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Pavement Design and Construction Traffic for Pavement Design July 2007 Newton C. Jackson Joe P. Mahoney Traffic for Pavement Design Learning Objectives Understand Equivalent Single Axles Loads Why are they needed. How are they calculated. How were they developed.

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pavement design and construction traffic for pavement design

Pavement Design and ConstructionTraffic for Pavement Design

July 2007

Newton C. Jackson

Joe P. Mahoney

traffic for pavement design learning objectives
Traffic for Pavement DesignLearning Objectives
  • Understand Equivalent Single Axles Loads
    • Why are they needed.
    • How are they calculated.
    • How were they developed.
  • Achieve a general understanding of typical axle and wheel loads (both highway and airfield).
  • Achieve a general understanding of typical tire pressures (both highway and airfield).
loads for pavement design
Loads for Pavement Design
  • References:
    • PGI, Module 4-Section 3
    • Topic Notes 2 (pdf file)
  • Duration: 1.5 hours
  • Topics
    • Introduction
    • Terminology
    • Axle load limits
    • FHWA Bridge Formula
    • Repetitions of wheel loads
      • Fourth power law
      • ESALs
    • Simplified method for calculating ESALs
loads introduction
  • Wheel loads—5,000 lb (truck) to 50,000 lb (Boeing 747)
  • Tire pressures
    • Autos: 200 kPa (30 psi)
    • Trucks: Range between 690 to 970 kPa (100 to 140 psi)
    • Boeing 747: 1380 kPa (200 psi)
    • USAF F15: 2350 kPa (340 psi)
  • Load repetitions
  • Axle and tire configurations
  • Distribution of loads across a lane or runway/taxiway—termed wander width.
  • Speed—in general—faster is better for pavements!
loads introduction5

Truck manufacturer (White Star) showing tandem axle with leaf spring suspension. Suspension systems also affect the dynamic wheel loads.

loads introduction6

6 tires

Boeing 777 with tridem gear.

loads introduction7

MD-10 with tandem gear plus a set of duals mid-body.

loads introduction b 36 bomber
Loads—IntroductionB-36 Bomber

Wheel diameter was 9 ft.Each wheel supported about 200,000 lb.

B-36 first flew on August 8, 1946.

Eventually, a dual tandem gear was adopted.


Class 9 truck typically with 5 axles (total) and 18 wheels (2 tandems and one single axle)

review aashto terminology in pgi and tn 2
Review AASHTO Terminology in PGI and TN 2

These definitions represent a sample of those included in Module 4, Section 3.

axle load limits
Axle Load Limits
  • Axle Load Limits—Axle limits not uniform across the U.S. Limits generally higher in other countries.
  • U.S.—single axle load limit—20,000 lb or 9.1 metric tons
  • France—single axle load limit—13 metric tons or 28,665 lb
  • New EU-wide limit is 11 metric tons or 24,255 lb.
axle load limits washington state legal wheel axle and gross vehicle weights
Axle Load Limits—Washington State Legal Wheel, Axle, and Gross Vehicle Weights

Source: PGI, Module 4, Section 3

fhwa bridge formula example 1
FHWA Bridge Formula—Example 1
  • Five axle truck—known dimensions
    • One single axle (steering axle) - 51 ft separation from steering axle to rear portion of back tandem
    • Two tandem axles (34 ft separation for tandems)
    • Each set centered 4 ft apart
  • Determine the maximum gross weight of the truck
  • Calculation
  • W = 500(5(51)/(5-1) + 12(5) + 36)

= 80,000 lb for the group of axles - steering to rear tandem

fhwa bridge formula example 3
FHWA Bridge Formula—Example 3

The question: A partial definition of a tridum axle is three axles whose extreme centers are not more than 144 in. (12 ft) apart.

Calculate the allowable loading according to the bridge formula:


W = 500(3(12)/(3-1) + 12(3) + 36) = 500(90) = 45,000 lb.

tire and contact pressures
Tire and Contact Pressures

load = (pressure)(area)

tire pressure = load/area

= P/r2


r = radius of tire contact,

P = total load on tire, and

Note: Tire pressures are not uniform but are assumed to be so for most pavement analyses.

repetitions of wheel loads 1
Repetitions of Wheel Loads (1)
  • Need to understand what is meant by the term Equivalent Single Axle Load (ESAL)
  • Understand that newer pavement design methods will use load spectra and such data is generated at truck weight stations.
repetitions of wheel loads 2
Repetitions of Wheel Loads (2)
  • Generalized “Fourth Power Law”
  • AASHTO Load Equivalencies
    • Developed from data obtained at the AASHO Road Test
    • ESALs widely used (in general) worldwide
    • Combines effects of various axle loads into one number, which can be used for design (equivalent single axle loads or ESALs).
    • Typical values for Load Equivalency Factors (LEFs)
  • Note log truck example
  • Calculation of LEFs—Formula derived from AASHO Road Test data. Separate formulas for flexible and rigid pavements.
aasho road test
AASHO Road Test

Truck configurations and axle weights

Typical track layout

(Loops 5 and 6)

aasho road test flexible experiment
AASHO Road Test—Flexible Experiment

AASHO Road Test Structural Design Thicknesses

aasho road test rigid experiment
AASHO Road Test—Rigid Experiment

AASHO Road Test Structural Design Thicknesses

  • The design concept of the equivalent single axle load (ESAL) emerged from the AASHO road test and its volumes of data.  Both the flexible and rigid ESAL equations and their corresponding calculated load equivalency factors (LEFs) are still used today in the 1993 AASHTO Guide.
  • ESALs (or E80s) are widely used to characterize design traffic throughout the world.
an approximate approach the 4 th power law
An Approximate ApproachThe 4th Power Law

Approximate LEF ~ (axle load in question/standard axle load)4

and typically the standard axle load is 18,000 lb. or 80 kN

an approximate approach the 4 th power law an example
If a truck is hauling rock and has 3 axles.

Steer axle: 20000 lb

Drive axle: 30000 lb

Rear axle: 30000 lb

Question: Approximately how many ESALs does this truck represent?


Steer: (20000/18000)4=1.5

Drive: (30000/18000)4=7.7

Rear: (30000/18000)4=7.7

An Approximate ApproachThe 4th Power LawAn Example

16.9 ESALs

simpified method for calculating esals
Simpified Method for Calculating ESALs
  • Forecasting bus and truck traffic—FHWA vehicle Classes 1 through 13.
  • Singles, Doubles, Trains—terms defined shortly.
  • Load equivalency factor approximations.
  • Special note is made of Bus ESALs.
  • Note conversion of flexible to rigid ESALs—be careful. Also note early Weigh-in-Motion results and WSDOT ESAL per vehicle approximations.
esals due to buses 2
ESALs Due to Buses (2)

Data for Seattle area buses—from about 1987 to 1993. Buses can be quite heavy and represent much of the traffic for pavement design in urban areas.

esal calculation 1
ESAL Calculation (1)
  • Traffic count or just skip to 2.
  • Count or estimate the number of heavy vehicles. Do not be concerned with cars—they do not weigh enough to matter.
  • Estimate heavy traffic growth rate over the design life of the pavement.
  • Select appropriate LEFs to convert truck and bus traffic to ESALs.
  • Compute ESALs for the design life.
esal calculation 2
ESAL Calculation (2)
  • The goal is to estimate ESALs over the design life of the pavement structure.
  • Typical pavement design lives are 20 to 50 years.
  • Best to start by calculating the ESALs/year then multiply by the design life.
esal calculation 3
ESAL Calculation (3)
  • Assume a road has a constant amount of trucks each day = 500 trucks
  • Each truck has the same ESAL/truck of 3.0
  • ESALs/year: (500 trucks/day)(3.0 ESALs/truck)(365 days/year) = 550,000 ESALs/year
  • If the pavement design life is 40 years and the truck traffic does not vary from year to year, then the total design ESALs = 22 million
esal calculation 4
ESAL Calculation (4)
  • What if the truck data from (3) increases by a rate of 2.5% per year. How does that effect the total design life ESALs?
  • ESALs/year for the 1st year = (500 trucks/day)(3.0 ESALs/truck)(365 days/year) = 550,000 ESALs/year
  • ESALs/year for Year 40 = 550,000(1 + i)40 = 550,000(1 + 0.025)40  1,500,000
  • (Average Year 1 and Year 40) x 40 years = 41,000,000 ESALs over a 40 year design life. Thus, almost double the ESAL level without consideration of a growth rate.
esal calculation 5
ESAL Calculation (5)

Assume a log truck has three axles:

(a) Truck tractor

• Steering axle (single axle) = 14,000 lb (62.2 kN)

• Drive axle (tandem axle) = 34,000 lb (151.1 kN)

(b) Trailer

• Pole trailer axle (tandem axle) = 30,000 lb (133.3 kN)

(c) The total equivalent damage by this truck is (pt = 3.0, SN = 3):

• Steering axle @ 14,000 lb = 0.47 ESAL

• Drive axle @ 34,000 lb = 1.15 ESAL

• Pole axle @ 30,000 lb = 0.79 ESAL

Total = 2.41 ESALs

(d) If a pavement was subjected to 100 of these trucks each day (in one direction) for 20 years (5 days per week), the total ESALs for this truck would be

  • (5 day/7 day)(365 days/year)(20 years)(100 tk/day)(2.41 ESAL/tk)= 1,256,643 ESAL  1,300,000 ESALs

This example uses actual LEFs from the AASHTO Design Guide; hence the use pt and SN (which are yet to be defined).

esal calculation 6
ESAL Calculation (6)
  • Now, let’s take a typical CUSA truck and sort out some ESAL calculations.
  • Number of axles?
  • Approximate weight of those axles?
  • How many per day? Days per year?