QUT Digital Repository: http://eprints.qut.edu.au/27085

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QUT Digital Repository:

http://eprints.qut.edu.au/27085

CRC for Construction Innovation (2005) Report : stochastic analysis of road asset data for maintenance cost prediction. CRC for Construction Innovation, Brisbane.

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Report

Stochastic Analysis of Road Asset Data for Maintenance

Cost Prediction

Research Project No: 2003-029-C-03

The research described in this report was carried out by:

Project Leader Arun Kumar

Researchers Saman De Silva

Richard Heaney

Noppadol (Anthony) Piyatrapoomi Andreas Nata-Atmadja

Project Affiliates Neil Robertson

Justin Weligamage

John Spathonis Dale Gilbert

Research Program: C

Delivery and Management of Built Assets

Project: 2003-029-C

Maintenance Cost Prediction for Roads Date: September 2005

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Distribution List

Cooperative Research Centre for Construction Innovation Authors

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TABLE OF CONTENT

Preface ii Executive Summary iii 1. Introduction 1 2. Method of Stochastic Analysis of Road Asset Condition 2 3. Categorisation of Road Pavement 2 4. Statistical Analysis 8 5. Conclusions 11

Appendix 12

References 38

Author Biography 39

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PREFACE

The report is part of CRC CI research project 2003-029-C “Maintenance Cost Prediction for Roads”. The aim of this research project is to develop a method for assessing reliable budget/cost estimates for road maintenance and rehabilitation investment. The method takes into account the variability of critical input parameters including road asset conditions and annual average daily traffic in the analysis.

The authors wish to acknowledge the Cooperative Research Centre for Construction Innovation (CRC CI) for their financial support. The authors also wish to thank Mr.

John Spathonis of Queensland Department of Main Roads, and Mr. Dale Gilbert of Queensland Department of Public Works for their constant support and feedback.

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EXECUTIVE SUMMARY

Reliable budget/cost estimates for road maintenance and rehabilitation are subjected to uncertainties and variability in road asset condition and characteristics of road users. The CRC CI research project 2003-029-C ‘Maintenance Cost Prediction for Road’ developed a method for assessing variation and reliability in budget/cost estimates for road maintenance and rehabilitation. The method is based on

probability-based reliable theory and statistical method. The next stage of the current project is to apply the developed method to predict maintenance/rehabilitation

budgets/costs of large networks for strategic investment. The first task is to assess the variability of road data. This report presents initial results of the analysis in assessing the variability of road data. A case study of the analysis for dry non reactive soil is presented to demonstrate the concept in analysing the variability of road data for large road networks. In assessing the variability of road data, large road networks were categorised into categories with common characteristics according to soil and climatic conditions, pavement conditions, pavement types, surface types and annual average daily traffic. The probability distributions, statistical means, and standard deviation values of asset conditions and annual average daily traffic for each type were quantified. The probability distributions and the statistical information obtained in this analysis will be used to asset the variation and reliability in

budget/cost estimates in later stage.

Generally, we usually used mean values of asset data of each category as input values for investment analysis. The variability of asset data in each category is not taken into account. This analysis method demonstrated that it can be used for practical application taking into account the variability of road data in analysing large road networks for maintenance/rehabilitation investment analysis.

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1. Introduction

The Cooperative Research Centre for Construction Innovation (CRC CI) in Australia led by RMIT University has developed a method for assessing variation and reliability in budget/cost estimates for road maintenance and rehabilitation. This method is based on probability-based reliability theory and statistical method. Details of the methodology are given in CRC-CI Report 2003-029-C-002 ‘Development of a Methodology for Assessing Variation in Maintenance and Rehabilitation Costs’.

The aim of the research work is to apply the method to assess variation and reliability in budget/cost estimates for maintenance and rehabilitation for large road networks.

Figure 1 shows a framework of this research study.

Step 1 Analysis stochastic characteristic of road asset condition for road networks

Step 2

Incorporate the stochastic characteristic of road asset

condition in budget/cost analysis

Step 3

Assess variation and reliability in budget/cost

estimates

Figure 1 Framework of study

The first task in the cost/budget analysis is to assess the variability or the stochastic characteristics of the road network. The report presents results of the stochastic analysis of road asset condition of a large road network located in the state of Queensland. To demonstrate the concept, national highways located in dry non reactive soils were used in the analysis. The analysis method is based on

categorising road networks into categories of common characteristics. The stochastic characteristic of road asset condition and road vehicles for each category is

statistically quantified. The overall categories and their associated road condition stochastic characteristics will eventually be used in Step 2 (in the above figure) for assessing the variation in budget/cost estimates.

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2. Method of Stochastic Analysis of Road Asset Condition

Road asset condition may include road pavement strength, pavement roughness, rutting of pavement surface, cracking, pothole and so forth. Factors that affect road asset condition may include road vehicles, climatic condition, soil condition, etc.

Piyatrapoomi et al (2005) identified that pavement strength, roughness, rutting and road user traffic made significant contribution to variation and reliability in budget/cost estimates. In this study, pavement roughness, rut depth and average annual daily traffic were extracted from Queensland Government Department of Main Road’s database. Pavement strength data will be collected in later stage. The steps of the analysis include;

1) Categorise road network into different categories, which each category has common characteristics.

2) Statistically quantify pavement roughness, rut depth, annual average daily traffic and pavement strength for each category.

3. Categorisation of Road Pavement

Categorisation criteria of road network are based on annual average daily traffic, pavement roughness conditions, climatic zones, soil conditions, surface types and base types. In this study two types of surface types including bitumen and asphalt concrete were used. Three types of pavement bases including flexible, semi rigid and full depth asphalt were used. Seven levels of annual average daily traffics were used including annual average daily traffic of less than 500, 501-1500, 1501-3000, 3001- 5000, 5001-10000, 10001-25000, and greater than 25000. Three pavement

roughness conditions were used including good in which international roughness index (IRI) is less than 2.31, fair in which IRI is greater than 2.31 and less than 4.2, and poor in which IRI is greater than 4.2. Four climatic and soil conditions were used including wet non reactive soils, dry and non reactive soils, wet reactive soil and dry reactive soils. Figure 2 shows climatic and soil conditions classified by Queensland Department of Main Roads for road asset management purposes. Green colour (G) represents wet non reactive soils, blue (B) represents dry reactive soils while red (R) represent dry non reactive soils, yellow represents wet reactive soil. Table 1

summaries the categorisation criteria used in the analysis.

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Figure 2 Climatic zones and soil conditions

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Table 1 Criteria used for categorising road pavements

Annual Average Daily

Traffic

Pavement Roughness

(IRI)

Surface Types Base Types

Climatic and Soil Types

< 500 Good

(IRI<2.31)

Bitumen Flexible Wet

non Reactive soil

501-1500 Fair

(2.31<IRI>4.2)

Asphalt concrete (AC)

Semi Rigid Dry

non Reactive Soil

1501-5000 Poor

(IRI>4.2)

Full Depth Asphalt

Wet Reactive Soil

5001-10000 Dry

Reactive Soil 10001-25000

>25000

For simplicity in identifying road categories, generic identifications were developed.

Descriptions of the generic identifications are described as follows:

For soil and Climatic conditions WNR = wet non reactive soil DR = Dry reactive soil DNR = Dry non reactive soil

For pavement roughness conditions Poor = IRI > 4.2

Fair = 2.31 < IRI < 4.2 Good = IRI <2.31

Note: IRI refers to International Roughness Index

For Pavement Surface Types AC = Asphalt concrete surfacing Bt = Bitumen surfacing

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For Pavement Types Flx = Flexible pavement SR = Semi rigid

FDA = Full depth asphalt

For Annual Average Daily Traffic (AADT)

< 0.5k = AADT less than 500 0.5k-1.5k = AADT between 501-1500 1.5k-3k = AADT between 1501-3000 3k-5k = AADT between 3001-5000 5k-10k = AADT between 5001-10000 10k-25k = AADT between 10001-25000

> 25k = AADT greater than 25000 Road Category Identification

Identification of a road category may be written as follows:

‘WNR-Good-Bt-Flx-(1.5k-3k)’

which is referred to a road category located in wet non reactive soil, IRI < 2.31, bitumen surfacing, flexible pavement type, ADDT between 1501-3000, respectively.

National highways located in dry non reactive soil were used to demonstrate the analysis concept. The national highways were categorised according to the criteria given in Table 1. Eighteen categories were obtained from the categorisation. It must be noted that only the categories that have data were obtained. Tables 2 give categories of the national located in dry non reactive soil.

In ‘ID’ column of Table 2, R1-R18 represents road categories in red areas (i.e. dry non reactive soil). As described above, In ‘Description’ column of Tables 2, ‘DNR’

stand for dry non reactive soil. ‘Good’ means roughness of IRI less than 2.31. ‘Fair’ is IRI is greater than 2.31 but less than 4.2, while ‘Poor’ means IRI is greater than 4.2.

‘Bt’ stands for bitumen surfacing while ‘AC’ stands for asphalt concrete. ‘Flx’ means flexible pavement, SR refers to semi rigid pavement. The terms ‘0.5k, 1.5k, 3k, 5k, 10k, 25k’ refer to annual average daily traffic of 500, 1500, 3000, 5000, 10000 and 25000, respectively.

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Table 2 Road Categories for Dry Non Reactive Soil

No ID Description Climatic

Zone Surface

Type Pavement

Type Roughness

IRI AADT

1 R1 DNR-Good-Bt-Flx-(<0.5k) Dry Non Reactive

Bitumen Flexible < 2.31 <500

2 R2 DNR-Good-Bt-Flx-(0.5k-1.5k) Dry Non

Reactive Bitumen Flexible < 2.31 501-1500 3 R3 DNR-Good-Bt-Flx-(1.5k-3k)

Dry Non

Reactive Bitumen Flexible < 2.31 1501-3000 4 R4 DNR-Good-Bt-Flx-(3k-5k)

Dry Non

Reactive Bitumen Flexible < 2.31 3001-5000 5 R5 DNR-Good-Bt-Flx-(5k -10k)

Dry Non Reactive

Bitumen Flexible < 2.31 5001-10000

6 R6 DNR-Good-Bt-Flx-(10k-25k) Dry Non

Reactive Bitumen Flexible < 2.31 10001-25000 7 R7 DNR-Fair-Bt-Flx-(<0.5k)

Dry Non

Reactive Bitumen Flexible 2.31-4.2 <500 8 R8 DNR-Fair-Bt-Flx-(0.5k-1.5k)

Dry Non

Reactive Bitumen Flexible 2.31-4.2 501-1500 9 R9 DNR-Fair-Bt-Flx-(1.5k-3k)

Dry Non Reactive

Bitumen Flexible 2.31-4.2 1501-3000

10 R10 DNR-Fair-Bt-Flx-(3k-5k) Dry Non

Reactive Bitumen Flexible 2.31-4.2 3001-5000

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Table 2 Road Categories for Dry Non Reactive Soil /Continued.

No ID Description Climatic

Zone Surface Type Pavement

Type Roughness

IRI AADT

11 R11 DNR-Fair-Bt-Flx-(5k-10k) Dry Non Reactive

Bitumen Flexible 2.31-4.2 5001-10000

12 R12 DNR-Fair-Bt-Flx-(10k-25k) Dry Non

Reactive Bitumen Flexible 2.31-4.2 10001-25000 13 R13 DNR-Poor-Bt-Flx-(<0.5k)

Dry Non

Reactive Bitumen Flexible >4.2 <500 14 R14 DNR-Poor-Bt-Flx-(0.5k-1.5k)

Dry Non

Reactive Bitumen Flexible >4.2 501-1500

15 R15 DNR-Good-AC-Flx-(0.5k-1.5k) Dry Non Reactive

AC Flexible <2.31 501-1500

16 R16 DNR-Good-AC-Flx-(1.5k-3k) Dry Non

Reactive AC Flexible <2.31 1501-3000

17 R17 DNR-Fair-AC-Flx-(0.5k-1.5k) Dry Non

Reactive AC Flexible 2.31-4.2 501-1500

18 R18 DNR-Good-Bt-SR-(0.5k -1.5k)

Dry Non

Reactive Bitumen Semi Rigid < 2.31 501-1500

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4. Statistical Analysis

This section presents results of statistical analysis of road asset condition and annual average daily traffic for each category. As mentioned, Piyatrapoomi et al (2005) found that pavement strength, roughness, rut depth and annual average daily traffic were significant contributions in the variation in budget/cost estimates. Probability distributions, means and standard deviation values of pavement roughness, average rut depth and annual average daily traffic were quantified. Pavement strength

information will be collected and presented at a later stage.

Table 3 presents probability distributions, means and standard deviation values of pavement roughness, average rut depth and annual average daily traffic of the identified eighteen categories. Appendix shows theoretical cumulative probability distributions that are in good-fit with the road data for dry non reactive soils. For roughness, the majority of probability distributions of the eighteen categories were found to have good-fit with beta general distributions. Logistic, log normal and normal distributions were also found to be in good-fit with the data in some categories. For average rut depth, the most common probability distributions that are in good-fit with the data were found to be log normal distributions. For annual average daily traffic, the data were not in good-fit with any probability distributions. This may be due to the fact that the annual average daily traffic data were collected at certain locations and in some cases via weigh in motion (WIM) at some locations. Thus, the data were dictated by locations of collection. However, the data show some trend in good fit with triangular and exponential distributions.

In Appendix, details of statistical parameters of the probability distributions are given below:

BetaGeneral(α1,α2, min, max): Beta General probability distribution is specified with shape parameters, α1,α2, minimum and maximum values.

Expon(β): Exponential distribution is specified with a decay constant β.

Logistic(α, β): Logistic distribution is specified with a location parameter, α, and a scale parameter, β.

Loglogistic(γ, α, β): Log logistic distribution is specified with a location parameter, γ, a shape parameter, α, and a scale parameter, β.

Lognorm(µ, σ): Lognormal distribution is specified with mean, µ, and standard deviation, σ.

Normal(µ, σ): Normal distribution is specified with mean, µ, and standard deviation, σ.

Triang(mim, most likely, max): Triangular distribution is specified with a minimum value, most likely and a maximum value.

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Table 3 Probability Distributions, Means and Standard Deviation Values of Road Categories for Dry Non Reactive Soil

ID Description Roughness (IRI) Rut Depth (mm) AADT

Mean SD Probability Distribution

Mean SD Probability Distribution R1 DNR-Good-Bt-Flx-(<0.5k) 2.32 0.39 Beta General 4.52 1.97 Log Normal 322 52 Triangular R2 DNR-Good-Bt-Flx-(0.5k-1.5k) 1.70 0.35 Beta General 4.54 2.37 Log Normal 970 244 Normal R3 DNR-Good-Bt-Flx-(1.5k-3k) 1.72 0.36 Beta General 4.20 2.29 Log Normal 1990 337 Exponential R4 DNR-Good-Bt-Flx-(3k-5k) 1.82 0.34 Beta General 4.24 2.61 Log Normal 3420 386 Exponential R5 DNR-Good-Bt-Flx-(5k -10k) 1.80 0.37 Beta General 3.43 1.72 Log Normal 6154 424 Exponential R6 DNR-Good-Bt-Flx-(10k-25k) 1.70 0.31 Beta General 4.60 1.53 Normal 10035 - -

R7 DNR-Fair-Bt-Flx-(<0.5k) 2.30 0.48 Beta General 6.14 3.06 Log Normal 311 54 Triangular R8 DNR-Fair-Bt-Flx-(0.5k-1.5k) 2.90 0.46 Beta General 5.88 2.74 Log Normal 953 210 Triangular R9 DNR-Fair-Bt-Flx-(1.5k-3k) 2.96 0.47 Beta General 5.53 2.75 Log Normal 1940 428 Exponential R10 DNR-Fair-Bt-Flx-(3k-5k) 2.89 0.43 Beta General

4.55 2.46 Log Normal 3300 267 Exponential

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Table 3 Probability Distributions, Means and Standard Deviation Values of Road Categories for Dry Non Reactive Soil /Continued.

ID Description Roughness (IRI) Rut Depth (mm) AADT

Mean SD Probability Distribution

Mean SD Probability Distribution R11 DNR-Fair-Bt-Flx-(5k-10k) 2.90 0.46 Beta General 4.35 1.33 Log Normal 6063 152 Exponential R12 DNR-Fair-Bt-Flx-(10k-25k) 2.64 0.37 Log Normal 5.40 1.29 Log Normal 10035 - -

R13 DNR-Poor-Bt-Flx-(<0.5k) 5.07 2.0 Log Normal 6.91 4.0 Log Normal 299 64 Exponential R14 DNR-Poor-Bt-Flx-(0.5k-1.5k) 4.98 1.92 Log Normal 6.13 2.98 Log Normal 960 205 Triangular R15 DNR-Good-AC-Flx-(0.5k-1.5k) 1.57 0.36 Log Normal 6.04 1.67 Normal 795 159 Triangular R16 DNR-Good-AC-Flx-(1.5k-3k) 1.60 0.34 Log Normal 2.47 0.97 Log Normal 2211 345 Triangular R17 DNR-Fair-AC-Flx-(0.5k-1.5k) 1.83 0.33 Normal 4.01 1.34 Log Normal 720 233 Exponential R18 DNR-Good-Bt-SR-(0.5k -1.5k) 1.32 0.27 Log Logistic 3.48 1.54 Log Normal 940 - -

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5. Conclusions

This report presents a stochastic analysis of road asset condition and annual averaged daily traffic for large road network. National highways located in dry non reactive soils were used in the analysis to demonstrate the concept. The national highways can be grouped into eighteen categories with common characteristics of soil and climatic conditions, road pavement conditions, pavement types, surface types, annual average daily traffic. The probability distributions and statistical means and standard deviation values of roughness, average rut depth and annual average daily traffic were quantified for each category.

The result of the analysis indicated that beta general distributions were found to give good-fit to the cumulative probability distribution of roughness data. Log normal distributions were found to be in good-fit with the average rut depth data, while triangular and exponential distributions could be used to model the probability distributions of annual average daily traffic. For annual average daily traffic, analysts need to observe the distribution of the data before deciding whether the triangular or exponential distributions should be used.

The probability distribution, mean and standard deviation obtained in this analysis will be used for assessing variation and reliability in budget estimates for road

maintenance and rehabilitation.

Auslink network of 4,500 km was selected as a case study for

maintenance/rehabilitation investment analysis. A complete analysis of the stochastic characteristic of the 4,500 km Austlink network will be presented in CRC CI Report 2003-029-C/04 (December 2005).

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Appendix

This appendix presents comparisons between theoretical cumulative probability distributions and cumulative distributions of data for roughness, average rut depth and annual average daily traffic for dry non reactive soils. Figures (A1-R1) to (A18- R18) show the comparison of the theoretical cumulative probability distributions and cumulative distribution of roughness. Figures (B1-R1) to (B18-R18) show the

comparisons of the theoretical cumulative probability distributions and cumulative probability distributions of average rut depth. Figures (C1-R1) to (C15-R17) show the comparisons of the theoretical cumulative distributions and cumulative distributions of annual average daily traffic.

BetaGeneral(1.7984, 1.4878, 0.70783, 2.3225)

X <= 2.190 95.0%

X <= 0.935 5.0%

0 0.2 0.4 0.6 0.8 1

0.6 1.05 1.5 1.95 2.4

IRI CUMULATIVE PROBABILITY (Fx) Data

Beta General Distribution

Figure A1-R1. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT<500 (DNR-Good-Bt-Flx- (<0.5k)

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BetaGeneral(2.3394, 1.1415, 0.74070, 2.3117)

X <= 2.260 95.0%

X <= 1.143 5.0%

0 0.2 0.4 0.6 0.8 1

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

CUMULALATIVE PROBABILITY (Fx)

Data

Figure A2-R2. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=501-1500 (DNR-Good- Bt-Flx-(0.5k-1.5k)

BetaGeneral(2.3314, 1.3553, 0.71245, 2.3115)

X <= 2.228 95.0%

X <= 1.078 5.0%

0 0.2 0.4 0.6 0.8 1

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

CUMULATIVE PROBABILITY (Fx)

Data

Figure A3-R3. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=1501-3000 (DNR-Good- Bt-Flx-(1.5k-3k)

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BetaGeneral(1.9751, 1.0374, 0.88888, 2.3100)

X <= 2.269 95.0%

X <= 1.193 5.0%

0 0.2 0.4 0.6 0.8 1

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

Data

Figure A4-R4. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=3001-5000 (DNR-Good- Bt-Flx-(3k-5k)

BetaGeneral(0.73516, 0.57209, 1.1600, 2.2900)

X <= 2.281 95.0%

X <= 1.196 5.0%

0 0.2 0.4 0.6 0.8 1

1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

CUMULATIVE PROBABILITY (Fx)

Data

Figure A5-R5. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=5001-10000 (DNR- Good-Bt-Flx-(5k-10k)

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BetaGeneral(1.3108, 1.3686, 1.1187, 2.3040)

X <= 2.199 95.0%

X <= 1.210 5.0%

0 0.2 0.4 0.6 0.8 1

1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

Data

Figure A6-R6. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=10001-25000 (DNR- Good-Bt-Flx-(10k-25k)

BetaGeneral(0.90248, 1.6903, 2.3200, 4.2333)

X <= 3.883 95.0%

X <= 2.361 5.0%

0 0.2 0.4 0.6 0.8 1

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

IRI

Data

Figure A7-R7. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT<500 (DNR-Fair-Bt- Flx-(>0.5k)

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BetaGeneral(0.81247, 1.8889, 2.3200, 4.2597)

X <= 3.803 95.0%

X <= 2.345 5.0%

0 0.2 0.4 0.6 0.8 1

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

Data

Figure A8-R8. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=501-1500 (DNR- Fair-Bt-Flx-(0.5k-1.5k)

BetaGeneral(0.84343, 1.6990, 2.3200, 4.2646)

X <= 3.887 95.0%

X <= 2.352 5.0%

0 0.2 0.4 0.6 0.8 1

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4

IRI

Data

Figure A9-R9. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=1501-3000 (DNR- Fair-Bt-Flx-(1.5k-3k)

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BetaGeneral(0.95775, 2.3474, 2.3200, 4.2807)

X <= 2.357 5.0%

X <= 3.719 95.0%

0 0.2 0.4 0.6 0.8 1

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2

IRI

Data

Figure A10-R10. Cumulative probability distributions of roughness for dry non

reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=3001-5000 (DNR-Fair-Bt-Flx-(3k-5k)

BetaGeneral(0.78982, 1.8542, 2.3200, 4.2401)

X <= 3.792 95.0%

X <= 2.343 5.0%

0 0.2 0.4 0.6 0.8 1

2.18 2.685 3.19 3.695 4.2

IRI

Data

Figure A11-R11. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=5001- 10000 (DNR-Fair-Bt-Flx-(5k-10k)

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Lognorm(0.30755, 0.36548) Shift=+2.33316

X <= 3.260 95.0%

X <= 2.375 5.0%

0 0.2 0.4 0.6 0.8 1

2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3

IRI

Data

Lognormal Distribution

Figure A12-R12. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=10001- 25000 (DNR-Fair-Bt-Flx-(10k-25k)

Pearson5(1.2720, 0.39478) Shift=+4.12761

X <= 7.68 95.0%

X <= 4.20 0.8%

0 0.2 0.4 0.6 0.8 1

4 6 8 10 12 14 16 18 2

IRI

Data

Pearson5 Distribution

0

Figure A13-R13. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI >4.2, AADT<501 (DNR-Poor- Bt-Flx-(<0.5k)

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Pearson5(1.0919, 0.24432) Shift=+4.15935

X <= 7.697 95.0%

X <= 4.236 5.0%

0 0.2 0.4 0.6 0.8 1

4 5 6 7 8 9 10 11 1

IRI

Data

Pearson5 Distribution

2

Figure A14-R14. Cumulative probability distributions of roughness for dry non reactive soil, bitumen surfacing, flexible pavement, IRI >4.2, AADT=501-1500 (DNR- Poor-Bt-Flx-(0.5k-1.5k)

Lognorm(0.65109, 0.35585) Shift=+0.91437

X <= 2.239 95.0%

X <= 1.161 5.0%

0 0.2 0.4 0.6 0.8 1

1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

Data

Figure A15-R15. Cumulative probability distributions of roughness for dry non reactive soil, asphalt concrete surfacing, flexible pavement, IRI <2.31, AADT=501- 1500 (DNR-Good-AC-Flx-(0.5k-1.5k)

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Lognorm(7.1379, 0.34409) Shift=-5.5387

X <= 2.179 95.0%

X <= 1.048 5.0%

0 0.2 0.4 0.6 0.8 1

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

Data

Figure A16-R16. Cumulative probability distributions of roughness for dry non reactive soil, asphalt concrete surfacing, flexible pavement, IRI <2.31, AADT=1501- 3000 (DNR-Good-AC-Flx-(1.5k-3k)

Lognorm(144400, 0.45997) Shift=-144397

X <= 3.704 95.0%

0 0.2 0.4 0.6 0.8 1

2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

IRI

Figure A17-R17. Cumulative probability distributions of roughness for dry non reactive soil, asphalt concrete surfacing, flexible pavement, 2.31< IRI <4.2, AADT=501-1500 (DNR-Fair-AC-Flx-(0.5k-1.5k)

(27)

Normal(1.83216, 0.32986)

X <= 2.375 95.0%

X <= 1.290 5.0%

0 0.2 0.4 0.6 0.8 1

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

IRI

Figure A18-R18. Cumulative probability distributions of roughness for dry non reactive soil, asphalt concrete surfacing, semi rigid pavement, IRI <2.31, AADT=501- 1500 (DNR-Good-AC-SR-(0.5k-1.5k)

Lognorm(4.7802, 1.9646) Shift=-0.26431

X <= 8.20 95.0%

X <= 2.04 5.0%

0 0.2 0.4 0.6 0.8 1

0 5 10 15 20 25 30

RUT DEPTH (mm)

Data

Figure B1-R1. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT<500 (DNR- Good-Bt-Flx-(<0.5k)

(28)

Lognorm(5.0802, 2.3653) Shift=-0.53647

X <= 9.01 95.0%

X <= 1.69 5.0%

0 0.2 0.4 0.6 0.8 1

0 5 10 15 20 25

RUT DEPTH (mm)

Data

Figure B2-R2. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=501-1500 (DNR-Good-Bt-Flx-(0.5k-1.5k)

Lognorm(4.1884, 2.2921) Shift=+0.014281

X <= 8.54 95.0%

X <= 1.60 5.0%

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 1

RUT DEPTH (mm)

Data

6

Figure B3-R3. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=1501-3000 (DNR-Good-Bt-Flx-(1.5k-3k)

(29)

Lognorm(3.8886, 2.6120) Shift=+0.34800

X <= 9.16 95.0%

X <= 1.53 5.0%

0 0.2 0.4 0.6 0.8 1

0 1 2 3 4 5 6 7 8 9 10 11

RUT DEPTH (mm)

Data

Figure B4-R4. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=3001-5000 (DNR-Good-Bt-Flx-(3k-5k)

Lognorm(2.9670, 1.7200) Shift=+0.46662

X <= 6.69 95.0%

X <= 1.53 5.0%

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 1

RUT DEPTH (mm)

Data

4

(30)

Normal(4.5956, 1.5316)

X <= 7.115 95.0%

X <= 2.076 5.0%

0 0.2 0.4 0.6 0.8 1

1 2 3 4 5 6 7 8

RUT DEPTH (mm)

Data

Normal Distribution

9

Lognorm(6.4385, 3.0616) Shift=-0.30391

X <= 11.92 95.0%

X <= 2.46 5.0%

0 0.2 0.4 0.6 0.8 1

0.5 6.4 12.3 18.2 24.1 30

RUT DEPTH (mm)

Data

Figure B7-R7. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT<500 (DNR- Fair-Bt-Flx-(>0.5k)

(31)

Lognorm(7.4644, 2.7427) Shift=-1.6636

X <= 10.92 95.0%

X <= 2.24 5.0%

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 16 1

Data

8

Figure B8-R8. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=501-1500 (DNR-Fair-Bt-Flx-(0.5k-1.5k)

Lognorm(5.4951, 2.7545) Shift=+0.034975

X <= 10.74 95.0%

X <= 2.29 5.0%

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 16 1

RUT DEPTH (mm)

Data

8

Figure B9-R9. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=1501-3000 (DNR-Fair-Bt-Flx-(1.5k-3k)

(32)

Lognorm(4.6483, 2.4576) Shift=-0.10384

X <= 9.20 95.0%

X <= 1.71 5.0%

0 0.2 0.4 0.6 0.8 1

0 2 4 6 8 10 12 14 1

RUT DEPTH (mm)

Data

6

Figure B10-R10. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=3001-5000 (DNR-Fair-Bt-Flx-(3k-5k)

Lognorm(6.5316, 1.3363) Shift=-2.1869

X <= 6.741 95.0%

X <= 2.399 5.0%

0 0.2 0.4 0.6 0.8 1

2 3 4 5 6 7 8

RUT DEPTH (mm)

CUMULATIVE PROBABILITY (Fix)

Data

9

Figure B11-R11. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=5001- 10000 (DNR-Fair-Bt-Flx-(5k-10k)

(33)

Lognorm(4.8163, 1.2952) Shift=+0.58515

X <= 7.768 95.0%

X <= 3.600 5.0%

0 0.2 0.4 0.6 0.8 1

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

RUT DEPTH (mm)

Data

Figure B12-R12. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI <4.2, AADT=10001- 25000 (DNR-Fair-Bt-Flx-(10k-25k)

Lognorm(6.4032, 4.0026) Shift=+0.50747

X <= 14.47 95.0%

X <= 2.62 5.0%

0 0.2 0.4 0.6 0.8 1

0 5 10 15 20 25 30

RUT DEPTH (mm)

Data

Figure B13-R13. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI >4.2, AADT<501 (DNR-Poor- Bt-Flx-(<0.5k)

(34)

Lognorm(4.9461, 2.8912) Shift=+1.1790

X <= 11.60 95.0%

X <= 2.93 5.0%

0 0.2 0.4 0.6 0.8 1

2 4 6 8 10 12 14

RUT DEPTH (mm)

Data

Figure B14-R14. Cumulative probability distributions of average rut depth for dry non reactive soil, bitumen surfacing, flexible pavement, IRI >4.2, AADT=501-1500 (DNR- Poor-Bt-Flx-(0.5k-1.5k)

Normal(6.0140, 1.6724)

X <= 8.76 95.0%

X <= 3.26 5.0%

0 0.2 0.4 0.6 0.8 1

1 2 3 4 5 6 7 8 9 10 11

RUT DEPTH (mm) CUMULATIVE PROBABILITY (Fx) Data

Normal Distribution

Figure B15-R15. Cumulative probability distributions of average rut depth for dry non reactive soil, asphalt concrete surfacing, flexible pavement, IRI <2.31, AADT=501- 1500 (DNR-Good-AC-Flx-(0.5k-1.5k)

(35)

Lognorm(2.1862, 0.97116) Shift=+0.23150

X <= 4.247 95.0%

X <= 1.226 5.0%

0 0.2 0.4 0.6 0.8 1

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

RUT DEPTH (mm)

Data

Figure B16-R16. Cumulative probability distributions of average rut depth for dry non reactive soil, asphalt concrete surfacing, flexible pavement, IRI <2.31, AADT=1501- 3000 (DNR-Good-AC-Flx-(1.5k-3k)

Lognorm(38252, 1.5174) Shift=-38247

X <= 7.243 95.0%

X <= 2.300 5.3%

0 0.2 0.4 0.6 0.8 1

2 3 4 5 6 7 8

RUT DEPTH (mm)

9

Figure B17-R17. Cumulative probability distributions of average rut depth for dry non reactive soil, asphalt concrete surfacing, flexible pavement, 2.31< IRI <4.2,

AADT=501-1500 (DNR-Fair-AC-Flx-(0.5k-1.5k)

(36)

Lognorm(10.724, 1.3392) Shift=-6.7158

X <= 6.342 95.0%

X <= 1.956 5.0%

0 0.2 0.4 0.6 0.8 1

0 1 2 3 4 5 6 7

RUT DEPTH (mm)

8

Figure B18-R18. Cumulative probability distributions of average rut depth for dry non reactive soil, asphalt concrete surfacing, semi rigid pavement, IRI <2.31, AADT=501- 1500 (DNR-Good-AC-SR-(0.5k-1.5k)

Triang(231.01, 269.00, 467.25)

X <= 418.9 95.0%

X <= 252.2 5.0%

0 0.2 0.4 0.6 0.8 1

200 250 300 350 400 450 500

AADT

Data

Triangular Distribution

Figure C1-R1. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT<500 (DNR-Good-Bt-Flx-(<0.5k)

(37)

Triang(318.06, 1236.0, 1456.1)

X <= 1344 95.0%

X <= 547 5.0%

0 0.2 0.4 0.6 0.8 1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

AADT

Values in Thousands

Data

Figure C2-R2. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=501-1500 (DNR-Good-Bt-Flx-(0.5k-1.5k)

Expon(284.09) Shift=+1513.64

X <= 2365 95.0%

X <= 1528 5.0%

0 0.2 0.4 0.6 0.8 1

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

AADT

Data

Exponential Distribution

Figure C3-R3. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=1501-3000 (DNR-Good-Bt-Flx-(1.5k-3k)

(38)

Expon(386.22) Shift=+3033.58

X <= 4191 95.0%

X <= 3053 5.0%

0 0.2 0.4 0.6 0.8 1

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5

AADT

Data

Figure C4-R4. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=3001-5000 (DNR-Good-Bt-Flx-(3k-5k)

Expon(129.87) Shift=+5911.50

X <= 6301 95.0%

X <= 5918 5.0%

0 0.2 0.4 0.6 0.8 1

5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8

AADT

CUMULATIVE PROBABILTY (Fx)

Data

Figure C5-R5. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, IRI <2.31, AADT=5001-10000 (DNR-Good-Bt-Flx-(5k-10k)

(39)

Expon(70.674) Shift=+234.939

X <= 446.7 95.0%

X <= 238.6 5.0%

0 0.2 0.4 0.6 0.8 1

200 250 300 350 400 450 500

AADT

Data

Figure C6-R7. Cumulative probability distributions of annual average daily traffic (AADT) for dry non reactive soil, bitumen surfacing, flexible pavement, 2.31< IRI

<4.2, AADT<500 (DNR-Fair-Bt-Flx-(>0.5k)

Triang(359.34, 1250.00, 1250.00)

X <= 1227.4 95.0%

X <= 560.0 5.1%

0 0.2 0.4 0.6 0.8 1

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

AADT