015
2000 353 87598 0.193 0.096 0.005
2001 356 59830 0.750 0.501 0.089
2002 298 41157 0.510 0.362 0.056
2003 136 23436 0.192 0.111 0.004 0.004
9922: 1-275, Tampa
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2003 34 84545 1521 392 25 8 1 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2003 34 84545 1.799 0.464 0.030 0.009 0.001
9923: 1-95, Jacksonville
No data was available from this site.
9924: 1-110, Pensacola
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 202 194583 1447 312 15 3 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 202 194583 0.744 0.160 0.008 0.002
9925: US-92, Deland
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 248 67844 2499 635 19 2 0 0
2003 169 52404 2231 615 20 1 1 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 248 67844 3.683 0.936 0.028 0.003
2003 169 52404 4.257 1.174 0.038 0.002 0.002
9926: 1-75, Tampa
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 158 571238 38034 18087 410 84 20 7
2003 126 582217 11823 2493 321 86 27 6
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 158 571238 6.658 3.166 0.072 0.015 0.004 0.0012
2003 126 582217 2.031 0.428 0.055 0.015 0.005 0.0010
9927: SR-546, Lakeland
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 320 262155 755 179 33 15 3 0
2003 138 108706 295 63 14 5 1 0
#OF %> %> %> %> %> %>
YEAR000 150000
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 320 262155 0.288 0.068
2003 138 108706 0.271 0.058
0.013
0.013
0.006
0.005
0.001
0.001
9928: 1-10, Walton Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 154 590918 3946 863 235 82 29 8
2003 75 255814 12713 2217 144 55 18 4
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 154 590918 0.668 0.146 0.040 0.014 0.005 0.0014
2003 75 255814 4.970 0.867 0.056 0.021 0.007 0.0016
9929: US-1, Edgewater
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 93 11805 20 4 0 0 0 0
2003 66 3390 6 6 2 0 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 93 11805 0.169 0.034
2003 66 3390 0.177 0.177 0.059
9930: US-1, Miami
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 425 81082 722 427 39 2 2 1
2003 208 37431 150 81 12 0 0 0
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2002 425 81082 0.890 0.527 0.048 0.002 0.002 0.0012
2003 208 37431 0.401 0.216 0.032
9931: Turnpike, Sumter Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 180 725162 33099 13734 842 57 13 0
2002 25 101323 1808 650 96 27 2 0
2003 156 563854 30742 13494 612 138 40 6
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 180 725162 4.564 1.894 0.116 0.008 0.002
2002 25 101323 1.784 0.642 0.095 0.027 0.002
2003 156 563854 5.452 2.393 0.109 0.024 0.007 0.0011
9932: Turnpike, Osceola Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 208 409997 28542 19491 5744 1956 833 186
2002 232 484283 26145 17329 4680 1657 723 219
2003 4 6942 369 257 73 24 10 3
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 208 409997 6.962 4.754 1.401 0.477 0.203 0.0454
2002 232 484283 5.399 3.578 0.966 0.342 0.149 0.0452
2003 4 6942 5.315 3.702 1.052 0.346 0.144 0.0432
9934: Homestead Ext, Dade Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 16 30289 230 102 12 1 0 0
2002 79 238014 7591 4690 765 92 40 17
2003 201 430259 25881 16925 2978 192 106 31
#OF %> %> %> %> %> %>
YEAR85,000 90,000 105,000 120,000 135,000 150,000
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
2001 16 30289
2002 79 238014
2003 201 430259
0.759
3.189
6.015
0.337
1.970
3.934
0.040
0.321
0.692
0.003
0.039
0.045
0.017 0.0071
0.025 0.0072
9935: US-27, Palm Beach Co.
YEAR #OF WT > WT > WT > WT > WT > WT >
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 145 364949 22170 14014 2481 39 12 0
1999 144 350648 55989 40870 8674 24 6 2
2000 231 588584 21551 11158 751 34 15 1
2001 253 840365 9662 4077 341 65 10 4
2002 150 504232 38625 20387 1101 73 21 3
2003 94 223640 24650 14785 988 32 11 3
#OF %> %> %> %> %> %>
YEAR
DAYS VEHICLES 85,000 90,000 105,000 120,000 135,000 150,000
1998 145 364949 6.075 3.840 0.680 0.011 0.003
1999 144 350648 15.967 11.656 2.474 0.007 0.002 0.0006
2000 231 588584 3.661 1.896 0.128 0.006 0.003 0.0002
2001 253 840365 1.150 0.485 0.041 0.008 0.001 0.0005
2002 150 504232 7.660 4.043 0.218 0.014 0.004 0.0006
2003 94 223640 11.022 6.611 0.442 0.014 0.005 0.0013
9936: 1-10/SR-8, Lake City
# OF WT >
DAYS VEHICLES 85,000
1998 129 424264 4102
1999 155 659277 4871
2000 217 972530 11280
2001 157 806091 27243
2002 252 1051368 64182
2003 144 438662 28509
YEAR #OF %>
DAYS VEHICLES 85,000
1998 129 424264 0.967
1999 155 659277 0.739
2000 217 972530 1.160
2001 157 806091 3.380
2002 252 1051368 6.105
2003 144 438662 6.499
WT >
90,000
1440
1976
5345
15053
36897
13936
%>
90.000
0.339
0.300
0.550
1.867
3.509
3.177
WT> WT> WT> WT>
105,000 120,000 135,000 150,000
213 65 20 1
293 88 20 3
511 111 29 3
1563 142 40 8
3787 245 88 21
1066 138 49 15
%> %> %> %>
105,000 120,000 135,000 150,000
0.050 0.015 0.005 0.0002
0.044 0.013 0.003 0.0005
0.053 0.011 0.003 0.0003
0.194 0.018 0.005 0.0010
0.360 0.023 0.008 0.0020
0.243 0.031 0.011 0.0034
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PROBABALISTIC ASSESSMENT OF BRIDGE LOADING CONCURRENT WITH PERMIT VEHICLES By MATTHEW CRIM A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTE R OF ENGINEERING UNIVERSITY OF FLORIDA 2005
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Copyright 2005 by Matthew Crim
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This document is dedicated to my pare nts who have supported me throughout my undergraduate and graduate careers.
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iv ACKNOWLEDGMENTS I would like to thank my committee chair and cochair Dr. Scott Washburn and Dr. Kurtis Gurley for their continued support and guidance. I would also like to thank Vivek Pahariya and Seokjoo Lee for their he lp in writing Visual Basic code.
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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES...........................................................................................................viii LIST OF FIGURES...........................................................................................................ix ABSTRACT....................................................................................................................... xi CHAPTER 1 INTRODUCTION........................................................................................................1 Problem Statement........................................................................................................1 Background...................................................................................................................2 Bridge Rating System............................................................................................2 Floridas WIM Polling System..............................................................................3 Definition of a Permit Vehicle..............................................................................3 Permit issuance...............................................................................................4 Permit types....................................................................................................4 Objectives and Tasks....................................................................................................5 2 LITERATURE REVIEW.............................................................................................6 Studies Pertaining to Bridge Loading...........................................................................6 FDOT Literature.........................................................................................................10 3 PRELIMINARY ANALYSIS OF WE IGH-IN-MOTION DATA: SINGLE VEHICLE MODELING.............................................................................................11 Retrieval of Data from FDOT.....................................................................................11 Conversion of Data.....................................................................................................14 Preliminary Analysis of WIM Data............................................................................15 Initial Analysis of Data from All WIM Stations Combined................................15 Generating Extreme Value Hi stograms from WIM Data....................................18 Meaning of the extreme value histogram.....................................................20 Modeling the extreme value histogram........................................................20 Application of the extreme value model......................................................24 Extensions of the extreme value model........................................................27
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vi Difficulties with the WIM Datasets............................................................................28 Inconsistent Formatting in WIM Data Files........................................................29 Blank Data Files..................................................................................................29 Same Vehicle Entry Recorded More than Once..................................................30 End of Month Carryover into the Subsequent Month.........................................31 Multiple Days of Data in a File wi th No Reset of the Vehicle Count.................32 Naming of Combined Files by the Last Day.......................................................33 Resolving Problems with WIM Files..................................................................33 4 PERMIT VEHICLE ANALYSIS: REGIONAL VEHICLE MODELING...............36 Formatting and Processing.........................................................................................36 Zones for Permit Vehicle Travel................................................................................38 Difficulties with the Permit Vehicle Datasets............................................................41 Unknown Routes.................................................................................................41 Routes through Non-Contiguous Regions...........................................................43 Determination of Multiple Vehicles on a Bridge................................................43 Blanket and Trip Pe rmit Impli cations.................................................................43 Probabilistic Modeling of the Permit Vehicle Data....................................................45 Regional Probabilistic Modeling of the Permit Vehicle Data.............................46 Conclusions.........................................................................................................48 5 ANALYSIS OF WEIGH-IN-MOTI ON HEADWAY DATA: CONCURRENT VEHICLE MODELING.............................................................................................49 Headway Analysis......................................................................................................49 Identification of WIM Sites to Conduct Headway Analysis......................................52 Analysis of the Four Chosen WIM Sites.............................................................55 Bridge Length Determination..............................................................................57 Speed Determination...........................................................................................57 Headway Determination at the Four WIM Sites........................................................58 Results........................................................................................................................ .60 Generating Concurrent Vehicle Hi stograms from Headway WIM Data............63 Modeling the Extreme Value Histogram Concurrent Permit Vehicles............65 Interpretation of the Extreme Value Histogram..................................................69 Applications of Extreme Valu e Concurrent Weight Models..............................70 6 SUMMARY AND RECOMMENDATIONS............................................................72 Summary.....................................................................................................................72 Recommendations.......................................................................................................74 APPENDIX A FDOT CLASSIFICATION SCHEME F................................................................76 B WIM DATA SUMMARY..........................................................................................78
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vii C SUMMARY OF FILES CONTAINI NG MULTIPLE DAYS OF DATA.................93 LIST OF REFERENCES...................................................................................................98 BIOGRAPHICAL SKETCH...........................................................................................100
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viii LIST OF TABLES Table page 3-1 Overview of the 37 WIM stations............................................................................12 3-2 Contents of a selected WIM file...............................................................................13 3-3 A key to the column fields for Table 3-2.................................................................14 3-4 Summary of WIM data.............................................................................................17 3-5 WIM stations with an inconsistent file format.........................................................29 3-6 WIM stations and years that contain blank files......................................................30 3-7 WIM file 99350110.021_VTR.................................................................................33 3-8 List of the files with multiple days of data for the site 9921, year 2001..................34 4-1 Examples of processed permit vehicle records........................................................41 4-2 Routes not accounted for in the permit records........................................................42 5-1 Headway data statistics............................................................................................51 5-2 Results from the ArcMap analysis of bridges..........................................................54 5-3 Average speeds and bridge lengths..........................................................................57 5-4 Summary of headway results...................................................................................61 5-5 Summary of the travel di rection of 80,000+ lb vehicles..........................................62 5-6 Summary of same direction concurrent permit vehicles compared to all 80,000+ lb vehicles.................................................................................................................62
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ix LIST OF FIGURES Figure page 3-1 Weight category percentages out of all vehicles over 85,000 lbs............................17 3-2 WIM station 9932, the full year of data from 2001.................................................19 3-3 WIM station 9932 (vehicles greater than 70,000 lbs)..............................................20 3-4 Example of a maximum likelihood func tion for WIM data as a function of ........23 3-5 Exponential PDF model and normali zed histogram (WIM station 9932)...............23 3-6 First three months of data for 2001 from WIM station 9932...................................25 3-7 Exponential PDF model and normalized histogram (first three months from WIM station 9932)...................................................................................................25 3-8 WIM station 9901, the full year of data from 1998.................................................26 3-9 Exponential PDF model and normali zed histogram (WIM station 9901)...............27 4-2 Regional partitioning of Florida for cla ssification of travel for permitted vehicles greater than 160,000 lbs...........................................................................................40 4-3 Histogram of all permit vehicle data excluding weight over 1,000,000 lbs.............46 4-4 The exponential PDF model on the nor malized extreme value histogram..............46 4-5 Exponential PDF models on the normalized extreme histogram.............................47 5-1 Headway frequency histograms...............................................................................52 5-2 Locations of the four WIM sites selected for headway analysis..............................55 5-3 Detailed view of the four WIM sites selected for headway analysis.......................56 5-4 Histogram of total weight passing WI M station 9913 in a 3-second interval..........63 5-5 Histogram of total weight passing WI M station 9926 in a 3-second interval..........64 5-6 Histogram of total weight passing WI M station 9932 in a 2-second interval..........64
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x 5-7 Histogram of total weight passing WI M station 9936 in a 2-second interval..........65 5-8 Exponential PDF model and normali zed histogram (WIM station 9913)...............67 5-9 Exponential PDF model and normali zed histogram (WIM station 9926)...............68 5-10 Exponential PDF model and normali zed histogram (WIM station 9932)...............68 5-11 Exponential PDF model and normali zed histogram (WIM station 9936)...............69
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xi Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering PROBABALISTIC ASSESSMENT OF BRIDGE LOADING CONCURRENT WITH PERMIT VEHICLES By Matthew Crim May 2005 Chair: Scott Washburn Cochair: Kurtis Gurley Major Department: Civil and Coastal Engineering Multi-presence factors in the AASHTO bri dge code are designed to account for the occurrence of multiple lanes experiencing maximum standard AASHTO loads. Permit (overweight) vehicles repres ent a source of loading that exceeds standard vehicle weights. The presence of a single permit vehi cle in addition to the loads from standard weight vehicles is arguably accounted for implicitly in the multi-presence factors. However, there is a concern that such multi-presence factors do not account adequately for the occurrence of more than one permit vehicle on a given bridge simultaneously. The objective of this project was to devel op a probability-based model to determine whether the occurrence rate of multiple permit vehicles on a given bridge is significant. Further, the model delineates the relative probability of the combined weight of concurrent permit vehicles. The model is si te-specific, dependent upon the frequency of truck travel along a given route.
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xii This project used information from th e 37 Weigh-In-Motion sensors around the state of Florida. Weigh-In-Motion (WIM) sensors are commonly us ed to obtain truck weight data on major roadways throughout the state, employing passive weighing techniques so the operator is unaware that th e truck is being monitored. An evaluation of the Florida Department of Transportations (FDOT) WIM stations was done. Numerous irregularities in the data were found during the evaluati on process. A major issue that was encountered was the fact that the WIM sensors did not record any truck weights greater than 160,000 lbs. An additional source of data was obtained from the FDOT and used to analyze the permit vehicles reco rds over 160,000 lbs. These vehicles were evaluated using a regional analysis. Using multiple years of data from the WIM sensors, a model was created to predict the presence of multiple permit vehicles concurrently on a bridge. The model was run on four of the most heavily traveled among the 37 WIM stations. The four particular WIM stations were chosen because they contai ned a high volume of trucks passing over the sensor, numerous trucks over 85,000 lbs, severa l bridges within a 15 mile radius, and together the sites represent di fferent regions of the state. Results indicate a significant number of observations of concurrent permit vehicles at each of the four analyzed stations. Th e resultant probability models of combined weight of concurrent vehicles represent an extreme loading condition with a considerable chance of occurrence.
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1 CHAPTER 1 INTRODUCTION Problem Statement Multi-presence factors in the AASHTO bri dge code are designed to account for the occurrence of multiple lanes experiencing maximum standard AASHTO loads. Permit (overweight) vehicles repres ent a source of loading that exceeds standard vehicle weights. The presence of a single permit vehi cle in addition to the loads from standard weight vehicles is arguably accounted for implicitly in the multi-presence factors. However, such an assumption needs to be ve rified based on the specifications for permit vehicle weights and traffic patterns within the state of Florida. In addition, the presence of multiple permit vehicles in configurations th at result in loads in critical locations may conceivably exceed the capacity of the bridge. This study examined the loads (additional trucks or otherwis e) that should be considered concurrent with the different permit loads for the purpose of calculating appropriate operating ratings Existing Weigh-In-Moti on and other records were analyzed to develop a probabili stic model of the relative likelihood of various concurrent vehicle combinations to describe realisti c worst case loading configurations. The outcome will be used by Florida Department of Transportation (FDOT) engineers evaluating the existing bridge rating system. This chapter presents a brief background and necessary definitions, followed by the specific objectives of the research.
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2 Background Truck travel has steadily increased in the recent years, and the amount of overweight trucks on the roadwa ys has also increased. Tr ucks that exceed 80,000 lbs are considered overweight, and need special pe rmission from the FDOT to operate on state roadways. Additionally, trucks that exceed le ngth and height limits ar e rarely allowed to operate without a permit. Typically, these lo ads are short haul vehicles such as solid waste trucks and concrete mixers. Although these vehicles are above the legal limits, they are allowed to operate on the roadway due to grandfat her provisions in state statutes, and are referred to as exclusion vehicles [1]. With the large amount of trucks on the roadway, both over and under the permit threshold limit of 80,000 lbs, monitoring the truc k traffic flow is cr ucial to preserving Floridas roadways and bridges. Weigh-In -Motion (WIM) sensors are commonly used to obtain truck weight data on major roadways throughout the state, employing passive weighing techniques so the operator is unaware that the truck is being monitored. This study analyzed the WIM data collected in th e state of Florida in order to develop a statistical model of extreme loads on bri dges due to overweight vehicles. More specifically, WIM data will be used to determine the likelihood of the occurrence of multiple heavy (permitted) vehicles on a given bridge simultaneously. The outcome of this study will provide information to FDOT engineers evaluating the state of Floridas bridge rating system. Bridge Rating System Load rating is a component of the bridge inspection process. It consists of determining the safe load carry ing capacity of bridges on an individual basis. The load rating process estimates the live load capacity of a structure based on its current condition
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3 through analysis or a load test. It determin es if specific overweight vehicles can safely cross the structure, and whether a stru cture needs to be weight restricted. In addition, every bridge has an invent ory rating and an operating rating. These factors are used when evaluating the load rating of the bridge. The inventory rating represents the load level which can safely be placed on an existing structure for an indefinite period of time. The operating rating represents the absolute maximum permissible load level to which th e structure may be subjected [2]. Floridas WIM Polling System Florida has implemented a system of so ftware programs that, every night, automatically poll each of the (approximate ly 37) WIM monitoring stations throughout Florida and process the collected data. While the computer is polling the field counters for their data, it is also processing the data from stations previously captured. All the binary files are converted to ASCII. Count and classification reco rds are generated from WIM files. If these data pass some elementary filters, they are summarized by station, date, and direction and written to the database tables. Once the database is populated, the data are edited for quality [3]. Count and classification records ar e generated from WIM files. Definition of a Permit Vehicle According to the Florida Department of Transportations Trucking Manual, a permit vehicle is any vehicle th at needs special permission to operate on the roadway [4]. An overweight/oversized permit is required to move a vehicle or combination of vehicles of a size or weight that exceeds the maximum size or weight established by law over state highways. Except for certain vehicles exempt by law, any vehicle that exceeds the following size or weight limitations is not allowed to move without a permit:
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4 1. The maximum width of the vehicle or vehicle combination and load exceeds 102 in. or exceeds 96 in. on less th an 12 ft wide travel lane. 2. The maximum height of the vehicle or ve hicle combination and load exceeds 13 ft 6 in. 3. The maximum length of a single-unit vehicl e exceeds 40 ft. The trailer of the combination unit exceeds 48 ft. A 53 ft trailer with a kingpin distance which exceeds 41 ft, measured from the center of th e rear axle, or group of axles, to the center of the kingpin of the fifth-wheel connection. The front overhang of the vehicle extends more than 3 ft beyond th e front wheels or front bumper if so equipped. 4. The gross weight of the vehicle or vehicle combination and load exceeds 80,000 lbs. Permit issuance The intent of the law under which the FDOT issues vehicle movement permits is to protect motorists from traffic hazards caused by the movement of overweight and oversized vehicles or loads on state highw ays [4]. This ensures the comfort and convenience of other motorists on the highw ays and guards against undue delays in normal flow traffic. The permit process is also intended to minimize damage to pavement, highway facilities and structures, thus protecting the inve stment in the state highway system. Additionally, the permit process assist persons, companies or organizations with special transportation n eeds involving size and we ight. Furthermore, permits are fee based, which will recover the DOTs administrative costs, as well as any wear caused to the state highway system by the permitted loads. Permit types Overweight vehicles require either a trip-based or blanket permit. A trip-based permit is used to cover a vehicles move fr om the origin to the destination for one particular trip, allowing that trip to occur w ithin five days of permit issuance. However, if the truck or trailer is overs ized in any way, the return tr ip (empty) may be included on
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5 the permit. Trip based permits are genera lly issued for vehicles over 160,000 lbs, and often include route restrictions in which the permit is only valid if traveling over specific roads. Trip permits are more restrictive than blanket permits. Blanket permits are issued to vehicles for a twelve month period of time. The vehicle can make as many trips as needed, as long as it is within th e twelve month period. Blanket permits are generally issu ed for vehicles under 200,000 lbs. Objectives and Tasks The first objective was a literature review The literature review traced the development of the current AASHTO provisi ons for bridge loading, and identified existing studies on extreme traffic loads, permit vehicle routes, and statistical characterizations of traffic flow over bri dges. The FDOT Weigh-In-Motion and other data records related to both permit and other vehicles were examined for relevant information. The second objective was the id entification and classifica tion of specific bridges within close proximity to WIM stations. The subjects of st udy for vehicle loading were bridges, but the available information on ve hicle weight and frequency of occurrence exists at the WIM stations. Identifying bri dges close to WIM stations will justify the extrapolation of WIM-based probability models to the nearby bridges. The third objective was the development of a probabilistic model of concurrent vehicles. The collected information on the frequency, routes, and weights was used to develop a probabilistic model describing the likelihood of conc urrent vehicles on bridges with permit vehicle traffic. Th is portion of the model (concu rrent use) will not directly address critical locat ions for loading.
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6 CHAPTER 2 LITERATURE REVIEW The current AASHTO provision s for bridge loading account for the occurrence of multiple lanes experiencing the maximum st andard AASHTO loads. Permit vehicles represent a source of loading that exceeds sta ndard vehicle weights. The presence of multiple permit vehicles on a single bridge is not directly accounted for. A large number of papers were reviewed to identify any other studies that pertained to the work done in this study. The following text will summa rize the articles that were found. Studies Pertaining to Bridge Loading A study by Chou et al. [5] discussed a me thod to evaluate overweight permit applications received in the state of Tennessee. A detail ed structural analysis was required for all vehicles with a gross we ight over 150,000 lbs. Due to the volume of overweight permit applications received, this policy resulted in a large demand in manhours to perform the structural analysis. C hou et al. developed an empirical method to efficiently extract any suspicious overweight vehicles requesting a permit. The method utilized the route type, the co mbined effect of truck gross weight, axle loads, and axle spacing to assess the trucks effect on Tennesse e highway bridges. An allowable weight curve was empirically developed to dete rmine whether a permit request should be granted, rejected, or granted with restrictions. This re duced the detailed structural analyses required by about 50%. The results of the study also reduced the cost of the analyses and structural risk.
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7 All states issue special permits for truc k loads exceeding the weight limit of the highway jurisdiction. This causes structural stress levels higher than those induced by normal truck traffic. A study by Fu and HagElsafi [6] discussed a method to develop live load models including over-load trucks, a ssociated reliability models for assessing structural safety of highway bridges, a nd proposed permit load factors for over-load checking in the load and resistance factor fo rmat. The average bridge safety assured by the current AASHTO codes was used as the sa fety target in determining the load and resistance factors in the proposed procedure. The procedure proposed by Fu et al. will be useful to U.S. highway agencies as it can be used by engineers responsible for checking overloads for permit issuance. This method may be included in specif ications for bridge evaluation subject to overweight trucks. A study by Cohen et al. [7] presented a new method for predicting truck weight spectra resulting from a change in truck we ight limits. This method was needed to estimate impacts of the change on highway bridges such as accelerated fatigue accumulation. This model was based on freight transportation behavior, and it was flexible for both across-the-board and local changes without re striction on the truck types to be impacted. Using data from Arkans as and Idaho, it was shown that the proposed method can capture effects of truck weight limit change on truck weight histograms and on resulting steel bridge fatigue. A study by Ghosn [8] developed a new truc k weight formula that regulates the weight of heavy trucks and axle groups. The formula was developed based on rational safety criteria. The procedure used to obtai n the proposed formula utilized a reliability
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8 analysis such that the projected truckload e ffect will produce a uniform reliability index for existing bridges designed accord ing to current AASHTO criteria. A sensitivity analysis that was performed in the second of a two paper sequence by Ghosn and Moses [9] showed how the expected number of bridge de ficiencies could be reduced if different truck wei ght regulations were adopted, or if different bridge safety criteria were used in the deri vation of the truck weight formula. An analysis of twelve typical bridge configurations confirmed the re sults obtained from the generic analysis of the bridges taken from the National Bridge Inve ntory (NBI) files. The analysis indicated few bridges would need rehabilitation if opera ting stress criteria were used for bridge evaluation. However, several of these bridge s would be considered deficient if working stress design stresses were used as the rating criteria. A study by Brillinger [10] studied at risk analysis in a format non-specific to vehicles and/or bridges. Brillinger looke d at low probability-high consequence events, events that lead to damage, loss, injury, death, and environmental impairment. Based on his findings Brillinger believes that the demand for risk anal ysis is growing steadily, in part because the costs of replacing destroyed structures are growing and in part because of the steady increase in the population livi ng in hazardous areas. The article had two examples, the first one was seismic risk analysis and the second was forest fire probabilities. The method of risk analysis could be applied to predicting when multiple overweight trucks would app ear on a given bridge, a low probability-high consequence event. Another study by Brill inger et al. [11] expanded on the forest fire study done in the previous paper.
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9 A study by Fu et al. [12] researched the e ffects that various ex isting and projected truck configurations have as live load ings upon bridges which exist on the National Bridge Inventory (NBI). The study found that the live load truck capacity of existing bridges on the NBI was highly depende nt upon the selection of the AASHTO Specification alternate, the an alysis methodology, and assumpti ons used in applying the specification. A study by Croce and Salvatore [13] presen ted a general theoretical stochastic traffic model that can be used in the assessmen t of existing bridges, as well as the design and analysis of bridges with less traditional schemes or subjected to particular traffic conditions. The model is intended for appl ications, not only to background studies for calibration of traffic load models in new bri dge codes, but also in all those cases where precise evaluation of traffic effects are required. A study by Galambos [14] presented a comparison of the AASHTO design live loadings for bridges with various other load ing situations. Situations include normal permit overloads and abnormal permit loads among other loadings. Galambos concluded that the bridge load rating pr ocess needs to be improved. Also, a standard load rating vehicle test and met hod should be employed. A study done by Kolozsi et al. [15] discusse d a computer program that was used to determine routes for permit vehicles in Hunga ry. Weigh-In-Motion measuring units were usually applied along highly trafficked road s and close to major bridges to monitor weight. A noticeable difference between stat ic mass and the loads of the moving vehicle were found. The moving vehicle mass was al so found to be higher than the considered factors of the dynamic design specifications.
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10 A study by Fryba [16] looked at the fatigue li fe of railway bridges. Fryba used the Palmgren-Miner theory of linear cumulative damage as a basis. Fryba looked at the effect of different parameters on the estimati on of the bridge fatigue life. It was found that the rise in speeds of the traffic loads has re sulted in shortened bridge life. It was also found that the increase in the number of stress cycles per year, the standard deviation of stress, and an increase in the mean value of the traffic loads diminish the life of the bridge. The majority of articles that were found focus on the effects of overweight trucks once they are on the bridges. None of the articles were found on the travel patterns of overweight trucks, and the occurrence of c oncurrent vehicles on the same bridge. Nevertheless, each article listed has inform ation that is relevant to this study. FDOT Literature Three documents supplied by the Florida De partment of Trans portation were used to get a better understanding of the project. The first document was the Bridge Load Rating, Permitting and Posting Manual [2], which provided information on the load rating process the FDOT used. The second document was the Automated Editing of Traffic Data in Florida [3]; it provided insight into the Weigh-In-Motion polling process used and the editing process that the FDOT us ed to filter out erroneous data. The third document was the Trucking Manual [4], it was used to get information on the types of permits the state of Florida issued along w ith when, why, and how permits were granted.
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11 CHAPTER 3 PRELIMINARY ANALYSIS OF WEIGH-IN-MOTION DATA: SINGLE VEHICLE MODELING The state of Florida has 37 Weigh-In-Mo tion (WIM) sites dispersed across the state. The truck data that these sites collect was downloaded to the FDOT central office in Tallahassee. This chapter focuses on the contents of the WIM data records, examples of preliminary analysis of these data, probabi listic modeling of the o ccurrence of a single vehicle weight, and a discussion on problem s identified within the data files. Retrieval of Data from FDOT Retrieval of the weigh-in-motion data for the project came from the statistics office under Richard Reels supervision. The data were copied onto a hard drive and brought back to the University of Florida. Ther e were approximately 25,300 files of data that were collected and stored on the hard drive from January 1998 to August 2003. Each file consists of the individual samples of WIM data collected during one 24-hour period at one WIM station. Thus one WIM station could produces 365 files per year. A given file may range from a few dozen to a few thousand individual samples of vehicle information. Some WIM sites have data from all five years; others only have data from part of that time frame. This is due to a specific site not being ope rational for a period of time. Another reason for an incomplete five year time period was time constraints in the collection process at the FDOT. The data retrieved from the FDOT were in ASCII format. An overview of the 37 WIM sites such as site location, county, and number of lanes can be found in Table 3-1.
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12 An example of the contents of any given data file can be seen in Table 3-2. A key explaining each column in Table 3-2 can be f ound in Table 3-3. As can be seen in Tables 3-2 and 3-3, the WIM files contain details of the trucks being sampled, including date, time, and lane of travel (implies direction), vehicle class, travel speed, gross weight, and weight of each axle. Table 3-1. Overview of the 37 WIM stations Site Site Location County Number of Lanes Lane Orientation Original Sensor Existing Sensor Date Changed Dates Copied 9901I-10, MonticelloJefferson4OE-OWDAW-200 DAW-1906/1/2003 1/98-12/99; 1/01-8/03 I-75, MicanopyDAW-200 I-75, Micanopy-SBDAW-200 9905SR-9/I-95, JacksonvilleDuval6OS-ONDAW-190 DAW-190 1/01 8/03 9906I-4, DeltonaVolusia4OE-OWADR-WIM ADR-WIM 1/01 8/03 9907US-231, YoungstownBay4ON-OSDAW-100 DAW-100 1/01 8/03 9908US-319, Trk Rt, TLHLeon4OE-OWDAW-200 DAW-200 1/98 8/03 9909US-19, ChieflandLevy4ON-OSDAW-200 DAW-1908/14/2001 1/01 8/03 9913Trnpk, St.Lucie Co.St. Lucie4OS-ONDAW-100 DAW-100 1/01 8/03 9914SR-9A/I-295, Duval Co.Duval4ON-OSADR-WIM ADR-WIM 1/01 8/03 9916US-29, PensacolaEscambia4ON-OSDAW-190 DAW-190 1/01 8/03 9917US-41, Punta GordaCharolette4OS-ONDAW-200 DAW-1905/2/2002 1/01 8/03 9918US-27, ClewistonHendry4ON-OSDAW-100 DAW-100 1/01 8/03 9919I-95, MalabarBrevard4ON-OSDAW-100 DAW-1906/23/2003 1/01 8/03 9920I-75, Sumter Co.Sumter4ON-OSADR-WIM DAW-19010/2/2003 1/02 8/03 9921SR-5, Martin Co.Martin4ON-OSDAW-100 DAW-1904/11/2003 1/98 8/03 9922I-275, TampaHillsborough6ON-OSDAW-200 DAW-1907/21/2003 1/02 8/03 9923I-95, JacksonvilleDuval4ON-OSDAW-200 DAW-200 1/02 8/03 9924I-110, PensacolaEscambia4OS-ONDAW-200 DAW-200 1/02 8/03 9925US-92, DelandVolusia4OW-OEDAW-200 DAW-200 1/02 8/03 9926I-75, TampaHillsborough6ON-OSDAW-200 DAW-200 1/02 8/03 9927SR-546, LakelandPolk4OE-OWDAW-200 DAW-200 1/02 8/03 9928I-10, Walton Co.Walton4OW-OEDAW-200 DAW-200 1/02 8/03 9929US-1, EdgewaterVolusia4ON-OSDAW-200 DAW-1904/11/2003 1/02 8/03 US-1, MiamiDAW-200 US-1, Miami-SBDAW-200 9931Trnpk, Sumter Co.Sumter4ON-OSDAW-100DAW-1001/01 8/03 9932Trnpk, Osceola Co.Osceola4ON-OSDAW-100DAW-1001/01 8/03 9934Homestead Ext, DadeMiami-Dade7 ( 4S,3N)OS-ONDAW-100DAW-1906/3/20021/01 8/03 9935US-27, Palm Beach Co.Palm Beach4OS-ONDAW-100DAW-1904/11/20031/98 8/03 9936I-10/SR-8, Lake CityColumbia4OW-OEDAW-100DAW-1901/30/20031/98 8/03 9937SR-87, MiltonSanta Rosa4ON-OSDAW-100DAW-1905/23/20021/98 8/03 9938SR-83/US-331, FreeportWalton2ON-OSDAW-100DAW-1001/98 8/03 9939SR-2, GracevilleHolmes2OE-OWDAW-100DAW-1001/98 8/03 9940SR-267, QuincyGadsden4OS-ONDAW-100DAW-1001/98 8/03 9942SR-85, Laurel HillOkaloosa2ON-OSDAW-100DAW-1001/98 8/03 9943SR-10/US-90, CypressJackson2OE-OWDAW-100DAW-1001/98 8/03 9944SR-69, SelmanCalhoun2OS-ONDAW-100DAW-1001/98 8/03 9946SR-363, St. MarksWakulla2OS-ONDAW-100DAW-1001/98 8/03 ON-OS 6 ON-OS 6 Alachua Miami-Dade 9904 9930 1/01 8/03 1/02 8/03 DAW-1904/15/2002 DAW-1903/21/2003 *OW, OE, OS, and ON represent the outside w estbound, eastbound, southbound, and northbound lanes. E.g. OE-OW means lane 1 refers to th e outside eastbound lane and lane 4 refers to the outside westbound lane.
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13 Table 3-2. Contents of a selected WIM file (50 columns of data)
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14 Table 3-3. A key to the co lumn fields for Table 3-2 *The values can be found in the Automated Editin g of Traffic Data in Florida on pages 12-13. Conversion of Data The 25,300 files needed to be arranged properl y for the requirements of the project. A directory structure was create d to organize the data. E ach file contained one days worth of data consisting of hundreds of truck entries. A folder was created for each of the 37 sites. Within each sites folder, the data were furthe r subdivided into the specific year that it pertained to.
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15 Preliminary Analysis of WIM Data After the data were organized into the prope r folder system, a pr eliminary statistical analysis was initiated. This section presents some of the original schemes applied to characterize the WIM data in a probabilistic framework. A global perspective was first used, in which the data from all WIM stations were combined to provide a view of the overall relative likelihood of h eavy vehicle travel in Florida. Extreme value analysis was then applied to data from specific WIM sites over various time frames. The results of the analyses presented in this chapter represen t a starting point for feedback to the FDOT project manager. Subsequent meetings narrowe d the scope of the anal ysis to best fit the intended use of the project results, and are the subject of Chapter 5. Initial Analysis of Data from All WIM Stations Combined There were several steps taken that perfect ed what information needed to be pulled out of each file. A Visual Basic progra m was written to extract the minimum and maximum vehicle classification, the mini mum and maximum wei ght, and the total number of vehicles for each day of data. The classification of the vehicles comes from the classification scheme F from the FDOT which can be found in Appendix A. From the preliminary analysis of the data, it was found that the files consisted of only vehicles that were classified as truc ks (i.e., cars and other non-FDOT-d efined-trucks were filtered out). The next step was to organize the weight of the vehicles into more precise groups. Since a permit vehicle is 80,000 lbs or greate r, the program only considered trucks greater that 85,000 lbs. 85,000 lbs was chosen to account for weight measurement error, thus ensuring that the vehicle needs a permit to operate. On top of the information that was pulled out of each file by the first version of the Visual Basic program, the total
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16 number of vehicles greater than 85,000 lbs, 90,000 lbs, 105,000 lbs, 120,000 lbs, 135,000 lbs, and 150,000 lbs were also recorded. The final step was to identify the vehicle classes that were carrying the heaviest loads. It is more significant if the weight of an extreme load is distributed over, for example, four axles rather than seven. In addition to the information extracted from each file in the second version of the program, the final version of the Visual Basic program identified the classification of any vehicle that was 150,000 lbs or greater. Table 3-4 presents the summary statistics from the combined WIM records of all stations and all years. Of all vehicles that were weighed at the WIM stations, 6.12% exceed 85,000 lbs. 85,000 lbs was the overweigh t threshold to determine the percent of overweight vehicles within si x ranges shown in Table 3-4. These are calculated as a percentage among only those vehicles that exceed 85,000 lbs. The highest recorded vehicle weight in any file was 160,000 lbs. The same information can be seen graphically in Figure 3-1. Detailed lists of the data broken down by years and site numbers can be found in Appendix B. The tables found in Appendi x B give a better perspective of the data that were ex tracted from each site and each year. This preliminary analysis of all WIM data confirmed the initial presumption that the WIM data ignores or otherwise filters any vehicle with a gross weight over 160,000 lbs. It was unclear at the start of the project whether this presump tion was correct, and whether it implied the need for additional data sets beyond the WIM site data. The 160,000 lbs maximum confirmed by this preliminar y analysis of all WIM data led to the acquisition of the permit data set th at is the subject of Chapter 4.
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17 Table 3-4. Summary of WIM da ta (all weight in 1000 lbs) Percentage of Weight within Weight Range Out of Vehicles Over 85,000 lbs only Total Recorded Vehicles Total Vehicles >85 Percent Vehicles >85 85 90 90 105 105 120 120 135 135 150 150 160 29,897,981 1,829,854 6.12% 60.49% 33.33%5.03%0.77% 0.31% 0.06% Figure 3-1. Weight categor y percentages out of all vehicles over 85,000 lbs Histograms could now be generated for diffe rent years at different sites. The problem with generating histograms with the data pulled from the WIM files was that it was very limited. The number of bins and th e bin widths were both fixed for the weight ranges shown in Table 3-4. The histograms that were generated also only apply to vehicle weights greater than 85,000 lbs, not the w hole data set. A broader analysis of the data was conducted to generate histograms that were more flexible in what they could present. This involved the development of a companion Visual Basic program for more generalized processing of the WIM files. The next several sections discuss the analysis of data at specific WIM sites usi ng an exponential probability model.
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18 Generating Extreme Value Histograms from WIM Data A Visual Basic program was created to examine all the WIM data files for a specified time period at a particular site. The program extracted the gross truck weight for every truck from every truck data file. Th e program then created a separate text file for each day, the contents of each consisted of only the gross weight for each truck record in the file. The program also created a table of contents file that contained a list of the names of all files that were processed. These files were then input into Mathcad [17] for analysis. An array of the gross weight data could then be read from a desired file. For example, the 99320101_11.txt file repres ents the file for January 11, 2001 at site 9932. Numerous days at a given site (or multiple sites) could be loaded, creating one large continuous array with all of the data for the files specified. A histogram could be created by inputting the data s ource and the number of bins. An example histogram is provided in Figur e 3-2 from the full year of data at a single WIM station. The WIM station is #9932 which is located on th e Florida Turnpike in Osceola County. The x-axis represents th e vehicle weight; the yaxis represents the number of trucks within each bin at that weight. The general sh ape of the resulting histogram is bi-modal with a peak near 20,000 lbs and another near 45,000 lbs. The lower peak is a distribution of unloaded trucks while the higher peak is the distribution of loaded vehicles.
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19 Figure 3-2. WIM station 9932, the full year of data from 2001. The focus of the project was to model the occurrence of heavy vehicles. Therefore the dataset was filtered to only look at the heav ier vehicles; the vehicles that were to the right of the second peak of the histogram. The histogram in this range appears to fit an exponential distribution, defined later in this chapter, as the monotonic decrease in probability from left to right. The portion of data that this study focuses on was the data over 80,000 lbs. For the histogram in this ex ample, a cut off of 70,000 lbs was chosen. Only the samples over this level were kept fo r further extreme value analysis. Figure 3-3 shows the histogram produced from the full year of data from 2001 for the vehicles over 70,000 lbs.
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20 Figure 3-3. WIM station 9932 (vehicles greater than 70,000 lbs) Meaning of the extreme value histogram To use the histogram to determine probabil ities, the data presented in Figure 3-3 needs to first be normalized so the area unde r the histogram equals one. The normalized histogram would then represent the proba bility, out of any vehicle between 70,000 and 160,000 lbs, of a given range of weights pa ssing the given WIM sensor over the time frame chosen for analysis. An explanation of this process is discussed in the next section. Modeling the extreme value histogram It was desired to create an analytical parametric function that represented the information provided in the normalized extreme va lue histograms of the data of interest. A convenient functional form would be flex ible enough to represent a variety of WIM data, from different WIM stations over va rious time frames. Thus a parametric probability density function (PDF ) was sought that fits the WIM data well. The focus was again restricted to the extr eme values of heavier vehicles.
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21 Fortunately, the monotonic nature of th e histogram above 70,000 lbs lends itself well to a simple PDF known as the e xponential PDF. The exponential PDF is xe x f ) ( (1) where x is the weight, and is the parameter that is optimized such that the error between the exponential PDF and the normalized hist ogram is minimized. The procedure to identify involves finding the peak in th e maximum likelihood function. Suppose that X is a random variable (such as weight) with the probability density function of ) ( x f, where is a generic single unknown parameter (such as ). Let x1, x2,, xn be the observed values in a random sample of size n (the weights from the WIM data). Then the likelihood function of the sample is ) ( ... ) ( ) ( ) (2 1 nx f x f x f L (2) which is the product of the model probability associated with each observed value. The value of the likelihood function is a function of the unknown parameter and the data. The maximum likelihood estimator of is the value of that maximizes the likelihood of the function) ( L. That is, determine the value of that makes the product of the probabilities of the observations the highest. In the specific case of the exponent ial PDF, the likelihood function is ) ( ... ) ( ) ( ) (2 1 nx x xe e e L (3) The value of likelihood function ) ( L was plotted over a range of values of and the value of that corresponds to the peak value is the best descriptor of the data. Identifying the peak in the likelihood function was easily done in Mathcad using a built in optimization function.
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22 It was more convenient to take logari thms and work with the log-likelihood function. Since the logar ithm function is monotonic, the log-likelihood takes its maximum at the same point as the likelihood function presented in Equation (2). The likelihood function in this form is now a summ ation of the natural log of the probability of each sample (weight) rather than the produc t. The Mathcad function used to identify the maximum likelihood value is more reliable in this form: n i ix f L l1; log ) ( log ) ( (4) Figure 3-4 illustrates the resulting lo g maximum likelihood function (Equation 4) plotted vs. for the data used to create Figure 3-3. Before calculating the data were first linearly mapped from the 70,000 to 160,000 ra nge into a range of 0 to 1. This was done since the functional form of the exponent ial distribution has a lower bound of zero. The value of that provides the maximum value in this case was 6.621, calculated using a Mathcad optimization routine. This value was used to create the model and substituted back into the exponent ial PDF (Equation 1), in this casexe x f 621 6621 6 ) (. This analytical function (exponential PDF) now re presents the data over the range 0 to 1. In order to represent the da ta over the interval of 70,000 to 160,000 lbs, the analytical function needed to be adjusted to invert the data mapping. Since the interval had increased from 1 to 90,000, the exponential PDF needed to be divided by 90,000. In addition, the value of x would become 000 70 000 160 000 70 W The new exponential PDF equation in terms of the data in its original values W is 000 70 000 160 000 70000 90 1 ) (We W f (5)
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23 The exponential PDF in Equation (5) wa s graphed on top of the normalized histogram to demonstrate how closely the tw o curves match in Figure 3-5. Figure 3-5 represents the full year of data from 2001 fo r all the trucks weighing more than 70,000 lbs. The blue line represents the exp onential PDF model identified using maximum likelihood. This model was superimposed on the normalized histogram of the actual WIM data. Figure 3-5 denotes the no rmalized version of Figure 3-3. 05101520 1 105 5 1040 5 104 MaxLike Figure 3-4. Example of a maximum likeli hood function for WIM data as a function of Figure 3-5. Exponential PDF model and normalized histogram (WIM station 9932)
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24 Application of the extreme value model An exponential PDF model of extreme vehi cle weights was developed for many of the WIM stations over varying periods of time. This produced a view of the relative likelihood of heavy vehicles in various parts of Florida. Since the locations of the WIM stations were available, these distributions can be tied to bridges of interest. For example, the distribution fit to data from a WIM station along I-95 may vary considerably from a different station along I10. The difference may show a much higher probability that heavier vehicles will appro ach a particular bridge on the east coast compared to a bridge in the panhandle. These studies may also show a change in the weight distributions at the same station during different seasons. Two additional examples are presented. The first looks again at WIM station 9932, but only uses the data for the first three months of the year rather than the complete year. Figure 3-6 presents the full histogram of data from the first three months of 2001 from WIM station 9932. Figure 3-7 presents the resultant exponential PD F fit using maximum likelihood on the normalized extreme value hist ogram. From the full year to the first three months the parameter changed from 6.621 to 8.069.
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25 Figure 3-6. First three months of data for 2001 from WIM station 9932 Figure 3-7. Exponential PDF model and normali zed histogram (first three months from WIM station 9932) The second example uses the entire year of 1998 from WIM st ation 9901, located on I-10 near Monticello in Jefferson County. Figure 3-8 presents the full histogram of data from WIM station 9901. Figure 3-9 pres ents the resultant e xponential PDF fit using
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26 maximum likelihood on the normalized extreme value histogram. The cutoff point for the data from WIM station 9901 was 75,000 lbs instead of 70,000 lbs which was used for the previous two examples. The point wher e the exponential curve starts to develop differs from station to station; therefore the cutoff point was adjusted. From the full year (2001) at station 9932 to the full year (1998) at station 9901 the parameter changed from 6.621 to 20.323. Figure 3-8. WIM station 9901, th e full year of data from 1998
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27 Figure 3-9. Exponential PDF model and normalized histogram (WIM station 9901) A higher value indicates that the right tail of the distribution (the heaviest vehicle weights) were less probable when compared to low values of That is, the higher the the less likely heavier vehicles will be obs erved. Coupling such relative probability information with the frequency of observati ons of all trucks at a given WIM station provides a quantification of heavy vehi cles traveling along that WIM route. Extensions of the extreme value model Thus far the extreme value modeling of h eavy vehicles did not include information regarding the likelihood of multiple heavy ve hicles on a bridge. The histograms that were produced (e.g., Figures 3-2 and 3-3) do not use the time between individual WIM records as an input. However, the methodology presented above can be adjusted to take advantage of the time stamp of each record, which was provided in the WIM records. The modeling discussed above may be exte nded to include additional independent variables, such as time between WIM reco rds. This extension will be useful for
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28 identifying the likelihood of multiple heavy vehicles approaching bridges. For example, similar modeling techniques can be used to id entify probabilities for the total weight to pass a WIM station over a chosen time frame, say five minutes. A nother distribution can be developed to describe the average head way between adjacent weighted vehicles. Total weights could potentially exceed 160,000 lb s if several heavy vehicles are traveling close together. Short of pl acing WIM sensors immediately be fore a bridge of interest, this modeling method is valid for helping determine the probabili ty of simultaneous heavy vehicle loads on a bridge. The consideration of headway information in probability modeling was a subject that was pursued more rigorously in Chapter 5, when the analysis was shifted to target the likelihood of multiple heavy vehicles occurring within a specified length of road. This includes multiple vehicles traveling together, and vehicles traveling opposite directions which cross the same WIM sensor within a short time frame. The next section discusses in detail irre gularities identified within the WIM data provided by the FDOT during the co urse of the preliminary analyses discussed thus far. The forms, sources and significance of these ir regularities were investigated to determine whether they were likely to have a signifi cant impact on subseque nt data analysis. Difficulties with the WIM Datasets In the development of the Visual Basic programs and the preliminary analysis of the WIM data, numerous irregularities and difficulties were encountered. The next section will discuss some of the difficulties that have been observed with the contents of the WIM records. The next chapter moves fr om the WIM datasets to the permit vehicle records that contain informati on for vehicles over 160,000 lbs.
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29 There were six complications that were encountered when analyzing the WIM datasets. The first two complications were resolved, while the last four remain unresolved. The next six subs ections discuss these issues. Inconsistent Formatting in WIM Data Files The majority of the WIM data were set up so that each line of data represented all of the statistics for a single truck. Each new line represented a new truck that passed the sensor. Data at a few of the WIM stations were not broken up line by line for each truck that passed over the sensor; instead they we re one continuous line of data. The site numbers and years of data that had th e problem are listed in Table 3-5. A solution was reached using a Visual Basi c program. A rectangular box character, similar to the character shown in parenthese s (), separated adjacent entries on the same line. The Visual Basic program produced an id entical file in the correct format. Each time a box was encountered, a new line of text was created below the previous line. This process eliminated the continuous text string a nd organized the file in a line by line basis. Table 3-5. WIM stations with an inconsistent file format Site Number Years 9901 1998, 1999 9908 1998, 1999, 2000 9921 1998, 1999, 2000 9935 1998, 1999, 2000 9936 1998, 1999, 2000 Blank Data Files Any single data file contained the data collected during a 24-hour period at a particular WIM station. Some data files contained no data for a given day. Ordinarily, if there were no data for a given day, there wa s no file for that day. The assumption was made that there must have been some complication in sending the data from the site back to the DOT. These files were omitted from the data files used for analysis. The site
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30 numbers and years of data that contained bla nk files are listed in Table 3-6. The table does not indicate that an entire year of data was missing, only that one or more days in that year were blank. Table 3-6. WIM stations and years that contain blank files Site Number Year(s) Site Number Year(s) 9901 2001 9935 1999, 2000, 2003 9906 2001 9936 2001 9907 2002 9937 1998 9909 2001 9938 2000 9914 2001 9939 1998, 1999, 2000, 2003 9917 2001 9940 2003 9919 2001, 2002 9942 2000, 2001, 2002, 2003 9921 2000 9943 1999, 2003 9925 2002, 2003 9944 1998, 1999, 2001, 2003 9929 2003 9946 2000, 2003 9931 2001 Same Vehicle Entry Recorded More than Once Some data files contained many more entr ies than other files around the same time period (each file should be a single day). It was found that the large files were combining multiple records of days into one large file. This was not a big problem if any vehicle was simply recorded once, but stored in the wrong file (a different day). There was a time and date stamp associated with each record However, in some cases one or more of the days that were contained within the larg e file would also have its own VTR (vehicle truck record) file. This means that some days of data were represented twice in a dataset. There were two different situ ations, the first was when a day in the large file was identical to its VTR file, and the second situation was when it was not identical. An example of files with the fi rst problem was found in records 99320209.041_VTR and 99320209.051_VTR. The firs t file represents the day September 4, 2002 and is 508 KB; the second f ile represents September 5, 2002 and is 991 KB. The September 5th file contains data from both days. When splitting the
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31 September 5th file into two files, a 508 KB file and a 483 KB file were created which represent September 4th and 5th respectively. The two September 4th files were identical, therefore recording all th e data from September 4th twice. An example of files with the s econd problem was found in the files 99130202.111_VTR and 9932130202.121_VTR. The firs t file represents the day February 11, 2002 and is 166 KB; the second f ile represents the da y February 12, 2002 and is 816 KB. The February 12th file contains data from both days. When separating the February 12th file into two files a 390 KB file and a 426 KB file were created which represent the complete files for both days. The reason the February 11th file increased from 166 KB to 390 KB was that the 166 KB f ile only had the first 11 hours of the day, whereas the 390 KB file contained all 24 hours. This meant that a portion of February 11th was recorded twice. End of Month Carryover into the Subsequent Month This problem was an extension of the previous problem. The issue was still multiple days of data being combined into one data file. In some cases the day or days at the end of a given month were combined w ith the beginning days in the subsequent month. When multiple data files were co mbined into one they were arranged in ascending order, adding the next day to the e nd of the previous day. The particular problem in this case was that when the data switched from one month to the next, the data from the prior month did not have the proper month number in its date stamp, but rather has the month subsequent to it. An example of a file that has this problem was found in the file 99469812.021. This file should only contain the data from December 2, 1998. Instead it contained the data from November 30th, December 1st, and December 2nd. The day of data from
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32 November 30th had been improperly date stamped as December 30th, thus the file appears to contain December 30th, December 1st, and December 2nd. At this WIM station there was no November 30th file, but there was a separate December 30th file. The actual December 30th file and the part of the December 2nd file that contained data improperly stamped as December 30th have nothing in common (no repeats of specific vehicle weights or times). Thus, the conclusion was that November 30th was a part of the December 2nd record with an improper date stamp. Multiple Days of Data in a File with No Reset of the Vehicle Count This problem was similar to the previous tw o problems. It deals with multiple days of data being combined into one file. The end of any given day should result in a resetting of the time to midnight (00:00:00) and vehicle number to 1, thus providing a count of vehicles per day. The issue was that when the combined file switched from one day to the next, the survey hour, minute, sec ond, and vehicle number did not reset for the new day. A file with this problem wa s 99350110.021_VTR. This file was supposed to contain October 2, 2001 data. The record s within jumped dates from September 21st to October 21st to October 1st before a 24-hour period was completed and the time and vehicle number were reset. However, when it went from October 1st to October 2nd, it did not encounter this problem. Table 3-7 presen ts an example from portions of WIM station 9935 on October 2, 2001. This site contained mo re than one day of data without resetting the time stamp or vehicle number. The light grey highlight represents when the time stamp and vehicle number do not reset. The da rk grey highlight represents the correct reset of the time stamp and vehicle number.
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33 Table 3-7. WIM file 99350110.021_VTR File Type County Number Station Number Date Hour Minute Second Vehicle Number VTR 93 9935 9/21/200115540 146 VTR 93 9935 9/21/200115546 147 VTR 93 9935 9/21/2001 1 56 8 149 VTR 93 9935 10/21/2001 1 56 15 150 VTR 93 9935 10/21/200115742 151 VTR 93 9935 10/21/20011599 152 : : : : ::: : : : : : ::: : VTR 93 9935 10/21/2001142459 4241 VTR 93 9935 10/21/2001 14 25 6 4242 VTR 93 9935 10/1/2001 14 29 56 4252 VTR 93 9935 10/1/2001143326 4281 VTR 93 9935 10/1/2001143350 4283 : : : : ::: : : : : : ::: : VTR 93 9935 10/1/2001235819 3274 VTR 93 9935 10/1/2001235825 3275 VTR 93 9935 10/1/2001 23 58 34 3276 VTR 93 9935 10/2/2001 0 1 55 4 VTR 93 9935 10/2/20010820 9 VTR 93 9935 10/2/20010827 10 Naming of Combined Files by the Last Day The last problem identified in the WIM file s again deals with multiple days of data being combined into one file. Whenever multiple days of data were combined into one file, the file was named for the last day of reco rded data in the combin ed file. Looking at the file 99350110.021_VTR again, the file was supposed to re present October 2, 2001. This means that the last day in the file s hould be October 2, 2001. Instead the file continues to record days up to October 13th. Resolving Problems with WIM Files The underlying issue in the four unresolve d problems was that they all were combining multiple days of data into a single file. Each identified problem was slightly different, but inevitably came down to multiple days of data being recorded as a single
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34 day. To figure out how widesp read of a problem this was, an evaluation of the data needed to be done to see how many files co mbined data. A Visual Basic program was created to open each file and look for a change in the date. If the program came across a file with more than one date it would record the file name, the dates that it had combined in the file and the starting and ending hours fo r each of the dates. The starting and ending hours were recorded to check to see if an entir e day of data was recorded. A text file was created for each year at each of the 37 WIM stations summarizing all the files that were combining days of data. The text output fr om 2001 for site 9921 is shown in Table 3-8. Table 3-8. List of the files with multiple days of data for the site 9921, year 2001 Start Time End Time File Number File Name File Date Hr.Min.Sec.Hr.Min. Sec. 165 99210106.151_VTR6/14/20012 45 22 22 46 11 165 99210106.151_VTR6/15/20010 40 3 23 45 16 176 99210106.271_VTR6/26/200114 45 6 21 18 17 176 99210106.271_VTR6/27/20010 18 43 19 18 35 212 99210108.021_VTR8/1/20012 47 31 22 29 46 212 99210108.021_VTR8/2/20010 32 32 22 22 24 219 99210108.161_VTR8/15/200113 57 0 20 10 36 219 99210108.161_VTR8/16/20013 18 3 18 52 0 285 99210110.211_VTR10/20/20011 46 55 23 46 17 285 99210110.211_VTR10/21/20011 48 46 22 52 42 294 99210110.301_VTR10/29/20010 29 13 22 18 54 294 99210110.301_VTR10/30/20013 13 50 18 40 1 Once the evaluation of the dataset was complete, it was found that out of 25,300 files, 1,284 files recorded multiple days of data into one day. This is roughly 5% of the data files. Given the comple xities involved in untangling fi les that suffered from one or more of the above identified problems, th ere was not enough confidence that any one solution (algorithm) could be created to solve these issues within a reasonable time frame. Further, there was the possibility th at there were additional problems with these files that had not been identified. Thus fixing the identified problems would not guarantee that the data now offered a clean re presentation of the actua l vehicle travel at
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35 those WIM stations and days. It was important to make an effort to remove data that may contaminate the results of the statistical analys es. For this project, the files with multiple days of data were omitted from the analysis. A summary of all the files with multiple days of data can be found in Appendix C.
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36 CHAPTER 4 PERMIT VEHICLE ANALYSIS: REGIONAL VEHICLE MODELING The vehicle truck records that were obtained from the Florida Department of Transportations WIM sensors did not include records for trucks that weighed in excess of 160,000 lbs or had more than nine axles. Another source of data was required to account for vehicles that fit this description. As discussed in Chapter 1, the FDOT issued permits to vehicles that exceed standard size and/or 80,000 lbs. Each permit was recorded, and therefore served as a potent ial source of information for vehicles over 160,000 lbs. The permitting office supplied a hard copy of the permits issued to trucking companies in Florida from January 2002 to April 2004. Processing and analysis of these permit records is addressed in this chapter. Formatting and Processing The data supplied in the permit records c onsisted of: permit vehicle weight, vehicle width, permit number, the date the permit was issued, company name, permit type, permit class ID, vehicle route, and r oute restrictions. The categorie s with the most significance to the project were the vehicle weight, permit date, permit type, and route/restrictions. The hard copy of the permit listing obtained from FDOT was scanned into electronic format using optical character rec ognition software. An example of one of the scanned sheets is shown in Figure 4-1. The hundreds of pages of scanned data were carefully reviewed to find errors created during the scanning process. After the
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37 identifiable errors in the data had been fixe d, a categorization of where the trucks were traveling throughout th e state was needed. Figure 4-1. FDOT permit listing sheet s canned using optical recognition software Several of the companies on the list that had a large number of vehicles permitted were contacted for further information regard ing vehicle weight, permit date, and route.
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38 Many company representatives were hesitant to talk to someone inquiring about the movements of their permit vehicles, but se veral were forthcom ing and cooperative. It was found through these phone interviews that the weight on the FDOT permit was typically within 5% of the actual truc k weight. The permit date and permit type provided a window of time for the permit use. A blanket (B) permit is valid for one year, thus a single blanket permit may be used over the same route by the same vehicle multiple times. Blanket permits are used for vehicles that do not exceed 200,000 lbs. A trip (T) permit is valid for a single use to or from a destination. The trip permit allows the truck a five day travel window for its single use. Finally, the provided routes consist only of major roads. These major roads ha d restrictions listing specific locations off limits. Each companys representative clai med strict adherence to the permissions granted in the permit. The penalty of vi olation can severely damage the companys ability to co nduct business. Zones for Permit Vehicle Travel A goal of this project was to develop likelihood functions that describe the probability of excessive weight occurring al ong Florida bridges due to heavy vehicle traffic. Precise data records of vehicle we ight, location and time of travel were most useful for developing these functions. In the case of the permit records for vehicles over 160,000 lbs, the specific origin, destination, and route were not provided in the permit records. For example, a route may be listed simply as I-95, or SR-823, or some combination of roads. From the perspectiv e of this project, a single permitted vehicle may travel numerous times over a year (bla nket type), or a single time (trip type) anywhere along the listed route(s).
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39 The lack of specificity in vehicle location, time and frequency of travel necessitates a procedure to identify the most likely regions of travel within Florida for a given permit. The roads in the state needed to be divided in to regions to better determine what part(s) of Florida a given permit allowed travel. The determination of regions was conducted using ArcMap, a Geographic Information System (GIS) based software tool that is part of a larger software package called ArcGIS [18]. ArcMap can overlay user selected layers of data called shape files onto a map. Using the Florida Geographic Data Library (FGDL) [19], an image of all the counties in the state of Florida was loaded. Once the shape file was loaded, the state was divided into regions to better determine what part(s) of Florida the permitted vehicles were traveling in. Five regions were c hosen, each region havi ng at least one major metropolitan area, and a major interstate. Once the regions were determined, they could be used to designate which roads should be assigned to which region. Figure 4-2 shows the regional breakdown of Florid a developed for this study. The list of roads came from two different sour ces. The first list of roads came from the major roads shape file in the FGDL. The second list came from the FDOT website [20], from which a U.S. highways shape f ile and state highways shape file were downloaded. The two lists were loaded in to ArcMap, and the roads were broken down into the five regions. A Visual Basic program was written to comp are the roads that each truck used (as provided in the scanned, processed permit reco rds) to the roads in each region defined in Figure 4-2. An analysis of where the trucks were traveli ng within Florida (by region) was then determined. Many of the permit reco rds had routes that spanned more than one
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40 region. For example, permits that included I-95 as a route were in at least regions 2, 4, and 5. A random sample of five permit reco rds were pulled from the database to show what the records look like after the zone cl assification was done. These permit records are provided in Table 4-1. Figure 4-2. Regional partitioning of Florid a for classification of travel for permitted vehicles greater than 160,000 lbs
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41 Table 4-1. Examples of processed permit vehicle records WEIGHT PERMIT NUMBER PERMIT DATE COMPANY ROUTE PERMIT TYPE REGION 160000 53437 5-Feb-02 COMPANY A US-27, I-4, US-17, US-92 T 1 2 3 4 5 160000 87912 19-Jun-02 COMPANY B I-95 T 2 4 5 160000 67493 26-Mar-02 COMPANY C SR-823 T 5 180500 53555 5-Feb-02 COMPANY D I-75, I-10, US221, US-90 T 1 2 3 5 197000 60278 28-Feb-02 COMPANY E SR-37, SR-60, I-4 T 3 4 Difficulties with the P ermit Vehicle Datasets Overall, the issues and complications w ith the data within the permit vehicle listings were minimal. However, the detail within the permit vehicle datasets was fairly limited, and therefore the detail of what could be extracted was limited. The most significant example was a lack of specific time and location of travel for any given vehicle. Unknown Routes Some of the routes that were scanned into the database di d not appear in the list of roads in either the FGDL shape file or the FDOT website. To ensu re that no roads were left out, a third source, the Florida Traffic Information (F TI) 2002 CD [21] was used. Even after including this third source, there remained roads listed in the permit records that were still not accounted for. Every road that did not appear in any of the three sources was compared to the re sulting hard copy entry to ensu re there was no error in the route entry due to the scanning process. On e possible error source wa s a data input error in the hard copy of permit records supplied to the project by the FDOT.
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42 A list of the roads that did not show up in any of the three different sources were sorted by year and shown in Table 4-2. In spection was done to see whether an incorrect prefix explained the error. For example, since SR-27 could not be found, US-27 was checked. However, if US-27 had not existed or fit into the travel pattern of the vehicle given its other listed routes, the number rather than the prefix may have been incorrectly entered. It was not anticipated that the presen ce of these unaccounted for routes would substantially alter the results of the analysis of the permit vehicle datasets. Routes that could not be accounted for would simply be ig nored when assigning the region(s) to that permit record. This represented a small fraction of the total records available. Table 4-2. Routes not account ed for in the permit records 2002 2003 2004 SR-27 SR-648 SR-28 SR-484 SR-1 SR-532 SR-36 SR-672 SR-32 SR-532 SR-33A SR-540A SR-58 SR-675 SR-58 SR-588 SR-42 SR-587 SR-98 SR-689 SR-67 SR-672 SR-99 SR-640 SR-99 SR-702 SR-86 SR-782 SR-110 SR-672 SR-131 SR-788 SR-135 SR-828 SR-210 SR-709 SR-169 SR-812 SR-182 SR-846 SR-283 SR-778 SR-197 SR-828 SR-204 SR-864 SR-288 SR-854 SR-198 SR-846 SR-236 SR-896 SR-395 SR-866 SR-210 SR-896 SR-269 US-42 SR-455 US-21 SR-221 SR-957 SR-306 US-50 SR-466 US-24 SR-236 US-33 SR-460 US-94 SR-470 US-47 SR-280 US-39 SR-462 US-482 SR-475A US-701 SR-284 US-39 SR-466 US-92-BUS SR-512 SR-286 US-44 SR-466A I-575 SR-319 US-111 SR-470 I-594 SR-325 US-175 SR-328 US-275 SR-379 US-279 SR-395 I-45 SR-448 I-85 SR-485 I-294 SR-532 I-785 SR-587 I-810
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43 Routes through Non-Contiguous Regions When the permit vehicle records were a ssigned to regions, it was assumed that when a vehicle travels through multiple regions the regions would be adjacent to each other. When examining the permit records it was found that in some circumstances a vehicle would travel through tw o regions that were not cont iguous. An example of this was a truck permitted to use SR-80 and SR104. SR-80 runs through Lee, Hendry, and Palm Beach counties in south Florida (region 5). SR-104 is located outside Jacksonville in Duval County (region 2). The permit r ecords were double checked to guarantee there was not an error in the scanning process. Possi ble explanations for this could be that one or more routes were left off the FDOT permit re cords, or that one of the routes listed in the description are incorrect. Determination of Multiple Vehicles on a Bridge The major point of interest for this pr oject was modeling the probability of the occurrence of more than one heavy vehicle on a bridge at the same time. The permit data did not provide this data direc tly. The specific time or date of travel was not given, nor was the specific path from origin to destin ation provided. Without this information a concurrency evaluation could not be done for the vehicles over 160,000 lbs. Blanket and Trip Permit Implications Another significant consideration was contained within the legal travel conditions associated with each of the two permit types. In addition to the lack of specification of date and time of travel, blanket permits may be re-used over a one year period as often as needed. Thus, a single permit may represen t hundreds of individua l occurrences of a vehicle of that permitted weight traveling anyw here within its identified regions. Trip permits represent a single occurrence any time w ithin a five-day period within its regions.
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44 Accounting for the multiple trips per permit, for blanket-type permits, could be accomplished by simply weighting the number of individual blanket permits by a factor that represents an average number of trips pe r permit. However, such a factor was not easily determined, and would be better repres ented by a discrete ra ndom variable. The characterization of this random variable could be the topic of a subsequent study, but was beyond the scope of this study. The probabilistic modeling presented in th e next section did not account for this issue, and simply treats each permit entry as an individual occurrence of a weight within a region or regions. It was known that this approach would produce skewed results in the modeled probability density functions. Mo st likely this would manifest as an underestimation of the relative probability of weights closer to the low end of 160,000 lbs compared to the high end of 1,000,000 lbs. This was because the blanket permits were clustered between the 160,000 and 200,000 lb end of the weight range. Heavier vehicles were required to have trip permits (single occurrence only) rather than blanket (multi-trip potential). Within the context of the exponential dist ribution that was applied in the next section, this skewing of the data caus ed by counting blanket permits as a single occurrence will produce values that are too low. Reca ll from Chapter 3 that a larger value indicates a higher relative probability at the lower range of possible values for weight (the random variable). Thus, if lowe r weight vehicles were multi-counted due to blanket permit travel, a lower value would be expected corresponding to a steeper distribution that attenuates more quickly as it approaches higher weights.
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45 Probabilistic Modeling of the Permit Vehicle Data Rather than providing a mode l at individual WIM stations, the format of the permit vehicle data required that models represent trav el within the five re gions in Figure 4-2. This would make it more difficult to extrapolat e the models to indivi dual bridges, but the route restriction data helped to narrow down the possibilities. The weights from all the permit vehicle data were input into Mathcad for analysis. There were 8,968 permit vehicle records. Of the 8,968 records, nineteen were over 1,000,000 lbs. The highest weight that was found in the printouts was 8,300,000 lbs. They represent special cases where travel was closely monitored to guarantee precise route and speed restriction adherence. A ny bridges en route for these cases were specifically analyzed for the presence of th is vehicle, and no other vehicle was permitted on the bridge at the same time. Therefore, they do not represent a random occurrence of a heavy vehicle, and were left out of the analysis. A histogram was generated in the same ma nner as was used for the WIM data in Chapter 3. Figure 4-3 shows the histogram of all permit data (between the weights of 160,000 lbs and 1,000,000 lbs). The x -axis represents the ve hicle weight and the y -axis represents the number of trucks within each we ight category. The histogram is not nearly as smooth as the histograms generated for the WIM data. The reasons for this were that there was not as much data for vehicles ove r 160,000 lbs and the fact that the data were bunched into weight groups and do not represen t the exact weight of the vehicle. This was more evident as the weight got higher. Figure 4-4 shows the resultant exponential PDF fit using maximum likelihood on the normalized histogram.
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46 Figure 4-3. Histogram of all permit vehi cle data excluding weight over 1,000,000 lbs Figure 4-4. The exponential PDF model on the normalized extreme value histogram Regional Probabilistic Modeling of the Permit Vehicle Data When these records were divided into the regions of travel (F igure 4-2) the number of records became limited. Region 5 had the most permit vehicle records for one region with 236. The other four regions all had le ss than 80 vehicles that only passed through their region. With such a small number of vehicles it was hard to generate a histogram
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47 that has any statistical signifi cance. However, the benefit of having the five regions was the ability to look at truck tr avel throughout different parts of the state that encompass multiple regions. Using the regional partitioning of the stat e, an exponential PDF was generated for different parts of Florida. The four areas were the east coast of Florid a (regions 2, 4, and 5), the Florida panhandle (regions 1 and 2), cen tral Florida (regions 3 and 4), and south Florida (region 5). Each area was analyzed for vehicles between the weights of 160,000 lbs and 1,000,000 lbs. Figure 4-5 shows the exponential PDF models using the maximum likelihood function for the permit vehicl e data from different areas of Florida. Figure 4-5. Exponential PDF models on the normalized extreme histogram. A) East coast of Florida. B) Floridas panhan dle. C) Central Florida. D) South Florida
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48 The parameter was different for each area. The east coast of Florida had a parameter of 23.278, the Florida panhandle had a parameter of 25.373, central Florida had a parameter of 27.255, and south Florida had a parameter of 10.27. If the numbers of occurrences of blanket permit wei ghts were multi-counted as suggested in the previous section, these values would increase. Thus, the distributions in Figure 4-5 would become steeper, with a higher relative probability of the lowe r range of weights. Conclusions This information was presented to the FDOT project manager. After discussion of the limits of the permit data precision, it was concluded that only the WIM data would be used for subsequent analysis. Even with th e ability to separate the permit data into regions, the inability of the permit data to give specific times and locations of truck travel did not allow for an exact analysis of multiple vehicles on a bridge. The gap of information between the WIM data and the permit data prevented analysis of both at this time. Further modeling and analysis of the pe rmit vehicle data is left as a subject for a possible future project.
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49 CHAPTER 5 ANALYSIS OF WEIGH-IN-MOTION HEADWAY DATA: CONCURRENT VEHICLE MODELING The previous chapter presented the da tasets provided by the FDOT. Some preliminary statistical analyses and problems we re identified within the datasets. This chapter discusses the methods developed to eval uate concurrent vehicl es on a bridge at the same time. This final course of analysis was determined after consultation with the FDOT project manager. The fundamental approach was to model the measured headway between vehicles in order to evaluate the probability of conc urrent vehicles appearing at a given WIM station. Several WIM stations had more than one bridge within close proximity. Thus, the evaluation of multiple heavy vehicles at a WIM station could be extrapolated to the nearby bridges. An examination of all the WIM sites was conducted to find a small sample of sites that had the combination of a high percentage of tr ucks over 80,000 lbs, a high number of bridges close to the site, and a high volume of truck traffic. These WIM sites were then used for the remainder of the analyses. Headway Analysis Headway is defined by the Highway Capacity Manual as the time, in seconds, between two successive vehicles as they pass a point on the roadway, measured from the same common feature of both vehicles (for ex ample, the front axle or the front bumper) [20]. A Visual Basic program was created to load each WIM file and obtain the headway between pairs of vehicles. The program created a new file (per station, per day) that
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50 contained the list of the headways for all the ve hicles for each day of data. A master file with a list of all files produced was also crea ted. A sample of the headways at each site was taken to get an initial view of the distribution. This sample excluded all files that had any of the problems identified in Chapte r 3. Only the headway values that were between zero and thirty minutes were examined This eliminated any other irregularities in the WIM files. These processed headway files were then loaded into Mathcad for analysis. After anal yzing the headway data it was f ound that the distribution of the headway data followed an exponential curve. The histograms of headway data differed from site to site, but always followed an e xponential curve. A summary of the critical statistics for the headway data from all WIM sites is presented in Table 5-1. The total number of vehicles sampled were the vehicles that were within the zero to thirty minute headway range. The information presented in Table 5-1 represents a one or two year sample of data from each WIM station depe nding on the number of years of data that were collected. Examples of the headway histograms are s hown in Figure 5-1. Two histograms are displayed in Figure 5-1 showing WIM stat ions 9908 and 9940. WIM station 9908 is located on US-319 in Tallahassee and WIM st ation 9940 is located on SR-287 in Quincy. The two WIM stations are located in Le on and Gadsden counties, respectively.
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51 Table 5-1. Headway data statistics Headway Statistics (in seconds) Station Number of Vehicles Sampled Mean Standard Deviation Median Mode 9901 1,466,370 27.8335.19** 9904 939,314 20.5230.7612* 9905 874,402 17.4327.859* 9906 537,499 37.53102.33132 9907 106,634 90.03150.17422 9908 190,069 131.69222.93603 9909 54,652 247.57311.561322 9913 594,678 53.7277.12302 9914 1,393,713 14.4623.22** 9916 88,813 154.09226.37783 9917 37,587 252.80312.241413 9918 297,304 38.0963.20192 9919 902,377 16.0521.579* 9920 227,855 16.3222.3691 9921 77,563 247.86305.531390 9922 84,511 34.7151.83182 9924 127,763 103.25181.26442 9925 46,747 203.71275.881082 9926 1,114,120 20.0234.3610* 9927 105,252 102.84161.06503 9928 511,397 24.8931.79151 9929 8,613 364.69362.132492 9930 31,330 310.81342.851933 9931 547,775 23.8530.88142 9932 751,230 48.2663.4329* 9934 456,940 39.0193.00152 9935 672,615 38.8564.1618* 9936 1,445,407 21.0729.08** 9937 94,690 204.42280.751063 9938 105,565 192.17170.61992 9939 35,968 425.45418.162853 9940 132,696 226.23295.321203 9942 66,204 366.83379.852382 9943 105,655 270.49325.501542 9944 47,783 349.01365.552253 9946 78,319 413.74397.562843 *The values could not be calculated by Ma thcad because the dataset was too large.
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52 Figure 5-1. Headway frequency histograms. A) Represents s ite 9908. B) Represents site 9940 Identification of WIM Sites to Conduct Headway Analysis The ultimate goal of this project was to determine the probability of the existence of concurrent permit vehicles on a bridge. Since the headway data were coming from the WIM stations and not bridges, it was difficu lt to predict when exactly these vehicles would be on nearby bridges. A determination of which sites were in close proximity to bridges was conducted. The assumption was that the occurrence of concurrent permit
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53 vehicle at a given WIM site was as likely to have occurred at a nearby bridge. Thus, the concurrence study at a give n WIM station was extrapol ated to nearby bridges. Two shape files were downloaded from the FDOT website [18] to provide input to the GIS platform used in this study. The first one contained the location of the WIM sensors along Floridas roadways. The second contained bridge locations in the state of Florida. Using ArcMap, the layers were loaded along with the major roads and the county boundaries shape files from the Florid a Geographic Data Library (FGDL) [17]. A 15-mile radius was created around each of the WIM sites. Bridges within this 15-mile radius were pulled from the original shape file and assigned to the WIM station they pertained to. Four new shape files were created, each containing only the bridges that related to their respective WIM stations. Once the bridges were assigned to each WIM station, only the bridges that were located along the WIM route were extracted. For example, bridges that were on other majo r roads within the 15-mile radius were eliminated. Only a sample of the WIM sites had th is analysis conducted for them. From previous analyses (found in Appendix B), onl y the sites with a hi gh number of passing trucks and a high percentage of trucks over 85,000 lbs were considered. The WIM shape file did not contain the loca tions of WIM station 9914 or 9916. Since the WIM stations were not in the WIM shape file, they were also omitted from the analysis. Table 5-2 shows the results from the ArcMap analysis of the bridges within th e 15-mile radius of the WIM sites. The grey entries were the sites that were not evaluated in ArcMap; the four highlighted entries were the sites fo r which the detailed headway analysis was conducted. The four sites highlighted in Tabl e 5-2 were chosen because they contained a
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54 high volume of trucks passing over the sensor numerous trucks over 85,000 lbs, and several bridges within the 15-m ile radius. Additionally, this selection of sites provided some variance in regional location. Figure 52 shows the locations of the four selected WIM sites, as well as the regional partitioning of the state. Table 5-2. Results from the ArcMap analysis of bridges Site Bridges Region Trucks Years of Data % of Trucks >85,000 9901 16 1 3,590,58340.36 9904 30 2 943,09624.44 9905 2 1,064,20222.08 9906 26 4 540,93124.71 9907 17 1 468,16033.22 9908 8 1 869,12461.08 9909 4 2 208,21036.76 9913 29 4 1,121,712 3 4.31 9914 2 1,525,16424.08 9916 1 391,96735.04 9917 3 83,96021.17 9918 3 5 1,533,122310.07 9919 4 1,692,29730.96 9920 3 227,89913.89 9921 10 5 361,04360.35 9922 3 84,54511.80 9923 2 000 9924 15 1 194,58310.74 9925 7 4 120,24823.93 9926 78 3 1,153,455 2 4.32 9927 3 370,86120.28 9928 9 1 846,73221.97 9929 4 15,19520.17 9930 5 118,51320.74 9931 19 3 1,390,33934.72 9932 17 4 901,222 3 6.11 9934 5 698,56234.82 9935 4 5 2,872,41866.01 9936 16 2 4,352,192 6 3.22 9937 3 1 357,37453.65 9938 9 1 274,55034.33 9939 9 1 136,36363.14 9940 7 1 453,54162.02 9942 1 187,08164.26 9943 4 1 323,45669.60 9944 2 1 149,94669.09 9946 0 1 245,33567.40
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55 Figure 5-2. Locations of the four WIM sites selected for headway analysis Analysis of the Four Chosen WIM Sites The four chosen WIM stations were 9913, 9926, 9932, and 9936 (indicated in Figure 5-2). These WIM stati ons were looked at closely in ArcMap to include only the bridges along the route and to exclude any ove rpasses or exit ramps. After looking at the
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56 bridges a second time, the number of bridges was reduced to 11 bridges at WIM station 9913, 56 bridges at WIM station 9926, 15 brid ges at WIM station 9932, and 10 bridges at WIM station 9936. Figure 5-3 shows a close up view of each of the four WIM stations, the 15-mile radius, the WIM sensor, the rout e the WIM sensors are located on, the major roads in the area, and the br idges along the WIM route. Figure 5-3. Detailed view of the four WIM sites selected for headway analysis
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57 Bridge Length Determination Once the sites with multiple bridges were selected and documented, the length of the bridges around each of the four sites was de termined. Each of the bridges contained in the bridges shape file had attributes associ ated with them. One of those attributes was length. The length was pulled from the attrib utes table for each of the bridges. From these, the average bridge length was calcula ted for all the bridges within the 15-mile radius and used for each individual sites headway analysis. Speed Determination To ascertain an average speed that the trucks were traveling over the WIM sensor, a Visual Basic program was created to pull out the minimum, maximum, and average vehicle speeds for each WIM file. Once the av erage speed for vehicles in each WIM file was determined, yearly and overall speed averag es were calculated. Table 5-3 shows the average vehicle speeds and the average bridge lengths for the four sites. Total trucks refers to all trucks registered by the WI M station, not just those over 85,000 lbs. Table 5-3. Average spee ds and bridge lengths Site Year Total Trucks Avg. Speed Site Avg. Speed (mph) Avg. Bridge Length (ft) 2001 442627 67.38 2002 326560 66.61 9913 2003 266681 67.39 67.14 314.08 2002 532940 63.25 9926 2003 581476 63.21 63.23 317.84 2001 383310 66.31 2002 368393 68.08 9932 2003 6942 66.66 67.17 186.53 1998 413997 67.20 1999 583801 67.79 2000 783286 67.73 2001 536465 67.65 2002 1031798 68.50 9936 2003 433397 69.52 68.09 229.58
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58 Headway Determination at the Four WIM Sites Another Visual Basic program was written to give a more detailed evaluation of the headway of vehicles passing the four select ed WIM sites. The program extracted any vehicles that were within a user-specified head way time interval for each of the four sites. Using the average speed and average bridge length for each site (see Table 5-3), a specific headway time interval was calculate d for each site that would capture when multiple vehicles would be around each WIM st ation. This represents their potential concurrent occurrence on a bridge within the 15-mile radius area. The appropriate headway interval calculated for the f our WIM stations were as follows WIM Station 9913: 3 seconds WIM Station 9926: 3 seconds WIM Station 9932: 2 seconds WIM Station 9936: 2 seconds These headway intervals were rounded to the nearest second because the precision of the timestamp from the WIM files was integer seconds. The headway interval represents a period of time that captures any number of ve hicles that cross the WIM station, not just the time between two consecutive vehicles. The headways mentioned in the previous paragraph were calculated for vehicles that were traveling in the same direction. However, for vehicles traveling in opposing directions, the headway time was divided in ha lf. Since the vehicles were traveling in opposite directions, their speeds were additive A vehicle traveli ng 60 mph one way and another traveling 60 mph the other way equale d a total of 120 mph. This was twice the speed for the same distance (i.e. bridge lengt h), therefore, it equaled half the time. The Visual Basic program grouped vehicles into diffe rent headway groups based on the aforementioned headway input for the di fferent sites. The time stamp, lane of
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59 travel, and vehicle classification were also reco rded. The lane of travel was useful in the determination of what direction the vehicles were traveling when they appeared on the bridge, that is, whether the vehicles were traveling in the same direction or opposing directions. The program created a text file for each individual day of data. A summary file was also produced listing the total number of vehicles, the groups of two vehicles on the bridge, the groups of three vehicles on the bridge, the groups of four vehicles on the bridge, the groups of five vehicles on the br idge, the number of groups containing at least two vehicles 80,000 lbs or grea ter, and whether the 80,000 lb vehicles were traveling in the same direction or opposing directions. In addition to the output described in th e previous paragraph, the Visual Basic program created another file for each individu al day of data containing the summation of the weights of vehicles in each headway gr oup for that day. Along with the weight summation, the program also created a table of contents file th at contained a list of all the filenames that had the summati on of headway weight extracte d from them. These files were then input into Mathcad for analysis. In total, the Visual Basic program created four new files. For each individual day of data the program created two files, one containing the headway groups, and one containing the summation of weight from each headway group. For example, when the file 99130202.011_VTR was processed, the files 99130202.011_VTR.txt and 99130202.011_VTRWT.txt were created. For each year of data that were processed, a stat.txt and a toc.txt file were created. The stat.txt file contains the summary information from all the *_VTR.txt files a nd the toc.txt file was the file that was read into Mathcad containing all the names of the *_VTRWT.txt files.
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60 Results The occurrence of concurrent vehicles each 80,000 lbs or greater was a rare event when compared to the amount of trucks trav eling Floridas roads. Site 9926 had the highest percentage of concurrent 80,000+ lb ve hicles on a bridge for a single year with 0.26%. This was relative to the total trucks passing over the WIM station. Even though the rate was relatively small, the frequency of this event occurring was not negligible. For example, in 2002 at site 9936 there were 789 instances where at least two 80,000 lb vehicles were within two seconds of each othe r at the location of the WIM sensor. That translates to an average of just over two times every day for the entire year. In the case of site 9926, the phenomenon of two 80,000 lb vehi cles occurred four times a day for the year of 2002. Table 5-4 shows the results from the head way analysis. The table shows the total trucks passing the WIM site, the groups of two, three, four, and five vehicles on a bridge (i.e., within the calculated headway for that WIM site as defined earlier), and the percent of the total vehicles in each of those groups relative to the total number of trucks passing the given WIM station that year. The last four columns show the frequency of two concurrent vehicles over 80,000 lbs, the percen t of those vehicles out of the total truck population passing the WIM station, the freque ncy of three concurrent vehicles over 80,000 lbs, and the percent of those vehicles out of the total truck population passing the WIM station, respectively.
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61 Table 5-4. Summary of headway results Groups of 2 Groups of 3 Groups of 4 Groups of 5 2 Vehicles > 80,000 lbs 3 Vehicles > 80,000 lbs Site Year Total Trucks Sum PercentSum PercentSum Percent Sum PercentSum PercentSum Percent 2001 442627 25335 5.72%7580.17%150.003% 1120.03% 2002 326560 17562 5.38%4750.15%30.001% 1470.05% 9913 2003 266681 14429 5.41%3270.12%30.001% 3090.12%10.0004% 2002 532940 63200 11.86%37530.70%1370.026%6 0.001%13950.26%50.0009% 9926 2003 581476 85833 14.76%63111.09%3050.052%10 0.002%7430.13%60.0010% 2001 383310 6931 1.81%560.01% 610.02% 2002 368393 7527 2.04%620.02% 870.02% 9932 2003 6942 133 1.92% 1998 413997 19283 4.66%2440.06% 440.01% 1999 583801 30197 5.17%4380.08% 500.01% 2000 783286 41364 5.28%6140.08% 950.01%10.0001% 2001 536465 29065 5.42%4710.09% 2290.04% 2002 1031798 53546 5.19%9340.09%10.0001% 7890.08% 9936 2003 433397 13826 3.19%2240.05%30.001% 3340.08%20.0005%
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62 Of the vehicles over 80,000 lbs that arrive d within the given headway interval for each of the four WIM stations, the majority (at least 70%) of these vehicles were traveling in the same direction. Table 55 shows the results for the case of only two concurrent vehicles near the WIM station. The fifteen instances when there were three permit vehicles occurring near the WIM sta tion, twelve times (80%) two of the three vehicles were traveling in the same direction. Three times (20%) all three vehicles were traveling in the same direction. Table 5-5. Summary of the travel direction of 80,000+ lb vehicles Traveling in the Same Direction Traveling in Opposing Directions Site 2 Vehicles > 80,000 lbs VehiclesPercent VehiclesPercent 9913 568 486 85.56% 82 14.44% 9926 2138 1516 70.91% 622 29.09% 9932 148 125 84.46% 23 15.54% 9936 1541 1382 89.68% 159 10.32% Table 5-6 presents a comparison of the num ber of vehicles app earing concurrently at the WIM station that were 80,000 lbs or great er traveling in the sa me direction to the total number of vehicles 80,000 lbs or greater passing the WIM station. Table 5-5 and 56 together show that, although concurrent perm it vehicles travel the same direction 70% of the time, this concurrence occurs as onl y a small percentage of total permit vehicle traffic. This suggests that permit vehicles traveling in convoys close enough to allow concurrent bridge loading was the excep tion rather than the trend or rule. Table 5-6. Summary of same direction concurrent permit vehicles compared to all 80,000+ lb vehicles Permit Vehicles within Headway Interval Traveling in the Same Direction Site Total Permit Vehicles Frequency Percentage 9913 45,990 487 1.06% 9926 46,754 1518 3.25% 9932 45,083 125 0.28% 9936 127,818 1382 1.08%
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63 Generating Concurrent Vehicle Histograms from Headway WIM Data Using Mathcad to analyze the total concurrent weight information that was provided by the Visual Basic program, an id ea of the weight dist ribution over the given headway interval for each WIM station could be determined. In the same manner that the data were input to generate histograms in Chap ter 3, an array of the total weight data over the headway interval was read from a desired fi le. All the data from each year were input into Mathcad for each WIM station. The next four figures show the resultant histogram of the summation of the total weight pa ssing the WIM station within the assigned headway interval from the Mathcad analysis of the four WIM stations. Figure 5-4 shows the histogram for WIM stati on 9913, Figure 5-5 shows the histogram for WIM station 9926, Figure 5-6 shows the histogram for WI M station 9932, and Fi gure 5-7 shows the histogram for WIM station 9936. Figure 5-4. Histogram of total weight pa ssing WIM station 9913 in a 3-second interval
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64 Figure 5-5. Histogram of total weight pa ssing WIM station 9926 in a 3-second interval Figure 5-6. Histogram of total weight pa ssing WIM station 9932 in a 2-second interval
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65 Figure 5-7. Histogram of total weight pa ssing WIM station 9936 in a 2-second interval Modeling the Extreme Value Histogram Concurrent Permit Vehicles The minimum total weight that two conc urrent permit vehicles should weigh is 160,000 lbs (assuming they are loadedi.e., not empty on a return trip). Thus the modeling of an extreme value histogram evaluated weights a bove this threshold. All weights above this threshold were not necessarily combinations of permit vehicles; but combinations of any trucks that were captured within the headway interval. The lower limit of 160,000 lbs represents the minimum co mbined weight of two permit vehicles. This study assumes that the weight of four 40,000 lb vehicles was as significant as two 80,000 lb vehicles. The upper limit used differe d from site to site. The maximum weight of a group of vehicles within the assi gned headway at WIM station 9913 was 290,190 lbs, at WIM station 9926 it was 319,880, at WIM station 9932 it was 250,930, and at WIM station 9936 it was 276,940. It was desired to create an analytical parametric function that represented the information provided in the normalized extreme va lue histograms of the data of interest.
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66 A convenient functional form w ould be flexible enough to represent WIM data from the four different WIM stations. Thus a parame tric probability density function (PDF) was sought that fits the WIM data well. The focu s was restricted to the extreme values of total vehicle weights heavier than 160,000 lbs. The exponential PDF model was used to f it the extreme value histograms. The same process used to fit the extreme value histograms in Chapter 3 was used for this analysis, using a different range of W Equations (1) through (4) (see Chapter 3) apply to the extreme value modeling conducted in this chapter. Substituti ng the exponential PDF equation (xe x f** ) ( ) into the log maximum likelihood function, defined as n i ix f L l1; log ) ( log ) (, enables an optimization routine to be run in Mathcad to calculate the values. Since this chapter had a different range of weight data, Equation (5), found in Chapter 3, would change. Before calculating the data were linearly mapped from the 160,000 to 290,190 range (WIM station 9913) into a range of 0 to 1. The upper limit of the range changed for each of the four WI M stations depending on the maximum weight. This value was used to create the model and substituted back into the exponential PDF (Equation 1). In the case of WIM station 9913 it would be xe x f 638 6638 6 ) (. This analytical function (exponential PDF) now represents the data over the range 0 to 1. In order to represent the data over the interval of 160,000 to 290,190 lbs, the analytical function needed to be adjusted to invert the data mapping. Since the interval had increased from 1 to 130,190, the exponential PD F needed to be divided by 130,190. In
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67 addition, the value of x would become 000 160 190 290 000 160 W The new exponential PDF equation in terms of the data in its original values W is 000 160 190 290 000 160190 130 1 ) (We W f (6) The parameter for WIM station 9913 that provided the maximum value was 6.638. The exponential PDF for WIM st ation 9913 now takes the form of xe x f* 638 6638 6 ) ( The parameters for the other thr ee WIM stations were 8.933, 5.850, and 8.281 for WIM stations 9926, 9932, and 9936, respectively. Figures 5-8, 5-9, 5-10, and 5-11 s how the exponential PDF model and the normalized histogram of the summation of th e total weight equaling at least 160,000 lbs passing the WIM station in the headway interval from the Mathcad analysis of WIM stations 9913, 9926, 9932, and 9936, respectively. Figure 5-8. Exponential PDF model and normalized histogram (WIM station 9913)
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68 Figure 5-9. Exponential PDF model and normalized histogram (WIM station 9926) Figure 5-10. Exponential PDF model and normalized histogram (WIM station 9932)
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69 Figure 5-11. Exponential PDF model and normalized histogram (WIM station 9936) Interpretation of the Extreme Value Histogram Figures 5-8 through 5-11 represent cond itional probabilities. They provide probabilities of the total comb ined weight of vehicles given that the total combined weight of the vehicles at the WIM sensor wa s at least 160,000 lbs, which was equivalent to two permit vehicles. The conditi onal probability is represented as p w P, where w is any weight combinati on of vehicles and p is the event that a combination of vehicles is 160,000 lbs or greater. If the conditional pr obability is multiplied by the probability that a weight of at least 160,000 lbs shows up at the WIM sensor, the probability of that particular load combination can be found. This is represented as p P p w P w P (7) Referring to Table 5-4, two permit vehicles of at least 80,000 lbs (giving a total weight of at least 160,000 lbs) occur at any of the evaluated WIM stations at least once in the time span analyzed. This means that the probability of at least one weight
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70 combination of at least 160,000 lbs per WI M station in a given year was reasonably estimated at 100%. This simp lifies Equation (7) above to w P p w P (8) Thus Figures 5-8 through 5-11 can be view ed directly as the probability of the likelihood of total concurrent weight W within several years (n umber of years varies among stations, see Table 5-4). The histograms generated at the four WIM stations could not be used directly to represent the probability of total weight of concurrent permit vehicles at other locations around the state. The lambda values were cu stomized to the individual WIM stations using specific information of vehicle travel speed at the WIM station and average bridge length in the area. The WIM station was then used as a hypothetical bridge that would experience concurrent vehicle occurrence and re asonably be extrapolated to other bridges in the vicinity of and along the same route as the WIM station. This same method of analysis could be conducted at any of the other 33 WIM stations. An analysis of the surrounding bri dges within a specified radius from the WIM station and an analysis of the speed of th e vehicles passing the WIM station would first be conducted to accurately repr esent the conditions at each of the WIM stations. Once that information was evaluated, an extrem e value histogram and an exponential PDF fit could be determined at any ot her WIM station around the state. Applications of Extreme Value Concurrent Weight Models Concurrent is defined as the occurrence of more than one vehicle within an interval that is within the aver age length of nearby bridges on same route. Here are three
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71 examples of how the extreme value concurrent weight models (Figures 5-8 through 5-11) can be used. Given that multiple vehicles occurred c oncurrently at WIM station 9913, what is the probability that the total weight is be tween 200,000 and 250,000 lbs? The solution would be to integrate the normalized histogr am or fitted exponential PDF model between 200,000 and 250,000 lbs. The area is th e probability in decimal form. Given that multiple vehicles occurred c oncurrently at WIM station 9926, what is the probability that the total weight will exceed 280,000 lbs? The solution would be to integrate the normalized histogram or fitte d exponential PDF model from 280,000 lbs to the upper limit (319,880 lbs). Given that multiple vehicles occurred c oncurrently at WIM station 9936, what is the probability that the total weight is at most 230,000 lbs? The solution would be to integrate the normalized histogram or fitted exponential PDF model fr om the lower limit of 160,000 lbs to 230,000 lbs. These data are bounded between a lowe r limit of 160,000 lbs and an upper limit that ranges from 250,930 to 319,880 lbs depending on what site was being analyzed. The PDF model will not provide proba bilities of concurrent vehicles over the upper limit or under 160,000 lbs. That is, direct extrapol ation of the PDF mode l beyond its defined range is not valid. However, more data prov ided over a larger range of weights could be used to develop a similar model th at covers the ra nge of interest.
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72 CHAPTER 6 SUMMARY AND RECOMMENDATIONS This thesis documents a study on overwei ght vehicle travel specifically the characterization of concurrent permit vehicles on bridges at four di fferent WIM stations located in the state of Florida. The follo wing sections summarize contributions to and conclusions about, the research found in this document a nd present recommendations for future research. Summary Chapter 3 discussed the prelim inary analysis of the WIM data. An initial extreme value model was created along with the identi fication of numerous ir regularities in the data. Out of the 25,300 files, approximately 5% of the data files were not used due to these irregularities. The analysis of the da ta found that no WIM data file contained a weight greater than 160,000 lbs. This was due to a filter that was set to discard any data above that threshold. This filter was beyond th e control of the investigators, and filtered data was deemed irretrievable. A second source of data was needed to ev aluate the vehicles over 160,000 lbs. Chapter 4 discussed the use and limitations of the permit data. The permit data were scanned into electronic format and placed into on e of five partitioned regions of Florida. The permit data were then examined on a region al basis. It was c oncluded that only the WIM data would be used for subsequent analys is. Even with the ab ility to categorize the travel patterns of heavy vehicles from the permit data into regions, the inability of the
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73 permit data to give specific times and lo cations of truck trav el does not allow for quantitative analysis of multiple vehicles on a bridge. Chapter 5 discussed the development of a probabilistic model of concurrent vehicle weights at a WIM station using measured h eadway intervals determined by average speed and average length of bridges lo cal to the given WIM station. The results represent the likelihood of various levels of combined total weight from concurrent permit vehicles at the WIM station. A more specific (accura te) probability model would require the installation of WIM sensors on or next to bridges of interest. In the evaluation of the headway data, th is study observed an appreciable likelihood of permit vehicles (vehicles over 80,000 lbs) appearing concu rrently on each of the four analyzed WIM stations (Table 5-4). Thus, th e resultant probability models of combined weight of concurrent vehicles directly re present the likelihood of an extreme loading condition. Permit vehicles were traveling in the same direction in 70% of the observed concurrent cases. Although same direction concurrent permit vehicles account for a total of about 1% of the total number of observed permit vehicles among the four WIM stations, this still represents hundreds of concurrent vehicle loading events per year per analyzed WIM station. Thus, this was more than a negligible occurrence. The exponential PDFs generated from the four WIM stations (Figures 5-8 through 5-11) can be used to predict the probability of occurrence of the combined weight of concurrent vehicles around th e given WIM station. An assumption was made that this analysis data can be extrapolated to the nearby bridges on the same route as, and within 15 miles of, the WIM station. That is, it was reasonable to expect that the observed
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74 occurrences of concurrent permit vehicles co uld have as likely occurred at a nearby bridge, and thus Figures 58 through 5-11 can be applied directly to the bridges. The histograms generated at the four WI M stations cannot be used to give the probability of occurrence of concurrent pe rmit vehicles at other locations around the state. They can only be used to predict co ncurrent permit vehicle weights at or around the four WIM stations. Each of the four WIM stations used specific information of vehicle travel speed at the WIM station and av erage bridge length in the area. However, this same method of analysis could be conduc ted at any of the other 33 WIM stations. An analysis of the surroundi ng bridges within a specified radius from the WIM station and an analysis of the speed of the vehicl es passing the WIM station would first be needed to accurately represent the conditions at each of the WIM stations. Once that information is evaluated, an extreme value histogram and an exponential PDF fit could be determined at any other WIM station around the state. It needs to be reemphasized that the probability models of concurrent permit vehicle weight did not include weights from individual vehi cles that exceed 160,000 lbs. Although such vehicles were generally rare it was reasonable to assume that the probability models developed without these da ta were skewed in a non-conservative way toward a higher probability of lower concur rent weights. Additional data collection would be needed at WIM stations that retain 160,000+ lb vehicles to ascertain the impact of this unaccounted for data. Recommendations There is a need for the WIM data that is being processed to in corporate the weights of all vehicles that pass the sites. The in ability for the WIM sensors to record weight over 160,000 lbs severely limits the ability to perform a rea listic analysis of the most
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75 extreme weights. In addition, the difficulti es with the WIM data files, like combining multiple days of data into one file, need to be addressed and corrected. An overhaul of the WIM sensors and collection process is r ecommended to better reflect the increasingly likely occurrence of heavier vehicles. The project did not focus on i ndividual vehicles with spec ific axle configurations. The next step would be to look at individual vehicles with specific axle configurations that the FDOT has a special interest in. Weight by itself is only one factor, the axle configuration at any given weight can be anot her significant factor. A study that predicts the probability of these special interest ve hicles and the occurrence of concurrent combinations of special interest ve hicles on bridges is recommended. The project evaluated the permit vehicle records (veh icles over 160,000 lbs), but did not do an in-depth analysis of the data. One major obstacle was the inability to know how many trips a vehicle with a blanket permit makes within a year. Determining a system to weight blanket permits (how many trips per blanket) is recommended and would be the first step in the process to further analyze the permit vehicle records collected through 2004. However, future collection of such ve hicles at the WIM stations directly would be most beneficial.
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APPENDIX A FDOT CLASSIFICATION SCHEME F
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77
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78 APPENDIX B WIM DATA SUMMARY The content of this appendix summarizes th e preliminary analysis of the WIM data obtained from the FDOT. The data summari zed here contains data from every file acquired from the FDOT including files that contain multiple days of data. The subsequent pages present the name and loca tion of every site and are broken down in a yearly basis. Within each year are the numbe r of days of data, the total vehicles, the number of vehicles 85,000 lbs or greater, the number of ve hicles 90,000 lbs or greater, the number of vehicles 105,000 lbs or greate r, the number of vehicles 120,000 lbs or greater, the number of vehi cles 135,000 lbs or greater, a nd the number of vehicles 150,000 lbs or greater.
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79 9901: I-10, MonticelloYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 1998309824570447211342581003410 1999295783805161263519181347 20022681256199328716526532287913 2003179726009349012414281756021 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19983098245700.5420.1380.0310.0120.0040.0012 19992957838050.2060.0810.0240.0100.0040.0009 200226812561990.2620.1320.0520.0180.0060.0010 20031797260090.4810.1710.0590.0240.0080.00299908: US-319, TallahasseeYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 1998345182175258250849620 1999217128603160627332640 200018510991761720445700 200134819060571636874930 200231916971963229351600 2003184881053244119245410 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19983451821751.4170.2790.0270.0030.001 19992171286031.2490.2120.0250.0050.003 20001851099170.5610.1860.0410.006 20013481906050.3760.1930.0390.0050.002 20023191697190.3720.1730.0300.004 2003184881053.6821.3530.0510.0050.001
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80 9904: I-75, MicanopyYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200272234387144261004118341040 200316370870927461819633879265 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 2002722343876.1554.2840.7820.0040.002 20031637087093.8751.1560.0480.0110.0040.00079905: SR-9/I-95, JacksonvilleYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200214591446417635784654668175 20034314973844832042821630 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20021459144641.9280.8580.0600.0070.0020.0005 2003431497382.9941.3640.0550.0110.0029906: I-4, DeltonaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001245545530242631301813174230 2002532540126521840324400 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20012455455304.4482.3860.2410.0080.001 2002532540110.4417.2441.2760.016
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81 9907: US-231, YoungstownYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200120016385837062406363310 200220019469363694131673700 200312510960949773164583310 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20012001638582.2621.4680.2220.0020.001 20022001946933.2712.1220.3460.004 20031251096094.5412.8870.5320.0030.0019909: US-19, ChieflandYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001612020446725213000 20022461318181335483651107521 200321156188261723100 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200161202042.3111.2470.064 200224613181810.1316.3460.8400.0040.0020.0008 2003211561880.4650.1280.0050.0029913: Turnpike, St.Lucie Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200127048132211923869748592521964103 2002214364043128279552478925291040115 20031632763472359515745467021731152329 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20012704813222.4771.8071.0100.5240.2000.0214 20022143640433.5232.6241.3160.6950.2860.0316 20031632763478.5385.6981.6900.7860.4170.1191
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82 9914: SR-9A/I-295, Duval Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20012651419714577013050627856020 20022110545045552424201100 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200126514197144.0642.1490.1960.0040.0001 2002211054504.3202.2990.1910.0019916: US-29, PensacolaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200124117637676734858802500 200225412594360863795597300 200318589648598444521252521 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20012411763764.3502.7540.4550.003 20022541259434.8323.0130.4740.002 2003185896486.6754.9661.3970.0060.0020.00119917: US-41, Punta GordaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20022344438587645629300 200316739575108396510 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 2002234443851.9741.0270.0650.007 2003167395750.2730.0990.0150.0130.003
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83 9918: US-27, ClewistonYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001310657107687114461967175561 2002277573517647324478776892640 2003138302498209381408427602870 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200131065710710.4576.7901.0220.0080.0010.0002 200227757351711.2877.8091.3410.0050.001 20031383024986.9224.6560.9120.0090.0029919: I-95, MalabarYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20011729323458136398555498263 20021537543406917309930459112 2003256121197861163000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20011729323450.8730.4270.0590.0110.0030.0003 20021537543400.9170.4110.0400.0080.0010.0003 20032561221.32915.3422.9049920: I-75, Sumter Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20034422789988696959945168 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 2003442278993.8920.3050.0430.0200.0070.0035
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84 9921: SR-5, Martin Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19983417543322913113000 1999329735891578411000 200035387598169844000 20013565983044930053000 20022984115721014923000 20031362343645261100 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 1998341754330.3040.1740.017 1999329735890.2130.1140.015 2000353875980.1930.0960.005 2001356598300.7500.5010.089 2002298411570.5100.3620.056 2003136234360.1920.1110.0040.0049922: I-275, TampaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20033484545152139225810 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200334845451.7990.4640.0300.0090.0019923: I-95, JacksonvilleNo data was available from this site.9924: I-110, PensacolaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2002202194583144731215300 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20022021945830.7440.1600.0080.002
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85 9925: US-92, DelandYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200224867844249963519200 200316952404223161520110 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 2002248678443.6830.9360.0280.003 2003169524044.2571.1740.0380.0020.0029926: I-75, TampaYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2002158571238380341808741084207 200312658221711823249332186276 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20021585712386.6583.1660.0720.0150.0040.0012 20031265822172.0310.4280.0550.0150.0050.00109927: SR-546, LakelandYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2002320262155755179331530 20031381087062956314510 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20023202621550.2880.0680.0130.0060.001 20031381087060.2710.0580.0130.0050.001
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86 9928: I-10, Walton Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2002154590918394686323582298 20037525581412713221714455184 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20021545909180.6680.1460.0400.0140.0050.0014 2003752558144.9700.8670.0560.0210.0070.00169929: US-1, EdgewaterYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 200293118052040000 2003663390662000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200293118050.1690.034 20036633900.1770.1770.0599930: US-1, MiamiYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 20024258108272242739221 2003208374311508112000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 2002425810820.8900.5270.0480.0020.0020.0012 2003208374310.4010.2160.032
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87 9931: Turnpike, Sumter Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001180725162330991373484257130 2002251013231808650962720 20031565638543074213494612138406 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20011807251624.5641.8940.1160.0080.002 2002251013231.7840.6420.0950.0270.002 20031565638545.4522.3930.1090.0240.0070.00119932: Turnpike, Osceola Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001208409997285421949157441956833186 2002232484283261451732946801657723219 2003469423692577324103 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 20012084099976.9624.7541.4010.4770.2030.0454 20022324842835.3993.5780.9660.3420.1490.0452 2003469425.3153.7021.0520.3460.1440.04329934: Homestead Ext, Dade Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 2001163028923010212100 20027923801475914690765924017 20032014302592588116925297819210631 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 200116302890.7590.3370.0400.003 2002792380143.1891.9700.3210.0390.0170.0071 20032014302596.0153.9340.6920.0450.0250.0072
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88 9935: US-27, Palm Beach Co.YEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19981453649492217014014248139120 1999144350648559894087086742462 2000231588584215511115875134151 20012538403659662407734165104 20021505042323862520387110173213 200394223640246501478598832113 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19981453649496.0753.8400.6800.0110.003 199914435064815.96711.6562.4740.0070.0020.0006 20002315885843.6611.8960.1280.0060.0030.0002 20012538403651.1500.4850.0410.0080.0010.0005 20021505042327.6604.0430.2180.0140.0040.0006 20039422364011.0226.6110.4420.0140.0050.00139936: I-10/SR-8, Lake CityYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19981294242644102144021365201 19991556592774871197629388203 2000217972530112805345511111293 200115780609127243150531563142408 20022521051368641823689737872458821 2003144438662285091393610661384915 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19981294242640.9670.3390.0500.0150.0050.0002 19991556592770.7390.3000.0440.0130.0030.0005 20002179725301.1600.5500.0530.0110.0030.0003 20011578060913.3801.8670.1940.0180.0050.0010 200225210513686.1053.5090.3600.0230.0080.0020 20031444386626.4993.1770.2430.0310.0110.0034
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89 9937: SR-87, MiltonYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 1998190630372926149735200 1999250825093957184564620 20002241192534657223042100 2002123495697582189300 20031424300673419311200 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 1998190630374.6422.3750.0560.003 1999250825094.7962.2360.0780.0070.002 20002241192533.9051.8700.0350.001 2002123495691.5290.4400.0180.006 2003142430061.7070.4490.0260.0059938: SR-83/US-331, FreeportYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19983501136115753257182332 19993031264544733202883110 20007934485139076561000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19983501136115.0642.2630.0720.0030.0030.002 19993031264543.7431.6040.0660.0010.001 200079344854.0312.2180.177
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90 9939: SR-2, GracevilleYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19981919778151676100 19992552475759824310000 20003252729562131521000 200128825089103050836100 200233032941136165044000 20031551650351419511100 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 199819197781.5440.6850.0610.010 1999255247572.4150.9820.040 2000325272952.2751.1540.077 2001288250894.1052.0250.1430.004 2002330329414.1321.9730.134 2003155165033.1151.1820.0670.0069940: SR-267, QuincyYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 1998192738522896153854000 19992861016963087150540000 20009438085107548525210 2001357100330128742422000 20023319827556817718200 200315941303252749541 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 1998192738523.9212.0830.073 19992861016963.0361.4800.039 200094380852.8231.2730.0660.0050.003 20013571003301.2830.4230.022 2002331982750.5780.1800.0180.002 2003159413030.6100.1790.0220.0120.0100.002
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91 9942: SR-85, Laurel HillYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19981332052477031016000 199917639656177280136000 20002183237590935623000 200127140798212265615000 200223632758148752918110 20031642097090241032000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 1998133205243.7521.5100.078 1999176396564.4682.0200.091 2000218323752.8081.1000.071 2001271407985.2011.6080.037 2002236327584.5391.6150.0550.0030.003 2003164209704.3011.9550.1539943: SR-10/US-90, CypressYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 19981082313216761066102000 19991674764943952511151100 20003187266457093336255000 20013647476458613522212100 20023156793074814719735300 2003161373175936224247630 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 1998108231327.2454.6080.441 1999167476499.2245.2700.3170.002 2000318726647.8574.5910.351 2001364747647.8394.7110.2840.001 20023156793011.0136.9471.0820.004 20031613731715.9076.0080.1260.0160.008
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92 9944: SR-69, SelmanYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 199848582661035021000 1999209223672347130177110 200026623217127867429000 20012773859238432216180000 20023314634351603392591000 20031621360138810811200 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 199848582610.4706.0080.360 19992092236710.4935.8170.3440.0040.004 2000266232175.5052.9030.125 2001277385929.9585.7420.466 20023314634311.1347.3191.275 2003162136012.8530.7940.0810.0159946: SR-363, St. MarksYEAR # OF DAYS VEHICLES WT > 85,000 WT > 90,000 WT > 105,000 WT > 120,000 WT > 135,000 WT > 150,000 199812320703207677176000 19993486453845231674381210 20003535376136941420344000 20013624779731421500486100 20023293820129752018656000 20031612033517331279555000 YEAR # OF DAYS VEHICLES % > 85,000 % > 90,000 % > 105,000 % > 120,000 % > 135,000 % > 150,000 19981232070310.0283.7240.367 1999348645387.0082.5940.5900.0030.002 2000353537616.8712.6410.640 2001362477976.5743.1381.0170.002 2002329382017.7885.2831.717 2003161203358.5226.2902.729
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93 APPENDIX C SUMMARY OF FILES CONTAINING MULTIPLE DAYS OF DATA The content of this appendix summarizes th e number of corrupted files in the WIM dataset. Each line in the subsequent table contains the number of corrupted files for a particular year at a particular site, the total number of files for the particular year, and the percent of corrupted vehicles contained within the year. The last page of this appendix contains the total number of corrupted data files, the total number of data files, and the percent of corrupted files in the whole dataset.
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94 Site Year Files Containing Multiple Days of Data Total Number of Files (Days of Data) Percent of Corrupted Files 9901 1998 143094.53% 9901 1999 192956.44% 9901 2002 3728013.21% 9901 2003 11880.53% 9904 2002 2782.56% 9904 2003 01630% 9905 2002 2215813.92% 9905 2003 0470.00% 9906 2001 52452.04% 9906 2002 0530% 9907 2001 122035.91% 9907 2002 182297.86% 9907 2003 61254.80% 9908 1998 113453.19% 9908 1999 82173.69% 9908 2000 22030.99% 9908 2001 133513.70% 9908 2002 203246.17% 9908 2003 61843.26% 9909 2001 3614.92% 9909 2002 2726210.31% 9909 2003 02110% 9913 2001 112813.91% 9913 2002 102274.41% 9913 2003 31631.84% 9914 2001 42651.51% 9914 2002 0210% 9916 2001 122414.98% 9916 2002 232549.06% 9916 2003 01850% 9917 2002 212348.97% 9917 2003 11670.60%
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95 Site Year Files Containing Multiple Days of Data Total Number of Files (Days of Data) Percent of Corrupted Files 9918 2001 93102.90% 9918 2002 3827713.72% 9918 2003 31382.17% 9919 2001 51722.91% 9919 2002 111537.19% 9919 2003 020% 9920 2003 0440% 9921 1998 243417.04% 9921 1999 313299.42% 9921 2000 113523.13% 9921 2001 63561.69% 9921 2002 252988.39% 9921 2003 31362.21% 9922 2003 0340% 9924 2002 3220215.84% 9925 2002 212488.47% 9925 2003 131697.69% 9926 2002 51583.16% 9926 2003 21261.59% 9927 2002 133204.06% 9927 2003 41382.90% 9928 2002 61543.90% 9928 2003 0750% 9929 2002 8938.60% 9929 2003 6669.09% 9930 2002 274266.34% 9930 2003 42081.92% 9931 2001 151808.33% 9931 2002 0250% 9931 2003 31561.92% 9932 2001 102184.59% 9932 2002 172327.33% 9932 2003 040% 9934 2001 0160% 9934 2002 217926.58% 9934 2003 12010.50% 9935 1998 2314515.86% 9935 1999 3014420.83% 9935 2000 122315.19% 9935 2001 4225316.60% 9935 2002 2315015.33% 9935 2003 2942.13%
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96 Site Year Files Containing Multiple Days of Data Total Number of Files (Days of Data) Percent of Corrupted Files 9936 1998 21291.55% 9936 1999 91555.81% 9936 2000 2321710.60% 9936 2001 2615716.56% 9936 2002 52521.98% 9936 2003 11440.69% 9937 1998 81904.21% 9937 1999 3625014.40% 9937 2000 2422410.71% 9937 2002 101238.13% 9937 2003 01420% 9938 1998 53501.43% 9938 1999 4230313.86% 9938 2000 7798.86% 9939 1998 111915.76% 9939 1999 112554.31% 9939 2000 63251.85% 9939 2001 52881.74% 9939 2002 73302.12% 9939 2003 11550.65% 9940 1998 41922.08% 9940 1999 132864.55% 9940 2000 109410.64% 9940 2001 123573.36% 9940 2002 43311.21% 9940 2003 51593.14% 9942 1998 11330.75% 9942 1999 3117617.61% 9942 2000 122185.50% 9942 2001 32711.11% 9942 2002 52362.12% 9942 2003 51643.05% 9943 1998 101089.26% 9943 1999 3416720.36% 9943 2000 73182.20% 9943 2001 23640.55% 9943 2002 73152.22% 9943 2003 21611.24%
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97 Site Year Files Containing Multiple Days of Data Total Number of Files (Days of Data) Percent of Corrupted Files 9944 1998 0480% 9944 1999 62092.87% 9944 2000 152665.64% 9944 2001 32771.08% 9944 2002 73312.11% 9944 2003 11620.62% 9946 1998 21231.63% 9946 1999 103482.87% 9946 2000 113533.12% 9946 2001 33620.83% 9946 2002 23290.61% 9946 2003 11610.62% TOTAL 817140225.83%
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98 LIST OF REFERENCES 1. TRB Committee for the Truc k Weight Study. (1990), Truck Weight and Limits Issues and Options Special Report 225, Transporta tion Research Board, National Research Council, Washington DC. 2. FDOT State Maintenance Office. (1989), Bridge Load Rating, Permitting and Posting Manual Internal Report, Florida De partment of Transportation, Tallahassee, FL. 3. Reel, R. (Acquired 2002). Automated Editing of Traffic Data in Florida Transportation Statistics Office, Inte rnal Report, Florida Department of Transportation, Tallahassee, FL. 4. FDOT Office of Motor Carrier Compliance. (1998), Trucking Manual Florida Department of Transportation, http://www.dot.state.fl.us/MCCO/pdf/manual1998.pdf last accessed May 17, 2004. 5. Chou, K. C., J. H. Deatherage, T. D. L eatherwood., and A. J. Khayat. (1999). Innovative Method for Evaluating Ov erweight Permit Vehicles. Journal of Bridge Engineering, ASCE, 4(3), 221-227. 6. Fu, G. and O. Hag-Elsafi. (2000). Veh icular Overloads: Lo ad Model, Bridge Safety and Permit Checking. Journal of Bridge Engineering ASCE, 5(1), 49-57. 7. Cohen, H., G. Fu, W. Dekelbab, and F. Moses. (2003). Predicting Truck Load Spectra under Weight Limit Changes and It s Application to Steel Bridge Fatigue Assessment. Journal of Bridge Engineering ASCE, 8(5), 312-322. 8. Ghosn, M. (2000). Development of Tr uck Weight Regulati ons Using Bridge Reliability Model. Journal of Bridge Engineering ASCE, 5(4), 293-303. 9. Ghosn, M. and F. Moses. (2000). Eff ect of Changing Truck Weight Regulations on US Bridge Network. Journal of Bridge Engineering ASCE, 5(4), 304-310. 10. Brillinger, D. R. (July 2003). Ris k Analysis: Examples and Discussion. Proceedings of the Ninth International Conference on Applications of Statistics and Probability in Civil Engineering San Francisco, CA. 11. Brillinger, D. R., H. K. Preisler, and J. Benoit. (2003). Risk Assessment: A Forest Fire Example. In Festschrift for Terry Speed Lecture Notes in Statistics 40, IMS. Science and Statistics Berkeley, CA.
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99 12. Fu, C. C., D.R. Schelling, and B. M. Ayyub. (1992). Evaluation of Truck Configurations Based on Structur al Performance of Bridges. Journal of Advanced Transportation 26(3), 299-324. 13. Croce, P. and W. Salvatore. (2001). Stochastic Model for Multilane Traffic Effects on Bridges. Journal of Bridge Engineering ASCE, 6(2), 136-143. 14. Galambos, C. F. (1979). H ighway Bridge Loadings. Engineering Structures 1(5), 230-235. 15. Kolozsi, G., A. Szilassy, G. Agardy, and L. Gaspar. (June 2000). Permit Vehicle Routing System in Hungary: Protecting Br idges from Highly Loaded Vehicles. Transportation Research Circular 498: Pres entations from the Eight International Bridge Management Conference TRB National Research Council, Washington, DC, K-4. 16. Fryba, L. (1980). Estimation of Fatigue Life of Railway Bridges under Traffic Loads. Journal of Sound and Vibration 70(4), 527-541. 17. Mathcad, version 11.2a. (2003). Mathso ft Engineering & Ed ucation, Inc. http://www.mathcad.com last accessed March 24, 2005. 18. ArcGIS, version 8.3. (2002). ESRI Inc. http://www.esri.com last accessed March 24, 2005. 19. Florida Geographic Data Library. (July 200) Downloaded shape file data, Version 3. http://www.fgdl.org last accessed October 12, 2004. 20. FDOT Transportation Statistics Office. (2005). Downloaded shape file data, Florida Department of Transportation, http://www.dot.state.fl.us/plann ing/statistics/gis/default.htm last accessed January 28, 2005. 21. Florida Traffic Information 2002. (2002). Florida Department of Transportation, Tallahassee, FL, CD-ROM. 22. Transportation Research Board. (2000). Special Report 209: Highway Capacity Manual Transportation Research Board, Washington, DC, 4th Ed.
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100 BIOGRAPHICAL SKETCH Matthew Robert Crim is a 25 year old graduate student at the University of Florida. He received an undergraduate degree of Bachel or of Science in Civil Engineering from the University of Florida in December of 2002. He is currently working on his Master of Engineering degree from the Department of Civil and Coastal Engi neering, specializing in transportation. Matthew Robert Crim is a student memb er of the Institute of Transportation Engineers, the American Society of Civil Engineers, Chi Epsilon and Tau Beta Pi.
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