Lecture 8

Traffic Loading and Volume

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Introduction

Stresses in Multi-Layer Systems

Stresses in Flexible Pavements

WinJULEA

KENLAYER Stresses in Rigid

pavements

Characterization of Geomaterials

Constitutive Behavior

Stress Path Testing

AASHTO T-307

NCHRP 1-28A

Characterization of Asphaltic Materials

Viscoelastic Behavior

Binder and Mix Characterization

Superpave Binder Tests

AASHTO Mix Tests

Traffic

ESAL Concept

Axle Load Spectra

Design Methods

AASHTO Method

Flexible Pavement Design

Rigid Pavement Design

Asphalt Institute (AI)

TxDOT Method FPS21 Software

New Mechanistic Empirical DG MEPDG Software

Distresses in Pavements

Traffic Density Map

Variation of Layer Moduli with Time

Mo

du

lus

Damage Analysis (Miner’s Law)

Damage Ratio:

Dr: damage ratio at the end of the year.

ni,j: number of load repetitions for load j in period i.

Ni,j: allowable number of load repetitions for load j and period i.

m: number of load groups.

p: number of periods in each year.

p mi , j

r

i 1 j 1 i , j

nD

N

The procedures for the consideration of traffic effects for the analysis and design of pavements:

A. Fixed Traffic

B. Fixed Vehicle (Axle)

C. Variable Traffic and Variable Vehicle

Traffic Analysis Background

Pavement thickness is determined based on the application of the single wheel load.

Used in airport and industrial design (B-29 Bombers in WWII).

Analysis of the worst case scenario (the Heaviest Single Wheel Load-HSWL design)-used for stability analysis of pavement structures.

Number of load repetitions and therefore fatigue performance is not considered.

Fixed Traffic Procedure

Pavement thickness is determined by the number of repetitions of a standard vehicle or axle load.

Usually 18 kips or 80 KN axle load.

All other axle loads are converted to the 18-kip axle loads by Equivalent Axle Load Factor (EALF).

Summation of the equivalent effects of all axle loads over the design life (service life) gives the Equivalent Single Axle Load (ESAL) used for the design.

ESAL concept is used in AASHTO and Asphalt Institute (AI) pavement design methods.

Fixed Vehicle Procedure

Considers both traffic counts (number of load repetitions) and load magnitude for each individual passage of a specific axle.

Pavement responses (stresses, strains, and deformations) for each individual load repetition is used for the calculation of the damages imparted by the traffic loads.

Advantage: most accurate representation of the traffic loads, therefore currently used for the mechanistic design of pavements (MEPDG).

Disadvantage (I): computationally intensive.

Disadvantage (II): requires costly data collection instruments.

Variable Vehicle and Traffic Procedure

Characterization of Traffic Loads

Traffic loads along with environmental influences on the stiffness properties of the layers, impacts the cumulative damage of the pavements over time. Therefore it is necessary to properly account for the influence of traffic loads on the pavement life.

Traffic loads, the vehicle forces exerted on the pavement (e.g., by trucks, heavy machinery, airplanes), can be characterized by the following parameters:

Magnitude of the Axle Load

Axle and Tire Configuration

Repetition of Loads

Distribution of Traffic Across the Pavement

Vehicle Speed

Influence of Layer Configuration and Wheel Load on Pavements Responses

Determination of the Tire Footprint

Vertical Stress Distribution under Dual Wheel Load

Tire Test with SIM Pad under Heavy Vehicle Simulator (After de Beer and Fisher, 2002)

Measurements of Vertical Tire Contact Stresses for 215/75R17.5 Radial Tire

(After de Beer and Fisher, 2002)

5000 lb. Tire Load and 100 psi Tire Inflation Pressure.

Axle/Tire Combinations General Definitions

Axle and Tire Configuration

Axle configuration - number of axles sharing the same suspension system and the number of tires in each axle.

Multiple axles involve 2, 3 or 4 axles spaced 4 to 8 feet apart and are referred to as tandem, triple or quad, respectively.

They are treated differently than single axles due to the fact that the stress isobars might overlap ( therefore you need to use the superposition principle to properly calculate the pavement responses).

Distribution of the Stresses Induced by Multiple Wheel Assembly

Superposition Principle: in physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.

Superposition of Wheel Loads

Typical Axle Load Limits

Federal and State laws establish maximum axle and gross vehicle weights to limit pavement damage.

The simplest pavement structural model asserts that each individual load inflicts a certain amount of unrecoverable damage. This damage is cumulative over the life of the pavement and when it reaches some maximum value the pavement is considered to have reached the end of its useful service life.

Quantification of the traffic loads for analysis and design of pavements is done in two ways:

Equivalent Single Axle Load (ESALs)

Axle Load Spectra

Traffic Loads and Pavement Damages

Based on AASHO Road Test results, the most common approach is to convert wheel loads of various magnitudes and repetitions (“mixed traffic”) to an equivalent number of “standard” or “equivalent” loads.

The most commonly used equivalent load in the U.S. is the 80 kN (18,000 lb.) Equivalent Single Axle Load (ESAL).

Fi= Equivalent Axle Load Factor for the ith axle load group.

m= Number of axle load group

n= Number of passes of the ith axle group during the design period.

Equivalent Single Axle Loads (ESALs) Concept

i

m

i

i nFESAL

1

Load Equivalency Factor

Using the ESAL method, damage from all loads (including multi-axle loads) are converted to damage from an equivalent number of 18,000 lb single axle loads, which is then used for design.

A “load equivalency factor” represents the equivalent number of ESALs for the given weight-axle combination.

The new Mechanistic Empirical Design Guide (MEPDG) essentially does away with the ESAL concept and determines loading directly from axle configurations and weights.

This is a more precise characterization of traffic but relies on more detailed information that could also be used to calculate ESALs.

Typical load spectrum input would be in the form of a table that shows the relative axle weight frequencies for each common axle combination (e.g. single axle, tandem axle, tridem axle, quad axle) over a given time period.

Often, load spectra data can be obtained from weigh-in-motion stations.

Axle Load Spectra

Pavement Design

Axle Load Spectra- Example of Traffic Input

MADTT Class 4 Class 5 Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12 Class 13

January 588 2800 1216 502 250 527 485 51 142 124

February 598 2851 896 498 263 654 493 38 152 108

March 602 2864 1211 561 296 625 520 25 164 165

April 630 3001 1321 598 299 692 586 62 159 154

May 674 3213 1452 625 421 568 564 45 156 142

June 717 3415 1621 740 465 587 652 65 187 165

July 756 3602 1690 789 489 623 657 82 221 120

August 810 3859 1699 785 620 621 678 32 235 95

September 832 3962 1780 741 661 451 725 67 268 67

October 755 3455 1795 645 561 482 712 12 189 64

November 685 2699 1400 560 421 389 608 18 167 96

December 598 2760 1324 495 412 462 527 19 152 116

Total 8245 38481 17405 7539 5158 6681 7207 516 2192 1416

Hourly-AADTT %

Midnight 1:00 AM 8 0.6

1:00 AM 2:00 AM 9 0.7

2:00 AM 3:00 AM 12 0.9

3:00 AM 4:00 AM 16 1.3

4:00 AM 5:00 AM 25 2.0

5:00 AM 6:00 AM 36 2.8

6:00 AM 7:00 AM 45 3.5

7:00 AM 8:00 AM 68 5.3

8:00 AM 9:00 AM 78 6.1

9:00 AM 10:00 AM 76 5.9

10:00 AM 11:00 AM 78 6.1

11:00 AM Noon 82 6.4

Noon 1:00 PM 98 7.7

1:00 PM 2:00 PM 98 7.7

2:00 PM 3:00 PM 86 6.7

3:00 PM 4:00 PM 88 6.9

4:00 PM 5:00 PM 74 5.8

5:00 PM 6:00 PM 78 6.1

6:00 PM 7:00 PM 64 5.0

7:00 PM 8:00 PM 52 4.1

8:00 PM 9:00 PM 54 4.2

9:00 PM 10:00 PM 26 2.0

10:00 PM 11:00 PM 18 1.4

11:00 PM Midnight 10 0.8

1279 100.0

Hourly Distribution

Total

Start Time End Time

Axle Load Spectra-Annual Variation, Example

Example of Axle Load Spectra; Single Axles

Single Axles; 53-1002, 1992

0

2000

4000

6000

8000

10000

12000

14000

7 24 38 51 64 78 91 104

118

131

144

158

171

Load (kN)

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Example of Axle Load Spectra; Tandem Axles

Tandem Axles; 53-1002, 1992

0

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2000

3000

4000

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6000

7000

800013 49 76 102

129

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182

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236

262

289

316

342

Load (kN)

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Example of Axle Load Spectra; Tridem Axles

Tridem Axles; 53-1002, 1992

0

100

200

300

400

500

60027 73 100

127

153

180

207

233

260

287

313

340

367

393

420

Load (kN)

Num

ber

of

Axl

es

Daily Variation in Directional Flow (Troutville Weigh Station on I-81)

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2000

3000

4000

5000

6000

7000

8000

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

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SB I-81

Time-of-Day Variation

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150

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300

350

400

450

0 2 4 6 8 10 12 14 16 18 20 22 24

Time-of-day (h)

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SB I-81

Traffic Monitoring Technologies

Axle load data is collected by a combination of traffic data monitoring equipment, including:

Automatic Traffic Recorders (ATR)

Automated Vehicle Classifiers (AVC)

Weigh-In-Motion (WIM) systems

These systems are typically installed in the driving lanes and record data at normal driving speeds.

Static weigh scales, such as those installed in truck inspection stations are used for load enforcement, rather than for data collection purposes.

Automated Vehicle Recorder (AVR) Systems

The most common sensor is the inductive loop (length and speed).

Simple open wire loops embedded near the pavement surface.

Current and voltage are generated due to the passing of vehicles.

Cannot be used to differentiate between vehicle types.

Some sensors are placed overhead which can be moved between locations to provide short-term traffic count samples.

voltage Data Box

loop

Automated Vehicle Classifier (AVC) Systems

Record vehicle volumes by vehicle classification.

Vehicle classification is defined in terms of the number of axles and axle configuration.

Detect the number of axles and their spacing through a combination of vehicle and axle sensors.

Not all axle sensors can differentiate between two and four tires per axle (cannot distinguish Class 3 from Class 5 vehicles).

Axle detector

Loops

Automated Vehicle Classifier (AVC) Systems

Classifying vehicles through conventional AVC systems under variable speed is challenging.

Camera-based sensors used for general traffic data collection.

Although AVC data

contains more information

than AVR data, it still lacks

information about load of

the axles.

Weigh-in-Motion (WIM) Systems

Provide the load of each axle passing over the pavement section.

Consist of a combination of inductive loops for detecting vehicle speed and one or several axle load sensors.

Able to respond/recover quickly, allowing multiple closely-spaced axles to be weighed individually at highway speeds.

Example of a Load Cell WIM system (Courtesy of IRD Inc.)

Weigh-in-Motion (WIM) Systems

Measuring Systems: Load cell systems Strain-gauged plate Piezoelectric sensors

A polarization technique is used to produce piezoelectric sensitivity, whereby stress changes applied to the sensors generate a voltage differential between outer sheath and core.

This voltage signal is electronically processed to determine the axle load that applied the stress.

Measure dynamic rather than static axle loads. Dynamic axle loads can be substantially different than the static.

Types of Weight-in-Motion (WIM) More Than 1000 Working WIM Stations Installed Around The World ( more than 500 in USA).

Permanent

Fiber Optic Sensors, Multiple Sensor WIM (MS-WIM)

Portable Most WIM are also AVC

Piezoelectric sensors Load Cells Bending Plates

Capacitance Mat Capacitance Strip

Traffic Data for Pavement Design Input

Traffic data is collected with a combination of traffic monitoring technologies, including ATR (or AVR), AVC and WIM systems, distributed over the roadway network.

Some systems are permanently installed while others are installed temporarily over shorter periods of time and moved to other locations.

Appropriate factors are used to calculate the traffic volumes and axle loads over the desired interval.

Data need to be summarized as input to the pavement design process.

Traffic Analysis

Based on 18-kip single axle load

i 0 in ( n )GDL(365 )Yni : Total number of load repetitions to be used in design of the ith load group

(n0)i: Initial number of repetitions per day for the ith load group

G: Growth factor

D: Directional distribution factor

L: Lane distribution factor

Y: Design period in years

pi : Percentage of the total repetitions for the ith load group

Fi: Factor for equivalent single axle load

ADT0: Average daily traffic at the start of the design period

T: Percentage of trucks in ADT

A: Average number of axles per truck

ATADTFpn iii 00

Traffic Analysis

m

i i 0

i 1

ESAL p F ( ADT ) T A G D L ( 365 )Y

m: number of load groups

G: Growth factor

D: Directional distribution factor

L: Lane distribution factor

Y: Design period in years

pi : Percentage of the total repetitions for the ith load group

Fi: Factor for equivalent single axle load

ADT0: Average daily traffic at the start of the design period

T: Percentage of trucks in ADT

A: Average number of axles per truck

Predicting Future Traffic Volumes

1. Calculate total number of axle passes (for a given axle type) for the base year.

2. Estimate an annual growth rate based on historical traffic growth (e.g., 3 percent), (usually determined by economists).

3. Select an appropriate model for traffic growth (e.g., linear or exponential).

4. Use growth rate, base traffic, and appropriate model to estimate future traffic volumes.

Growth Factor

Assume yearly rate of growth and use average traffic at the start and end of the design period:

G = 1/2[1 + (1 + r) Y]

Use traffic at the middle of the design period (PCA):

G = (1 + r)0.5Y

The Asphalt Institute uses traffic over the entire design period:

(G)(Y) = [(1 + r)Y - 1] / r

History and Background Principles

for

the Calculation of Equivalent Axle

Load Factor (EALF)

AASHTO 1986/1993 Pavement Design Approach

Assign dimensionless pavement damage units to each axle configuration and load magnitude, referred to as Equivalent Single Axle Load (ESAL) factors.

The reference axle configuration/load for ESAL calculation is a single axle on dual tires inflated to 586 kPa (i.e., 85 lb/in2) carrying a load of 80 kN, (i.e., 18,000 lb)

Mathematically, the ESAL of an axle of load x is defined as:

tx

t

W

WEALF 18

Wtx= Number of x-axle load repetitions after time t. Wt18= Number of 18 kip axle load repetitions after time t.

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2

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23.3

2

18

2

2

18

1

081.040.0

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2.4log

log33.4

log79.4118log79.4log

LSN

LL

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LLW

W

xx

tt

t

x

t

x

t

tx

tx

t

W

WEALF 18

Equivalent Axle Load Factor (EALF) General AASHTO Equation

Based on AASHTO road test results, EALF can be calculated as:

Wtx= Number of x-axle load repetitions after time t. Wt18= Number of 18 kip axle load repetitions after time t. Lx= Load in kips on one single axle, one set on tandem axles and one set of tridem axles. L2= Axle code, 1 for single axle, 2 for tandem axle, and 3 for tridem axle. SN= Structural number. pt= Terminal serviceability Gt= Function of terminal serviceability 18= Value of x when Lx is equal to 18 kips and L2 is one.

AASHTO 1986/1993 Pavement Design Approach

For a given axle configuration and load, the ESAL factors depend on the thickness of the pavement layers and the terminal serviceability selected.

Thickness and strength of flexible pavement is measured by the structural number:

33322211 DmaDmaDaSN

where, D1, D2 and D3 are the layer thicknesses of the asphalt layer (inches), base layer and sub-base layer, respectively and m2, m3 are the drainage coefficients for the base and the sub-base, respectively

Failure Criterion Approach-EALF

The equivalent axle load factor can be determined using the transfer functions:

Fatigue

Rutting:

32

2

ff

f 1 t 1

f

t18 tx

tx t18

N f ( ) ( E )

WESAL Factor =

W

f2 is approximately 4

f5 is approximately 4

AI: f2= 3.291 Shell: f2= 5.671

AI: f5= 4.477 Shell: f5= 4

5

5

18

18

4

f

c

xc

tx

t

f

cd

W

WFactorESAL

fN

Fourth Power Rule 32

2

ff

f 1 t 1

f

t18 tx

tx t18

N f ( ) ( E )

WESAL Factor =

W

5

5

f

d 4 c

f

t18 cx

tx c18

N f ( )

WESAL Factor =

W

AI justification: for single axle load, it’s reasonable to assume that the tensile strains are directly proportional to the axle loads, therefore:

44

18 18

xx L

L

LEALF

Asphalt Institute (AI) used pt=2.5 and SN=5 as input the general AASHTO equation to generate this table.

Axle Load Limits

On the Interstate maximum allowable loads are:

Single axles/dual tires: 89 kN (20,000 lbs),

Tandem axles/dual tires:151 kN (34,000 lbs)

Tridem axles/dual tires:151 kN (34,000 lbs) (i.e., no additional load)

In addition, load on any group of consecutive axles must be lower than W (kN) (Bridge Formula):

where, L is the distance (m) between the extreme axles and N is the number of axles in the group.

3612

1

3048.0224.2 N

N

NLW

Summary- Traffic Analysis

Truck traffic loads are an essential input to pavement design.

The new mechanistic empirical pavement design approach requires detailed axle load spectra as input.

In practice, this data is collected through a combination of ATR, AVC and WIM systems distributed through the transportation network.