appendix ear rb tr quad axle report

7/30/2019 Appendix Ear Rb Tr Quad Axle Report

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Austroads ProjectReport

Estimates of Equivalent Load for aQuad Axle

This report is being released as a reference work. This report iscommissioned work and represents the views of the consultant andhas not been considered by the Austroads Council. The report is theresult of work undertaken on Austroads behalf, for the project onperformance based standards for heavy vehicles being managed bythe National Road Transport Commission.

Reviewed

Project Leader

Binh T Vuong

Quality Manager

Geoff W Jameson

RC2776-


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Although the Report isbelieved to be correct atthe time of publication,ARRB Transport researchLtd, to the extent lawful,excludes all liability for loss(whether arising undercontract, tort, statute orotherwise) arising from thecontents of the Report orfrom its use. Where suchliability cannot beexcluded, it is reduced tothe full extent lawful.Without limiting theforegoing, people should

apply their own skill andjudgement when using theinformation contained inthe Report.


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ESTIMATES OF EQUIVALENT LOAD FOR A QUAD AXLE


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Estimates of Equivalent Load for a Quad AxleFirst Published 2013

Austroads Inc. 2013

This work is copyright. Apart from any use as permitted under the Copyright Act 1968,no part may be reproduced by any process without the prior written permission of Austroads.

National Library of AustraliaCataloguing-in-Publication data:

Estimates of Equivalent Load for a Quad AxleISBN

Austroads Project No.

Austroads Publication No.

Project ManagerPhil W Rankine

Prepared byBinh Vuong

ARRB Transport Research Ltd

Published by Austroads IncorporatedLevel 9, Robell House287 Elizabeth Street

Sydney NSW 2000 AustraliaPhone: +61 2 9264 7088Fax: +61 2 9264 1657

Email: [email protected]

Austroads believes this publication to be correct at the time of printing and does not accept responsibility forany consequences arising from the use of information herein. Readers should rely on their own skill and

judgement to apply information to particular issues.
mailto:[email protected]:[email protected]


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ESTIMATES OF EQUIVALENT LOAD FOR A QUAD AXLE

Sydney 2001


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AUSTROADS PROFILE

Austroads is the association of Australian and New Zealand road transport and traffic authorities whosepurpose is to contribute to the achievement of improved Australian and New Zealand transport relatedoutcomes by:

developing and promoting best practice for the safe and effective management and use of the road system

providing professional support and advice to member organisations and national and international bodies acting as a common vehicle for national and international action

fulfilling the role of the Australian Transport Councils Road Modal Group

undertaking performance assessment and development of Australian and New Zealand standards

developing and managing the National Strategic Research Program for roads and their use.

Within this ambit, Austroads aims to provide strategic direction for the integrated development, managementand operation of the Australian and New Zealand road system through the promotion of national uniformityand harmony, elimination of unnecessary duplication, and the identification and application of world best

practice.

AUSTROADS MEMBERSHIP

Austroads membership comprises the six State and two Territory road transport and traffic authorities and theCommonwealth Department of Transport and Regional Services in Australia, the Australian LocalGovernment Association and Transit New Zealand. It is governed by a council consisting of the chiefexecutive officer (or an alternative senior executive officer) of each of its eleven member organisations:

Roads and Traffic Authority New South Wales

Roads Corporation Victoria

Department of Main Roads Queensland

Main Roads Western Australia

Transport South Australia Department of Infrastructure, Energy and Resources Tasmania

Department of Transport and Works Northern Territory

Department of Urban Services Australian Capital Territory

Commonwealth Department of Transport and Regional Services

Australian Local Government Association

Transit New Zealand

The success of Austroads is derived from the synergies of interest and participation of member organisationsand others in the road industry.


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EXECUTIVE SUMMARY

The National Road Transport Commission (NRTC) and Austroads are sponsoring two major projects that arecentral to the development of a Performance Based Standards (PBS) approach to the regulation of heavyvehicles in Australia. The two projects, 'Specification of Performance Standards for Heavy Vehicles (Project

A3)'and 'Documentation of the Performance of the Current Fleet (Project A4)', have the primary aims of:

1) determining and establishing agreement with the jurisdictions and industry on the 'standards' to apply foran agreed set of Performance Measures; and

2) documenting the performance of nominated vehicles within the current heavy vehicle fleet using cost-effective sources, including available records, calculation and the results of computer simulation.

There has been general agreement to adopt the performance measure of Gross Mass per vehicle Standard AxleRepetitions (SAR) for PBS vehicles. However, there is concern as to whether which performance level(standard) of this measure could be set to:

reflect the current specification in terms of Gross Mass limits for different fleet vehicle classes; and

protect existing pavements from excessive loads.

The calculation of SAR requires the use of equivalent loads of common axle groups, which cause samedamage as a Standard Axle, as given below.

Axle Group Singleaxle/singletyres

SAST

Singleaxle/dualtyres

SADT

Tandemaxle/singletyres

TAS

Tandemaxle/dualtyres

TADT

Triaxle/dualtyres

TRIDT

Load (kN) 53 80 90 135 181

Austroads (NRTC) recently commissioned ARRB Transport Research to carry out an investigation toestimate the equivalent load for a quad axle that can be adopted for the calculation of SARs for flexible

pavements. The 2001 Draft Austroads Guide has procedures for assessing quad axle damage to concretepavements.

A literature review of the current equivalent axle loads being adopted for flexible pavements by different roadauthorities throughout the world indicates that equivalent loads for quad axle have not yet been developed foruse in any pavement design procedures.

Different pavement design procedures adopt different standard axle loads, different pavement damage criteria,and different procedures for the determination of equivalent axle loads. As such the procedures for estimatingof equivalent axle loads adopted in other pavement design procedures may not be readily applied to theAustroads pavement design procedures to estimate equivalent loads for quad axle.

Four procedures were used to estimate the equivalent load of a quad axle, namely:

Extrapolation of the existing relationships between axle group load and number of tyre per axle group asadopted by different Road Authorities.

Extrapolation of the relationship of predicted surface deflection and number of tyre per axle group: The

Austroads mechanistic design procedures are used to calculate the surface deflection.

Extrapolation of the relationship of predicted critical strain and number of tyre per axle group: The

Austroads mechanistic design procedures are used to calculate the critical strain.

Calculation of Group Equivalence Factor using the South African method: The Austroads mechanistic

design procedures is used to predict pavement deflection, critical strain and design life.

Three granular pavements (which have thickness in the range of 250-480 mm and subgrade CBR in the rangeof 5-15%), one full depth asphalt pavement and one CTCR Subbase asphalt pavement were used in this study.

Comparison of the estimates of equivalent load of a quad axle derived by different procedures indicates thatthe load-extrapolation and critical strain-extrapolation procedures produce consistent estimates of equivalentload of a quad axle, which are in the range of 215-226 kN. These estimates are slightly lower than the

i


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estimates produced by the maximum deflection-extrapolation procedure (in the range of 222-247 kN), andmuch lower than the estimates produced by the South African approach (in the range of 266-339 kN). Giventhat the South African approach consistently produces higher estimates of equivalent loads for all axle grouptypes (tandem-axle, tri-axle and quad-axle), it is considered that this method is inconsistent with the currentAustroads accepted values. As such the South Africa approach will need to be investigated further,

particularly the consideration of the influence of axle spacing, tyre pressure, material type and damage criteria(for different pavement types and classes).

It is recommended that

As interim measure a quad axle of 221 kN (22.5 tonne) be considered to cause equivalent damage to a

Standard Axle.

Further investigation of the South African approach to changing elastic properties with axle loads and tyre

pressure to investigate the influence of nonlinear material properties on the estimates of equivalent axleloads.

Further analysis will be undertaken to confirm this equivalent load of quad-axle is appropriate in terms of

damage to pavements with asphalt and cemented materials.

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TABLE OF CONTENTS

Page1. Introduction.............................................................................................................................................................12.Equivalent Axle Loads Adopted in Various Countries............................................................................................13.Procedures for the Determination of Equivalent Axle Loads Adopted in Various Countries...............................2

3.1 Standard Axle Load (or Reference Axle Load).................................................................................................................23.2 Pavement Damage Criteria................................................................................................................................................23.3 Procedures Used to Derive Equivalent Axle Loads...........................................................................................................33.4 Procedures to Calculate Equivalent Axle of Loading........................................................................................................4

4.Estimation of Equivalent Loads for Quad Axle for Flexible Pavements (Austroads 1992)...................................54.1 Austroads Mechanistic Pavement Design Procedure for Flexible Pavements................................................................54.2 Procedures Used to Estimate Quad Axle Equivalent Load...............................................................................................7

5. Comparison of Estimates of Equivalent Loads of Quad Axle..............................................................................146. Summary................................................................................................................................................................177. Recommendation...................................................................................................................................................17

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TABLES

TABLE 1COMPARISON OF EQUIVALENT LOADS FOR AXLE GROUP TYPES FOR FLEXIBLE PAVEMENTS....2

TABLE 2

COMPARISON OF PROCEDURES FOR THE DERIVATION OF EQUIVALENT LOADS FOR AXLEGROUP TYPES..................................................................................................................................................................3

TABLE 3DAMAGE EXPONENTS FOR ALL PAVEMENT TYPES (AUSTROADS 1992)....................................................6

TABLE 4PAVEMENTS USED IN THE ANALYSIS.....................................................................................................................9

TABLE 5ESTIMATES OF EQUIVALENT LOADS FOR QUAD AXLE BASED ON EXTRAPOLATION OFEQUIVALENT SURFACE DEFLECTION....................................................................................................................9

TABLE 6ESTIMATES OF EQUIVALENT LOADS FOR QUAD AXLE BASED ON EXTRAPOLATION OFEQUIVALENT CRITICAL STRAIN.......................................................................................................................... ..11

TABLE 7ESTIMATES OF EQUIVALENT AXLE LOADS FOR GRANULAR PAVEMENTS USING GROUPEQUIVALENCE FACTOR (GEF) ...............................................................................................................................14

TABLE A1COMPARISON OF EQUIVALENT LOADS FOR AXLE GROUP TYPES (FLEXIBLE PAVEMENTS).........18

TABLE A2COMPARISON OF EQUIVALENT LOADS FOR AXLE GROUP TYPES (FOR RIGID PAVEMENTS)........22

TABLE A3AXLE GROUP LOAD FOR AUSTROADS LEF OF 1 (EROSION) AND COMPARISON WITH AASHTOPROCEDURE...................................................................................................................................................................24

FIGURES

FIGURE 1 EXTRAPOLATION OF EQUIVALENT LOAD OF A QUAD AXLE BASED ON EXITING

AUSTROADS RELATIONSHIP BETWEENLOAD PER AXLE GROUP AND NUMBER OF TYRES...........................................................................................8

FIGURE 2 EXTRAPOLATION OF EQUIVALENT SURFACE DEFLECTION OF A QUAD AXLE BASEDON EXITING RELATIONSHIPS BETWEEN CALCULATED SURFACE DEFLECTION PER AXLEGROUP AND NUMBER OF TYRES............................................................................................................................10

FIGURE 3 EXTRAPOLATION OF EQUIVALENT CRITICAL SUBGRADE STRAIN OF A QUAD AXLEBASED ON EXITING RELATIONSHIPS BETWEEN CALCULATED CRITICAL SUBGRADE STRAINPER AXLE GROUP AND NUMBER OF TYRES.......................................................................................................11

FIGURE 4 EXTRAPOLATION OF EQUIVALENT CRITICAL TENSILE STRAIN OF A QUAD AXLEBASED ON EXITING RELATIONSHIPS BETWEEN CALCULATED CRITICAL TENSILE STRAIN PERAXLE GROUP AND NUMBER OF TYRES................................................................................................................12

FIGURE 6 COMPARISON OF EQUIVALENT AXLE LOADS ACCEPTED BY DIFFERENT ROADAUTHORITIES THROUGHOUT THE WORLD.......................................................................................................15

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FIGURE 7 COMPARISON OF ESTIMATES OF EQUIVALENT LOADS OF A QUAD AXLE BASED ON

DIFFERENT EXTRAPOLATION APPROACHES....................................................................................................15

FIGURE 8 COMPARISON OF ESTIMATES OF EQUIVALENT LOADS FOR VARIOUS AXLE GROUPSPRODUCED BY THE AUSTROADS AND SOUTH AFRICAN MECHANISTIC DESIGN PROCEDURES(BOTH WITH THE SOUTH AFRICAN EDF)............................................................................................................16

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Estimates of Equivalent Load for a Quad AxleRC2776-

1. Introduction

The National Road Transport Commission (NRTC) and Austroads are sponsoring two major projects that arecentral to the development of a Performance Based Standards (PBS) approach to the regulation of heavy

vehicles in Australia. The two projects, 'Specification of Performance Standards for Heavy Vehicles (ProjectA3)'and 'Documentation of the Performance of the Current Fleet (Project A4)', have the primary aims of:

3) determining and establishing agreement with the jurisdictions and industry on the 'standards' to apply foran agreed set of Performance Measures; and

4) documenting the performance of nominated vehicles within the current heavy vehicle fleet using cost-effective sources, including available records, calculation and the results of computer simulation.

There has been general agreement to adopt the performance measure of Gross Mass per vehicle Standard AxleRepetitions (SAR) for PBS vehicles. However, there is concern as to whether which performance level(standard) of this measure could be set to:

reflect the current specification in terms of Gross Mass limits for different fleet vehicle classes; and

protect existing pavements from excessive loads.The calculation of SAR requires the use of equivalent loads of common axle groups, which cause samedamage as a Standard Axle, as given below.

Axle Group Singleaxle/singletyres

SAST

Singleaxle/dualtyres

SADT

Tandemaxle/singletyres

TAST

Tandemaxle/dualtyres

TADT

Triaxle/dualtyres

TRADT

Load (kN) 53 80 90 135 181

Austroads (NRTC) recently commissioned ARRB Transport Research to carry out an investigation toestimate the equivalent load for a quad axle that can be adopted for the calculation of SARs for flexiblepavements. The 2001 Draft Austroads Guide has procedures for assessing quad axle damage to concretepavements.

This report describes the investigation, which consists of three parts:

A review of Australian and overseas literature with respect to equivalent loads of axle groups that causeequal pavement damage to both flexible and rigid pavements.

A review of procedures/models currently being adopted to estimate the equivalent load of axleconfigurations with multiple axles (tandem, tridem and quad axles).

A study to estimate the equivalent load for a quad axle that can be adopted for the calculation of SARs for

flexible pavements using the Austroads pavement design procedures.

2. Equivalent Axle Loads Adopted in Various Countries

A literature review was conducted to compare the current equivalent axle loads being adopted for both flexibleand rigid pavements by different road authorities in different countries throughout the world. Appendix A

provides a summary of this literature review, including the background to the equivalent axle loads currentlyrecommended in the Austroads (1992) Pavement Design Guide.

Table 1 summarises the results of equivalent axle loads (or axle loads of equal damage) for flexible pavementsbeing adopted by different road authorities. The results indicate that equivalent loads for quad axle have notyet been developed for use in any pavement design procedures. Therefore, it is imperative to select a

procedure/model that can determine or estimate the equivalent loads for new axle configurations of future

Prepared by ARRB Transport Research Ltd1


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generations of heavy vehicles such as quad axle. The procedures/models currently being adopted to determineequivalent axle loads that cause equal pavement damage are briefly discussed below.

Table 1Comparison of Equivalent Loads for Axle Group Types for Flexible Pavements

AxleGroupType

Austroads(1992)1

AASHTO(1993)2

Departmentof Transport,South Africa

(1997)3

Ministry ofTransportation

(Canada)

LCPC andSETRA,

France (1997)

Department ofTransport,

Great Britain(1993)

SAST 53 kN NA 4 61 kN 61 kN NA 4 NA

SADT 80 kN 80 kN 80 kN 78 kN 130 kN NA

TADT 135 kN 151 kN 134 kN 126 kN 275 kN NA

TRIDT 181 kN 214-205 kN 187 kN. 172 kN 383 kN NA

Note 1: Tyre pressure of 550 kPa and axle spacing of 1320 mm were used in Austroads (1992)Note 2: Axle spacing of 1219 mm (4 ft) was used in the AASHTO Road TestsNote 3: Values derived using tyre pressure of 520 kPa and axle spacing of 1400 mmNote 4: AASHTO (1993) and LCPC and SETRA (1997) provide no guidance for SAST

3. Procedures for the Determination of Equivalent Axle Loads Adopted in VariousCountries

Table 2 compares various components of the procedures for determining/estimating equivalent axle loadsadopted by various road authorities throughout the world. The differences between the procedures adopteddifferent road authorities are briefly discussed below.

3.1 Standard Axle Load (or Reference Axle Load)

A Standard Axle load is often selected as the most common axle configuration, which is used as the referenceload to compare damaging effects of loads on different axle configurations.

Referring to Table 2, most road authorities (e.g. Austroads, AASHTO and Department of Transport SouthAfrica) define the Standard Axle as a dual-tyred single axle (SADT) transmitting a load of 80 kN to the

pavement. However, Ministry of Transportation in Canada adopts a slightly lower SADT load of 78 kN,whereas France adopts a much higher SADT load of 130 kN.

3.2 Pavement Damage Criteria

Pavement damage criteria describe a specific level of pavement damage to be used in the comparison of

damaging effects of loads on different axle configurations.Referring to Table 2, different road authorities adopt different damage criteria in the comparison of damagingeffects of loads on different axle configurations.

AASHTO (1993) equivalent axle loads were derived from data collected during the AASHO Road Test,

by referencing pavement damage toa terminal serviceability value (pt). Pavement designers may selectdifferent specific terminal serviceability values for different pavement types and classes in thedetermination of equivalent axle loads.

Austroads (1992) equal axle loads are based on the assumption that axle groups that produce same

maximum deflection for a given pavement would cause equal pavement damage. This principle wasreasonably well supported by limited data from the AASHO road test, from which Scalas (1970a)estimated relative destructive effects, used a number of pavements of known construction. Given that the



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pavement damage is not specifically defined, the comparison is strictly based on relative damage (ratherthan absolute damage).

The South African method (Prozzi and de Beer 1997) considers total pavement damagefrom damages

of individual layers in the pavement, in terms of fatigue failure for bound layers and deformation (orshearing) failure for granular layers and subgrade. As such the total life of an asphalt pavement with

cement-treated subbase may have different phases, including fatigue failure of the cement-treated subbasein phase 1, fatigue failure of the asphalt surface in phase 2 and shearing of the granular subbase and/orsubgrade in phase 3.

Highways Directorate of France refers pavement damage to the fatigue damage of the surface bound

layers caused by the applied axle loads.

Table 2Comparison of Procedures for the Derivation of Equivalent Loads for Axle Group Types

PavementDesign

Procedure

StandardAxle Load

Pavement Damage Criteria Procedures to derive axleload of equal damage

Procedures to calculateequivalent axle loads

Austroads(1992)

80 kN SADT Equal maximum surfacedeflection cause equalpavement damage

Response to load onpavements with chip sealand thin asphalt surfacingusing SAST, SADT, TADT,and TRIDT (one level of tyrepressure)

Standard Axles Repetitions(SAR) from mixed traffic(damage exponent varieswith distress mode) Equivalent Standard Axle(ESA) when the fourth powerlaw is applied

AASHTO(1993)

18 kips (80kN) SADT

Total pavement damage interms of terminalserviceability value (pt),

[pt = 2.0-3.0]

Performance data obtainedfrom AASHO Road Testusing SADT and TADT (onelevel of tyre pressure)

Equivalent Standard AxleLoad (ESAL) procedures toestimate equivalent loads forTRIDT (one level of tyrepressure) from performancedata of in-service pavements

Dept ofTransport

(South Africa)

80 kNSADT

Total pavement damagefrom damages of individuallayers in the pavement, interms of fatigue failure forbound layers anddeformation (or shearing)failure for granular layersand subgrade

Equivalent Damage Factor(EDF) procedures to estimateequivalent loads for SAST,TADT, TRIDT from totaldesign life (predicted withDOT SA mechanistic designprocedures)

Ministry ofTransp.(Canada)

78 kN SADT ? Equivalent Standard AxleLoad (ESAL) Procedures toestimate equivalent loads forSAST, TADT, TRIDT from

performance data of in-service pavements (?)

HighwaysDirectorate

(France)

130 kNSADT

Fatigue failure of surfacelayer

Axle Aggressiveness (A)Procedures to estimateequivalent loads for TADTand TRIDT fromperformance data (?)

3.3 Procedures Used to Derive Equivalent Axle Loads

A procedure to derive equivalent axle loads allows measuring/determining the axle configurations that are

considered equivalent to the Standard Axle load, i.e. all axle configurations produce the same the number ofrepetitions that causes the same pavement damage.



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Referring to Table 2, different road authorities adopt different methods for measuring/determining equivalentaxle loads.

In the AASHTO road tests, the number of repetitions of the SADT and TADT (with loads up to 133 kN

and 214 kN, respectively) that caused pavement damage to a terminal serviceability value could bedetermined. From the test results, it was possible to deduce the equivalent load for TADT (see Table 1)

that produced the same damage as the Standard 80 kN SADT.

Austroads (1992) derived the axle loads of equivalent damage for SAST, TADT and TRIDT (see Table

1) from deflection data produced by field testing with different axle groups on granular and thin asphalt-surfaced pavements (Scala 1970a, 1970b). In this field study, actual trucks with different axleconfigurations were loaded to different loads to determine the load for each axle configuration that

produced the same vertical pavement deflections as that produced by the Standard 80 kN SADT for eachpavement case.

3.4 Procedures to Calculate Equivalent Axle of Loading

Performance data obtained from in-service pavements are generally influenced by mixed traffic. To convert a

mixed traffic into the total design traffic, expressed in terms of equivalent Standard Axle loads (EASL),requires factors applied to each axle group, which are often called as Load Equivalency Factors (LEF).

Referring to Table 2, different LEF procedures are adopted in various pavement design procedures.

AASHTO (1993) firstly used the Equivalent Standard Axle load (ESAL) procedure to compare the

damage caused by different axle configurations. In this procedure, the damage caused by a passage of agiven axle over the pavement is described in terms of a unit damage caused by the standard 80 kN SADT.Using this concept, each axle type will have a Load Equivalency Factor, which is defined as:

unit damage caused by the passage of the axle/unit damage caused by the passage of a Standard Axleload (expressed in ESALs).

This concept can be extended to determine the load equivalency for each vehicle, which is the sum of the

LEFs of each axle group constituting the vehicle. As discussed above, AASHTO (1993) used theperformance data obtained from the AASHTO road tests to determine the equivalent loads for TADT.However, the equivalent load for TRIDT (see Table 1) was estimated using the EASL procedures and

performance data observed from in-service pavements.

Austroads (1992) uses Standard Axle Repetitions (SAR) to estimate design traffic from mixed traffic. In

this case, SAR is the number of Standard Axles that will provide the same damage as that caused by thevarious group types. Various values of damage exponents (4, 5, 7, 122) are used depending on distresstype. When using a damage exponent of 4, the Standard Axle Repetition is called Equivalent (ESA).Given that equivalent loads for SAST, TADT, TAST and TRIDT could be determined by deflection-to-load testing (see Table 1), these procedures are not used to predict equivalent axle loads.

Department of Transport South Africa (1997) used the procedures developed by Prozzi and de Beer

(1997) to determine the Equivalent Damage Factor (EDF), which is the number of repetitions of theStandard Load Configuration (identical to a Standard Axle) that will cause the same damage as the givenaxle group. In this procedure, the EDF recognises the influence of the axle spacing within an axle group(Group Equivalence Factor), the mass on the axle group (Axle Load Factor) and the tyre contact stress(Contact Stress Factor):

EDF = GEF x ALF x CSF (1)

where EDF = Equivalent Damage Factor,

GEF = Group Equivalence Factor,

ALF = Axle Load Factor, and

CSF = Contact Stress Factor.

GEF takes into account the effects of inter-axle spacing and represents the ratio between the allowableloading under the single axle to the life under a group with multiple axles (tandem and tridem axles). ALF



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assesses the influence of axle load and is the ratio between the allowable loading under 80 kN single axleto the life under an axle of any given group. CSF considers the effect of contact stress and is the ratio

between the allowable loading under a contact stress of 520 kPa to the life under any given contact stressat the same axle load of 80 kN.

Prozzi and de Beer (1997) incorporated the EDF procedures into the South African mechanistic design

procedures to predict equivalent loads for SAST, TADT and TRIDT (see Table 1) that produce the samethe total life as the Standard Load Configuration. In this method, fatigue life of a bound layer anddeformation life of a granular layer or subgrade are predicted from the critical strain or stress in the layersconcerned, which are calculated with a linear-elastic layered model. Material inputs into this model aredetermined from a suit of laboratory testing methods. The relationships between fatigue/deformation lifeand critical stress/strain (Transfer Functions) are developed based on both material performance data fromlaboratory testing and pavement performance data from accelerated pavement testing with the HeavyVehicle Simulator (HVS).

The method adopted by the Highways Directorate of France considers the Aggressiveness of an Axle,

which is based on the fatigue damage caused to the pavement. Aggressiveness, A, corresponds to thedamage caused by one passage of an axle load (P) compared to the damage due to one passage of the

reference isolated

1

axle load (PO). Aggressiveness (A) is determined using the following relationship(LCPC and SETRA 1997):

=PO

PkA (2)

where

A = Aggressiveness;

P = load on each axle of the axle group;

PO = reference axle (dual-wheel isolated [single] axle, weighing 130 kN);

= constant depending on pavement type (flexible, semi-rigid or concrete); and

k = constant depending on axle type (single, tandem or triaxle).

As the reference axle load is different from a Standard Axle, the French equivalent axles cannot bereadily compared to values derived using other pavement design procedures.

In summary, different pavement design procedures adopt different standard axle loads, different pavementdamage criteria, and different procedures for the determination of equivalent axle loads. As such the

procedures for estimating of equivalent axle loads adopted in other pavement design procedures may not bereadily applied to the Austroads pavement design procedures to estimate equivalent loads for quad axle.

4. Estimation of Equivalent Loads for Quad Axle for Flexible Pavements (Austroads1992)

4.1 Austroads Mechanistic Pavement Design Procedure for Flexible Pavements

The Austroads mechanistic pavement design procedure (Austroads 1992) for flexible pavements is based onsemi-empirical approach and has two components:

a pavement response model to predict critical strains in pavement layers under standard loads, and

various empirical performance relationships to estimate the allowable number of loading cycles ofstandard loads on the selected pavement.

For practical reasons, Austroads adopts the simple linear elastic layered model CIRCLY with the followingconsiderations in the selection of loading input and critical strains.

1 Isolated axle [group] is when the nearest axle is greater than 2 m distant.



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Loading input is expressed in terms of standard axles of equivalent damage, which equate to a standardsingle axle, dual tyre arrangement loaded to 8.2 tonne. In the standard analysis procedure with CIRCLY,the loading is simulated as a half-standard axle (i.e. only one pair of tyres) and only vertical loading (i.e.no shear force) being applied.

For pavements with bound surface layers that have high capacity to sustain high vertical and horizontal

stress (asphalt, cemented material and concrete), material fatigue is the major failure mode. CIRCLY canbe used to model the linear elastic behaviour of bound materials and produces consistent estimation ofmaximum tensile strain in each bound layer, the critical parameter for fatigue failure.

For predicting permanent deformation, the Austroads design method uses the maximum compressive strainat top of the subgrade as the performance index parameter.

The vehicle-pavement conditions applied in the standard analysis procedures with CIRCLY are equivalent tosteady speed travel without consideration of horizontal tyre force for uphill grade, turning, start-up and

breaking operations. Based on the above considerations, Austroads has established three empirical pavementallowable loading-critical strain relationships to predict bound layer fatigue cracking and deformation

performance, viz.

NDeform = (KDeform/SG )

7.14

(3)

NAC = (KAC /AC)5

(4)

NCT = (KCT /CT)12

(5)

Where

NDeform = Pavement deformation allowable loading, i.e number of loading repetitions (standard axle)which produce a terminal rutting and shoving (say 20 mm).

NAC = Asphalt fatigue allowable loading, i.e. number of loading repetitions (standard axle) whichproduce a terminal cracking of the asphalt layer.

NCT = Cemented material fatigue allowable loading, i.e. number of loading repetitions (standardaxle) which produce a terminal cracking of the cemented material layer.

SG = the magnitude of the peak vertical compressive strain at the top of the subgrade calculated

under vertical loading (without shear force) using CIRCLY.

AC = the magnitude of the peak horizontal tensile strain at bottom of the asphalt layer calculated

under vertical loading (without shear force) using CIRCLY.

CT = the magnitude of the peak horizontal tensile strain at bottom of the cemented material layer

calculated under vertical loading (without shear force) using CIRCLY.

In these relationships, deformation life or cracking life is expressed in terms of the loading index StandardAxles of allowable loading.

Austroads (1992) also assumes that there is a linear relationship between vertical loading and critical strain,which means that the damage exponents (DE) and criteria as given in Table 3 may also be applied to the load-damage relationships for analyses with different vertical loads (without shear forces).

Table 3Damage Exponents for All Pavement Types (Austroads 1992)

Distress Mode Critical Strain Criterion Constant

K

DamageExponent

DE

Asphalt fatigue Maximum tensile strain atbottom of asphalt layer

A function of bindercontent and mix stiffness

5

Cemented material Maximum tensile strain at A function of layer 12



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fatigue bottom of cemented materiallayer

stiffness

Total permanentdeformation

Maximum compressive strain attop of subgrade

8511 7.14

4.2 Procedures Used to Estimate Quad Axle Equivalent Load

It is imperative that the Austroads procedure for the determination of the equivalent axle loads (i.e. fieldtesting to determine equal maximum surface deflection) be used for quad axle to be consistent with the currentAustroads accepted values for SAST, SADT, TADT and TRIDT. However, it was commented by Prozzi andde Beer (1997) that the Austroads approach is only valid, or approximately valid, when the performance ofthe pavement is governed by the behaviour of the lower layers, i.e. selected layers or subgrade. Theapproach has some shortcomings due to the surface deflection not being directly related to some pavementresponse parameters. Therefore, there is a need to investigate the effects of material properties on the validityof the Austroads approach.

The Department of Transport South Africa has incorporated the Equivalent Damage Factor (EDF) procedureinto their mechanistic pavement design to predict equivalent loads for SAST, TADT and TRIDT. This EDF

procedure may also have the potential to be developed further for incorporation into the Austroads mechanisticdesign procedures to predict equivalent loads for different axle configurations, particularly for bound

pavements. Therefore, there is a need to investigate the incorporation of the South African EDF procedureinto the Austroads mechanistic design to determine validity of this approach.

Given the lack of field data for the determination of equivalent load for quad axle, it is proposed to use thefour following theoretical procedures to estimate the equivalent load for quad axle for flexible pavements:

Procedure 1: Extrapolation of the existing Austroads relationships between axle group load and number

of tyre per axle group.

Procedure 2: Extrapolation of the relationship of predicted surface deflection and number of tyre per axle

group The Austroads mechanistic design procedures are used to calculate the surface deflection.

Procedure 3: Extrapolation of the relationship of predicted critical strain and number of tyre per axle

group The Austroads mechanistic design procedures are used to calculate the critical strain.

Procedure 4: Calculation of Group Equivalence Factor using the South African method The Austroads

mechanistic design procedures are used to predict pavement deflection, critical strain and design life.

4.2.1 Extrapolation of Austroads Equivalent Loads for Common Axle Groups

Figure 1 shows the relationship between current Austroads accepted values of Equivalent Loads for axlegroup with dual tyres (SADT, TADT and TRIDT) and number of tyre per axle group.



19/40


Axle Group Load versus Number of Tyres

y = 28.559x0.7444

R2

= 0.9999

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Loa

dper

Ax

leGroup

(kN)

Austroads (1992)

SADT TADT TRIDT UADT

Figure 1 Extrapolation of equivalent load of a quad axle based on exiting Austroads relationship betweenload per axle group and number of tyres

The relationship inFigure 1 is best presented by the power function

Y = 31.9888 X0.6914

(with the fitting R2

= 0.997) (6)

where

Y = equivalent load per axle group (kN)

X = number of tyre per axle group

The estimate of the equivalent load for quad axle (X = 16 tyres) based on extrapolation of the aboverelationship is 225 kN.

4.2.2 Extrapolation of Predicted Surface Deflection

Three granular pavements with thin surface seal, which have thickness in the range of 250-480 mm andsubgrade CBR in the range of 5-15%, a full depth asphalt and an asphalt pavement with cemented subbase

were considered in this study. Their details are given in Table 4.



20/40


Table 4Pavements Used in the Analysis

PavementNo

Surfacethickness and

Type

Base Thicknessand Type

Upper SubbaseThickness and

Type

Lower SubbaseThickness and

Type

Subgrade

(CBR)

1 Sprayed seal 250 mmcrushed rock

- - 15


- - 10


- - 5

4 40 mm Size 14mm Mix

(2,200 MPa)

180 mm Size 20mm Mix

(2500 MPa)

- - 5

5 40 mm Size 14

mm Mix(2,200 MPa)

110 mm Size 20

mm Mix(2500 MPa)

120 mm CTCR

(2000 MPa)

200 mm granular 5

For each pavement, the Austroads mechanistic design procedures are used to calculate the maximum surfacedeflections (between or under the tyres) using the Austroads accepted values of Equivalent Loads for axlegroups with dual tyres (SADT, TADT and TRIDT), and the results are given in Table 5.

Referring to Table 5, for granular pavement with thin surface seals (Pavements 1, 2 and 3), the Austroadsaccepted Equivalent Loads for SADT, TADT and TRIDT produce similar maximum surface deflections.However, for bound pavements (Pavements 4 and 5), the Austroads accepted Equivalent Loads for SADT,TADT and TRIDT produce different maximum surface deflections. This may indicate that the Austroadsapproach for determination of equivalent axle loads based on equal maximum surface deflection (Scala 1970a,

1970b) may be applicable for granular pavement with thin surface seals, but not for pavements with boundmaterials.

Figure 2 shows the relationships between the predicted surface deflections for axle groups with dual tyres(SADT, TADT and TRIDT) and number of tyre per axle group.

The relationships inFigure 2 are best presented by the linear function

Y = a.X + b (7)

where

Y = predicted surface deflection for a given axle group


a and b are fitting constants.

These relationships were used to estimate the equivalent surface deflections for quad axle (that have 16 tyres).The Austroads design procedures were then used to calculate the quad axle loads that produce these equivalentsurface deflections. The results of equivalent surface deflections and equivalent quad axle loads are also givenin Table 5. Referring to Table 5, for granular pavements with thin surface seal (Pavements 1, 2 and 3), theestimated equivalent quad axle loads are in the range of 222-231 kN, with an average value of 226 kN. For

bound pavements (Pavements 4 and 5), the estimated equivalent quad axle loads are much higher (in the range243-247 kN). This indicates that the deflection-extrapolation procedure produces different estimates ofequivalent load for different pavement compositions.

Table 5Estimates of Equivalent Loads for Quad Axle Based on Extrapolation of Equivalent Surface Deflection



21/40


PavementNo

Equivalent Surface Deflection(mm)

Equivalent Axle Load, EAL(kN)

SADT TADT TRIDT QUAD SADT TADT TRIDT QUAD

1 0.58 0.57 0.56 0.55 80 135 181 222

2 0.71 0.70 0.70 0.69 80 135 181 224

3 0.93 0.96 1.00 1.04 80 135 181 231

4 0.57 0.64 0.72 0.79 80 135 181 243

5 0.47 0.56 0.64 0.73 80 135 181 247

Surface Deflection versus Number of Tyres

y = -0.0013x + 0.7144

R2

= 0.3784

y = 0.009x + 0.892

R2

= 0.9647

y = -0.0029x + 0.5939

R2

= 0.8052

y = 0.0184x + 0.4976

R2

= 0.9996

y = 0.0212x + 0.3876

R2

= 1

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Surface

De

flec

tion

(mm

)

Pav-1

Pav-2

Pav-3

Pav-4

Pav-5

SADTSAST TADT TRIDT QUADT

Figure 2 Extrapolation of equivalent surface deflection of a quad axle based on exiting relationships between calculatedsurface deflection per axle group and number of tyres

4.2.3 Extrapolation of Predicted Critical Strain

The Austroads mechanistic design procedures were used to calculate the equivalent critical strains (maximum

tensile strain at bottom of a bound layer and maximum strain at top of the subgrade under/between the tyres)using the Austroads accepted values of Equivalent Loads for axle groups with dual tyres (SADT, TADT andTRIDT). The results are given in Table 6.

Figure 3 shows the relationships between the predicted critical subgrade strain for axle groups with dual tyres(SADT, TADT and TRIDT) and number of tyre per axle group for all granular pavements with thin surfaceseal (Pavements 1, 2 and 3). Similarly,Figure 4 shows the relationships between the predicted critical tensilestrain for SAST, SADT, TADT and TRIDT and number of tyre per axle group for all bound pavements(Pavements 4 and 5).

The relationships inFigures 3 and 4 are best presented by the power function

Y = a.Xb

(8)

where



22/40


Y = predicted critical subgrade strain for a given axle group


a and b are fitting constants.

Table 6Estimates of Equivalent Loads for Quad Axle Based on Extrapolation of Equivalent Critical Strain

PavementNo

Distress Mode Equivalent Critical Strain(micro-strain)

Equivalent Axle Load, EAL(kN)

SADT TADT TRIDT QUAD SADT TADT TRIDT QUAD

1 SG Strain 709 597 540 503 80 135 181 221

2 SG Strain 682 563 503 465 80 135 181 220

3 SG Strain 710 599 542 504 80 135 181 226

4 Tensile strain in

AC Base

201 156 135 121 80 135 181 217

5 Tensile strain inCTCR Subbase

158 121 103 92 80 135 181 215

Subgrade strain versus Number of Tyres

y = 961.56x-0.2564

R2

= 0.9996

y = 1021.4x-0.2568

R2

= 0.9992

y = 957.76x-0.2272

R2

= 0.9994

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Cri

tica

lSu

bgra

de

Stra

in(micro-s

tra

in)

Pav-1

Pav-2

Pav-3

SADT TADT TRIDT QUADT

Figure 3 Extrapolation of equivalent critical subgrade strain of a quad axle based on exiting relationships betweencalculated critical subgrade strain per axle group and number of tyres



23/40


Critical Tensile Strain versus Number of Tyres

y = 330.94x-0.3658

R2 = 0.9957

y = 72.183x-0.232

R2

= 0.9979

y = 270.24x-0.3873

R2

= 0.9975

0

50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Cri

tica

lTens

ile

Stra

in(micro-s

tra

in)

Pav-4 (AC)

Pav-5 (AC)

Pav-5 (CTCR)


Figure 4 Extrapolation of equivalent critical tensile strain of a quad axle based on exiting relationships betweencalculated critical tensile strain per axle group and number of tyres

Using the regression relationships shown inFigure 3 and 4, the equivalent critical subgrade strain and criticaltensile strain for quad axle (that have 16 tyres) were extrapolated. The Austroads design procedures were thenused to calculate the quad axle loads that produce these equivalent critical subgrade strains and critical tensilestrains. The results of equivalent critical strains and equivalent quad axle loads are also given in Table 6.Referring to Table 6, for granular pavements with thin surface seal (Pavements 1, 2 and 3), the estimatedequivalent quad axle loads are in the range of 222-231 kN, with an average value of 222 kN. For bound

pavements (Pavements 4 and 5), the estimated equivalent quad axle loads are slightly lower (in the range 215-217 kN).

4.2.4 Estimates based on South African Damage Equivalence Factor Procedures

As discussed in Section 3 (also seeEquation 1), the South African Equivalent Damage Factor (EDF) is theproduct of Group Equivalence Factor (GEF), the Axle Load factor (ALF) and the Contact Stress Factor(CSF). For a group consisting of multiple single axles at a given axle spacing (SP) and a given tyre pressure

():

Group Equivalence Factor (GEF) is defined as the ratio between the allowable loading (N ISO) under an

isolated single axle of an axle group and the allowable loading (NG) under the axle group.

GEF =NISO /NG (9)

Axle Load Factor (ALF) is defined as the ratio between the allowable loading (NS) under the Standard 80

kN SADT and the allowable loading under an isolated single axle (NISO) of an axle group.

ALF =NS /NISO (10)

Contact Stress Factor (CSF) is defined as the ratio between the allowable loading (N S) under the Standard

80 kN SADT with standard tyre pressure and the allowable loading (N S) under a single 80 kN SADT

with the tyre pressure ().



24/40


CSF =NS /NS (11)

In this study, the following conditions were applied to be consistent with the Austroads Equivalent Loads forSAST, SADT, TADT and TRIDT (see Table 1):

an axle spacing (sp) of 1350 mm was applied for all axle groups TADT, TRIDT and QUADT;

a Standard SADT of 80 kN; and

a tyre pressure () of 550 kPa was applied to all axle groups (SADT, TADT, TRIDT and QUADT).

The current Austroads design procedures (Austroads 1992) do not cover changes of the elastic properties ofall layers with axle load level. In this study, it is also assumed that elastic properties are unchanged with axleload level. There is a need to consider changes in elastic properties with axle loads to investigate the influenceof nonlinear material properties on the estimates of equivalent axle loads.

It should be noted that the new Draft Austroads Guide (Austroads 2001) adopts a tyre pressure of 750 kPa forStandard Axle load without changing the values of Equivalent Loads for SAST, SADT, TADT and TRIDT. Itis recommended that this be investigated.

An axle group (with a total load of EGAL) will have the same damage as the Standard Axle load when

EDF = GEF x ALF x CSF = 1 (12)

Given that all axle groups have the same tyre pressure as the Standard SADT ( = 550 kPa),

CSF = 1 (13)

Therefore,Equation (12) can be rewritten as:

GEF x ALF x 1 = 1

ALF = 1/GEF (14)

Referring to Equations 3, 4 and 5 (also Table 3), the allowable loading is proportional to (1/Critical

Strain)

DE

. Therefore,Equation 10 can be expressed asALF =(Critical Strain under an isolated single axle/Critical Strain under 80 kN SADT)

DE(15)

The isolated single axle will have a load of:

ESAL = EGL/n

where

EGL = equivalent load of the axle group

ESAL = equivalent load of a single axle of the group

n = number of axles of the group.

Given that elastic properties were assumed to be unchanged with axle loads, critical strains are proportional toaxle load level. Therefore, ALF can be calculated as:

ALF = (ESAL/80)DE

(16)

Combining the two Equations (14) and (16), the equivalent single axle load (ESAL) of a group can becalculated as:

ESAL = 80/GEF

1/DE(17)

The equivalent load of an axle group (EGL) can be calculated as:

EGL = number of single axles in the group x 80/GEF1/DE

(18)

Equation (18) indicates that EGL is a function of number single axle in the group, Standard Axle load (80

kN) and Group Equivalence Factor (GEF).



25/40


The South African procedure for determining GEF is given inAppendix B. This procedure was used to derivethe GEF values for TADT, TRIDT and QUADT for all selected pavements in Table 4, and the results of GEFare given in Table 7.

Equivalent load of each axle group (EGAL) was calculated using Equation (17) and the results of EGAL forTADT, TRIDT and QUADT are also given in Table 7. Referring to Table 7, for granular pavements with thin

surface seal (Pavements 1, 2 and 3), the estimated equivalent quad axle loads are in the narrow range of 266-268 kN, which is much lower than the estimates for bound pavements (282 kN and 339 kN for Pavements 4and 5, respectively). This indicates that the South African procedure produce different estimates of equivalentload for different distress modes.

Table 7Estimates of Equivalent Axle Loads for Granular Pavements using Group Equivalence Factor (GEF)

PavementNo

Distress Mode Group Equivalence Factor (GEF) Equivalent Axle Load, EAL(kN)

TADT TRIDT QUAD TADT TRIDT QUAD

1 Critical SG Strain 1.86 2.79 3.73 147 208 266



4 Critical Tensilestrain in AC Base

0.96 1.33 1.77 161 227 285

5 Critical Tensilestrain in CTCR

Subbase

0.38 0.39 0.49 173 259 339

5. Comparison of Estimates of Equivalent Loads of Quad Axle

Figure 6compares the values of Equivalent Load for axle groups with dual tyres (SADT, TADT and TRIDT)accepted in various pavement design procedures throughout the world. It can be seen from Figure 6 that theAASHTO values for TADT and TRIDT are significantly higher than the others. It should be noted that theSouth African values were calculated using the South African mechanistic design procedures with the SouthAfrican EDF (Prozzi and de Beer, 1997). Referring to Figure 6, by using load extrapolation method,Austroads and Canadian Design procedures produce comparable estimates of equivalent load for quad axle(approximately 225 and 219 kN, respectively), which is much lower than those produced by the South Africanand AASHTO procedures (approximately 241 kN and 279 kN, respectively).

Figure 7 compares the estimates of equivalent load of a quad axle derived by all extrapolation proceduresadopted in this study (i.e. load-extrapolation, deflection-extrapolation and critical strain-extrapolation).Referring toFigure 7, load-extrapolation (Procedure 1) and critical strain-extrapolation (Procedure 3) producecomparable estimates of equivalent load for quad axle (in the range of 215-226 kN), which are lower thanthose produced by deflection-extrapolation (Procedure 2) (in the range of 222-247 kN).



26/40



y = 23.758x0.8806

R2

= 0.9989

y = 11.75x + 31.333

R2

= 0.9998

y = 13.375x + 26.667

R2

= 1

y = 28.559x0.7444

R2

= 0.9999

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Loa

dper

Ax

leGroup

(kN)

Austroads (1992)

AASHTO (1993) pt = 2.5

Sth. Africa

Ministry of Transpn(Canada)


Figure 6 Comparison of equivalent axle loads accepted by different road authorities throughout the world


50

100

150

200

250

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Loa

dper

Ax

leGroup

(kN)

Load Extrapolation

Critical Strain Extrapolation



Deflection Extrapolation




Figure 7 Comparison of estimates of equivalent loads of a quad axle based on different extrapolation approaches



27/40


Figure 8 compares the estimates of equivalent loads for axle groups with dual tyres (SADT, TADT andTRIDT) produced by the Austroads and South African mechanistic design procedures, both with the SouthAfrican EDF. Referring to Figure 8, the Austroads mechanistic design procedures with the South AfricanEDF consistently produce higher estimates of equivalent loads for axle groups with dual tyres than those

produced by the South African mechanistic design procedures with the South African EDF. It should be noted

that the equivalent loads for TADT, TRIDT and QUADT produced by the Austroads-South African EDFprocedures are consistently higher than those accepted by Austroads (say 9%, 15% and 21% for granularpavements, 19%, 26%, 30% for the full-depth asphalt pavement and 28%, 43% and 54% for the asphaltpavement with CTCR subbase). Given that the Austroads mechanistic design procedures with the SouthAfrican EDF also consistently produce higher estimates of equivalent loads for all axle groups than the currentAustroads accepted values (see Figure 8), it is considered that this method is not accepted at this stage andwill need to be investigated further. As discussed previously, there is a need to consider changes in elastic

properties with axle loads and tyre pressure to investigate the influence of nonlinear material properties on theestimates of equivalent axle loads. There is also a need to investigate the influence of damage criteria on theestimates of equivalent axle loads, i.e. the total damage criteria (i.e. combined fatigue life of bound layersand deformation life of granular layer and subgrade) and limited-damage criteria (either fatigue life of boundlayers or deformation life of subgrade).


50

100

150

200

250

300

350

0 2 4 6 8 10 12 14 16 18

Number of Tyres

Loa

dper

Ax

leGroup

(kN)

Pav-1,2,3 (SG Strain)

Pav-4 (AC Strain)

Pav-5 (CTCR Strain)

South Africa (existing)

Austroads (existing)


Austroads mechanistic

design procedures with

South Africa EDF

Figure 8 Comparison of estimates of equivalent loads for various axle groups produced by the Austroads and SouthAfrican mechanistic design procedures (both with the South African EDF)

There are two scenarios in the selection of equivalent axle loads:

Scenario 1: Acceptance of a single value of equivalent load for each standard axle group as currently

adopted in the Austroads Pavement Design Guide This will not cover influence of axle spacing, tyrepressure, material type and damage criteria (for different pavement types and classes).

Scenario 2: Acceptance of different values of equivalent load for each standard axle group to cover

influence of axle spacing, tyre pressure, material type and damage criteria This requires further work toprovide information for the above effects and revise the Austroads mechanistic pavement designprocedures.



28/40


For Scenario 1, given the smallest variation between the load-extrapolation and critical strain-extrapolation, itis likely that Austroads would accept the estimates of equivalent load for quad axle derived from these

procedures (in the range of 215-226 kN).

6. Summary

A literature review of the current equivalent axle loads being adopted for flexible pavements by different roadauthorities throughout the world indicates that equivalent loads for quad axle have not yet been developed foruse in any pavement design procedures.

Different pavement design procedures adopt different standard axle loads, different pavement damage criteria,and different procedures for the determination of equivalent axle loads. As such the procedures for estimatingof equivalent axle loads adopted in other pavement design procedures may not be readily applied to theAustroads pavement design procedures to estimate equivalent loads for quad axle.

Four procedures were used to estimate the equivalent load of a quad axle, namely:

Extrapolation of the existing relationships between axle group load and number of tyre per axle group as

adopted by different Road Authorities. Extrapolation of the relationship of predicted surface deflection and number of tyre per axle group: The

Austroads mechanistic design procedures are used to calculate the surface deflection.

Extrapolation of the relationship of predicted critical strain and number of tyre per axle group: The

Austroads mechanistic design procedures are used to calculate the critical strain.

Calculation of Group Equivalence Factor using the South African method: The Austroads mechanistic

design procedures is used to predict pavement deflection, critical strain and design life.

Three granular pavements (which have thickness in the range of 250-480 mm and subgrade CBR in the rangeof 5-15%), one full depth asphalt pavement and one CTCR Subbase asphalt pavement were used in this study.

Comparison of the estimates of equivalent load of a quad axle derived by different procedures indicates thatthe load-extrapolation and critical strain-extrapolation procedures produce consistent estimates of equivalentload of a quad axle, which are in the range of 215-226 kN. These estimates are slightly lower than theestimates produced by the maximum deflection-extrapolation procedure (in the range of 222-247 kN), andmuch lower than the estimates produced by the South African approach (in the range of 266-339 kN). Giventhat the South African approach consistently produces higher estimates of equivalent loads for tandem-axleand tri-axle than the existing Austroads accepted values, this method is unsuitable for estimating equivalentquad axle load. As such the South Africa approach will need to be investigated further, particularly theconsideration of the influence of axle spacing, tyre pressure, material type and damage criteria (for different

pavement types and classes).

7. Recommendation

It is recommended that

As interim measure a quad axle of 221 kN (22.5 tonne) be considered to cause equivalent damage to aStandard Axle.

Further investigation of the South African approach to changing elastic properties with axle loads and tyrepressure to investigate the influence of nonlinear material properties on the estimates of equivalent axleloads.

Further analysis will be undertaken to confirm this equivalent load of quad-axle is appropriate in terms ofdamage to pavements with asphalt and cemented materials.



29/40


Appendix ALiterature Review of Equivalent Axle Loads Adopted in Various Countries

A literature review of axle loads for equivalent damage was undertaken by Foley (2001) to compare the

current Austroads LEFs for flexible and rigid pavements with those of other countries. The data in Foley(2001) has been revised and is given below.

A.1 Equivalent Axle Loads for Flexible Pavements

Table A1 summarises information of equivalent axle loads for flexible pavements that is available from thecurrent published design guides and commentary documents relevant to Australia, the USA, South Africa,France, Great Britain and Canada.

Table A1Comparison of Equivalent Loads for Axle Group Types (Flexible Pavements)

AxleGroupType

AASHTO(1993)

pt2= 2.0-3.0

Austroads(1992)

Dept. ofTransport(Sth. Afr.)3

axle spacingof 1400 mm

HighwaysDirectorate

(France)

Dept. ofTransport

(UK)

Ministry ofTranspn(Canada)

SAST NA (Note 1) 53 kN 61 kN NA (Note 1) NA 61 kN

SADT 18 kips (80 kN) 80 kN 80 kN 130/130 kN NA 78 kN

TADT 34 kips

(151 kN)

135 kN 134 kN 4 275/2115kN NA 126 kN

TRIDT 48-46 kips

(214-205 kN)

181 kN 185 kN 6 383/263 kN NA 172 kN

1. AASHTO (1993) and LCPC and SETRA (1997) provide no guidance on the equivalent damage for these axle types.

A.1.1 USA

AASHTO (1993) recognises the origin of the development of the damage factors, which were derived from

data collected during the AASHO Road Test, by referencing them to a terminal serviceability value (p t). In

Table A1, equivalent loads are presented for a range of p t values between 2 and 3. The Equivalent Standard

Axle Load (ESAL) presented in Table A1 is the summation of equivalent 18,000 pound (80 kN) single axle

loads used to combine mixed traffic to design traffic for the design period (AASHTO 1993).

AASHTO also recognise the effect of different pavement strengths on the damage factors by tabulating thesevalues for a range of Structural Numbers (SN). The SN is an index derived from an analysis of traffic,roadbed soil conditions, and environment which may be converted to a thickness of the flexible pavementlayers through the use of suitable layer coefficients related to the type of material being used in each layer ofthe pavement structure (AASHTO 1993).

A.1.2 Australia

2 Terminal Serviceability Values.3 A proposed method to determine LEFs as contained in DoT (1997).4

Foley (2001) quoted a value of 132 kN for TADT.5 Masses for TADT and TRIDT axles have been calculated for the whole axle group.6 Foley (2001) quoted a value of 212 kN for TRIDT.



30/40


Potter (1999) recently conducted a review of the technical basis of the Austroads (1992) Pavement DesignGuide. One of the issue addressed by Potter is Axle Loads Which Cause Equal Damage.

As stated by Potter, in assessing the damaging effect of design traffic, an essential requirement is the ability tocompare damaging effects of loads on different axle configurations. In the Austroads Guide, the basis for thiscomparison is provided in Table 7.1 (reproduced above in Table 1), which lists, for the common axle

configurations, the axle load which will produce the same damage as a Standard Axle, a Standard Axle beingdefined as a dual-tyred single axle transmitting a load of 80 kN to the pavement.

Potter further reports that, during the mid-1960s, several independent analyses of AASHO Road Test datawere reported which inter alia provided estimates of the relative damaging effects of dual-tyred single axlesand dual-tyred tandem axles. Because these estimates were based on the performance of pavements withrelatively thick asphalt surfacings which were subject to freeze-thaw cycles, they were considered to be notdirectly applicable to the bulk of the Australian road network with its surfacing of chip seal or thin asphaltand not subject to freeze-thaw cycles7.

For these reasons, Scala (1970a) undertook a field study based on the premise (reasonably well supported bylimited AASHTO data8) that those axle groups that cause equal maximum deflection in the pavement causeequal pavement damage. The study was undertaken on a range of pavements, with both chip seal and thin

asphalt surfacing, in the Altona-Williamstown area of Melbourne. A scaled-up version of the BenkelmanBeam was used to record peak deflections for steer axle and triaxle deflections. A pad, approximately 50 mmthick, composed of industrial rubber conveyor belting, and with a transverse slit cut in it, was placed on theroad and a conventional Benkelman Beam was positioned transversely with its tip in the slit. Maximumdeflection was recorded as the axle (group) passed over the pad.

Scala reported that, with regard to the load on a single-tyred single axle which produces the same maximumdeflection as a Standard Axle:

The equivalent load by deflection tests is about 11.6 kip (51.6 kN).

and

In this paper 12 kip (53.4 kN) is used mainly for ease of computation.

As stated by Potter (1999), the only data in the paper was related to maximum deflection recorded for dual-tyred single and tandem axles. It is presented in the form of a plot of the ratio (tandem axle deflection)/(singleaxle deflection) versus the ratio (tandem axle load)/(single axle load). A broad range of deflection ratios is

plotted for each of six load ratios (corresponding to six days of testing). For three of the six load ratios, thereader is cautioned that the data may be affected by water penetration .

With regard to the load on a tandem axle group which produced the same maximum deflection as a StandardAxle, Scala (1970a) provided two values 28.9 kip (128.6 kN) and 29.2 kip (129.8 kN) in a summaryTable (Table VIII of Scala 1970a), together with the statement:

Assuming that a 30 kip tandem axle load gives a deflection of the same magnitude as an 18 kipsingle axle (dual tyre) load, .

With regard to the load on a triaxle group which produced the same maximum deflection as a Standard Axle,information in Scala (1970a) is restricted to the statement:

it is expected that the three axle group with a load of 40.7 kip (181.0 kN) would beequivalent (in terms of maximum deflection) to a single axle of 18 kip (90.1 kN).

7 In addition, the analyses did not encompass single-tyred single axles (steer axles) or triaxles. Steer axles wereconsidered to cause minimal damage at the AASHO Road Test and, hence, were not included in the analyses.Triaxles were not included in the AASHO performance studies.8 The AASHO road test, from which Scalas (1970a) estimated relative destructive effects, used a number ofpavements of known construction. These comprised pavements of thick asphalt (typically 100 mm to 150 mm) on

granular material. The granular pavement with thin bituminous surface did not perform well in the AASHO RoadTest, due to freeze-thaw effects, and consequently the data from this pavement type was not included in the abovederivation of the relative destructive effect of different loads.



31/40


Potter also reported that, in a report written approximately five months after the above paper, Scala (1970b)was much more focussed, stating that:

Using an 18 kip single axle load (dual wheel) as the standard axle load, equivalent repetitionsof other axle loads are given by:

(i) single axle (single wheel) (w/12)

4

(ii) single axle (dual wheel) (w/18)4

(iii) tandem axle (dual wheels) (w/30)4

During the NAASRA Economics of Road Vehicle Limits (ERVL) Study, Stevenson (1976) adopted thefollowing values, based on the above two Scala references and discussions with him:

single-tyred single axle 5.4 t (53.0 kN)dual-tyred single axle 8.2 t (80.4 kN)dual-tyred tandem axle 13.6 t (133.4 kN)dual-tyred triaxle 18.5 t (181.5 kN)

Potter (1999) further reported that, in the NAASRA (1979) Interim Guide to Pavement Thickness Design(IGPTD) the first three of the above values were adopted in its Table 2.15. It did not cater for triaxles, which

was considered by Potter to be most probably an oversight.

Finally, Potter (1999) reported that the Austroads Working Group, in its formulation of Table 7.1 in the 1992Guide, reviewed the above material and, in addition, values in use overseas. The largest discrepancy betweenthe above values and those in use overseas was for the dual-tyred tandem axle (see, for example, the values forAASHO and Asphalt Institute in Table VII of Scala (1970a)). Further, the Working Group noted Scalaslater adoption of 13.7 t for tandem axles (Scala 1977). On this basis, the Working Group opted for the values

presented in Table 7.1, and given in Table 1 of this report, as follows9:

single-tyred single axle 53 kNdual-tyred single axle 80 kNdual-tyred tandem axle 135 kNdual-tyred triaxle 181 kN

A.1.3 South Africa

The Department of Transport, South Africa (DoT 1997) recognise that factors other than axle group load,

such as inter-axle spacing and tyre contact stress, also influence pavement damage. As such, there is no one

equivalent load as per the current Austroads (1992) procedure.

The method of determining load equivalency is based upon the concept of equivalent pavement response,equivalent pavement damage. This concept has been used previously; for example, by Scala and Potter(1981) when they derived a method for the prediction of load equivalence factors for specialised vehicles. Inthe South African procedure, however, other criteria such as equivalent strain or stress levels in the materialshave been utilised, rather than the equivalent total deflection at the pavement surface used by Scala and Potter.

The method also assumes linear-elastic material characterisation.

The Equivalent Damage Factor (EDF) see Table A1 expresses the number of repetitions of the StandardLoad Configuration (identical to a Standard Axle) which would cause the same damage as the given axlegroup. As just discussed, the EDF recognises the influence of the axle spacing within an axle group (GroupEquivalence Factor), the mass on the axle group (Axle Load Factor) and the tyre contact stress (ContactStress Factor):

EDF = GEF x ALF x CSF

where EDF = Equivalent Damage Factor,

GEF = Group Equivalence Factor,

ALF = Axle Load Factor, and

9 Note that in Table 1, the Equivalent Standard Axle (ESA) is the number of Standard Axles that will provide thesame damage as that caused by the various group types. A damage exponent of 4 is inherent in this definition.



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CSF = Contact Stress Factor.

A.1.4 Great Britain

The Department of Transport, Great Britain (DoT 1993) uses a relatively simple approach to the

determination of pavement damage related to different axle groups. Individual axle groups are not

considered, but rather the vehicle types for which these axle groups form a part. Therefore each commercial

vehicle classification or type (defined as over 15 kN unladen weight) has a Wear Factor which is identical

to the (Loading) Factor (F) presented in Method 3 of Appendix E of Austroads (1992).

A.1.5 France

The method adopted by the Highways Directorate of France considers the Aggressiveness of an Axle,

which is based on the fatigue damage caused to the pavement. Aggressiveness, A, corresponds to the

damage caused by one passage of an axle load, P, compared to the damage due to one passage of the

reference isolated10 axle load, PO. Aggressiveness is determined using the following relationship (LCPC

and SETRA 1997):

=PO

PkA

where A = Aggressiveness;

P = load on each axle of the axle group;

PO = reference axle (dual-wheel isolated [single] axle, weighing 130 kN);

= constant depending on pavement type (flexible, semi-rigid or concrete); and

k = constant depending on axle type (single, tandem or triaxle).As the reference axle load is different from a Standard Axle, the French equivalent axles cannot be readilycompared to values derived using other pavement design procedures.

A.1.6 Canada

The Ministry of Transportation, Canada, established a set of LEFs following a nation-wide experiment

conducted during the late 1980s. These LEFs are as follows:

SAST: LEF =

9093.2

004836.0 xLoad

SADT: LEF =

9093.2

002418.0 xLoadTADT: LEF = 5403.2001515.0 xLoad

TRIDT: LEF = 1130.2002363.0 xLoad

where Load is the axle group mass in tonne.

The equivalent axle group loads given in Table A1 have been calculated using these relationships.

10 Isolated axle [group] is when the nearest axle is greater than 2 m distant.



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A.2 Equivalent Axle Loads for Rigid Pavements

Table A2 summarises information of equivalent axle loads for rigid pavements that is available from thecurrent published design guides and commentary documents relevant to Australia, the USA and France.

Table A2

Comparison of Equivalent Loads for Axle Group Types (for Rigid Pavements)

Axle Group Type AASHTO (1993)11

pt = 2.0-3.0Austroads (1992)12 Highways

Directorate(France)

Erosion Fatigue

SAST NA (Note 2) 80 kN 67 kN NA (Note 1)

SADT 80 kN 80 kN 80 kN 130 kN

TADT 129 kN 165 kN 191 kN 211 kN

TRIDT 171 kN 244 kN 385 kN 263 kN

Note 1 - AASHTO (1993) and LCPC and SETRA (1997) provide no guidance on the equivalent damage for these axle types.

A.2.1 USA

The AASHTO design procedure for rigid pavements is based upon AASHO Road Test pavement

algorithms. For this procedure, the equivalent number of 18 kip single axle load applications are calculated

and compared to the design number of equivalent Standard Axles. Load equivalency factors are used to

convert the actual traffic load spectrum into numbers of equivalent Standard Axles, in the same manner as

Austroads flexible pavement design (Method 1; Austroads 1992) for characterising initial daily traffic.

The AASHTO procedure is fundamentally different to the PCA method whereby the latter procedure has theability for individual loads on all four axle groups to be considered in the determination of the base slabthickness.

Using the example of a rigid pavement base slab thickness of 200 mm and a Terminal Serviceability of 2.5,the results of equivalent axle loads for SADT, TADT and TRIDT found in Tables D.13, D.14 and D.15AASHTO (1993) are presented in Table A2.

11 Estimates from AASHTO (1993) using a typical pavement example (Foley 2001).12 Estimates from Austroads (1992) using a typical pavement example (Foley 2001).



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A.2.2 Australia

Austroads (1992) recommends the use of the US Portland Cement Association (PCA 1984) method for

determining the thickness of concrete base. This method considers two modes of limiting distress in

concrete bases: (a) fatigue of the concrete slab and (b) erosion, a mode of distress related to the joint andplanned crack performance.

The Austroads procedure allows different masses on different axle group types to be assessed, but it does notcater for changes in axle spacing in multi-axle groups, or for wide super-single tyres, unlike proceduresdeveloped by others, such as Ioannides et al. (1998).

A simple design exercise was undertaken to gain an estimate of equivalent damage for both these distressmodes associated with the four axle load types. Note that the rigid pavement design procedure incorporatesestimates of repetitions of individual axle groups over the full load range for each axle group type.

Erosion AnalysisFor the erosion distress type, a trial pavement comprising a 210 mm thick undowelled plain concrete base

with shoulders and having an effective subgrade CBR of 75% was used. A design Load Safety Factor (LSF)of 1.2 was used. Using Table 9.3 of Austroads (1992) the following Erosion Factors for each axle group typewere derived.

Axle Group SAST SADT TADT TRIDT

Erosion Factor 1.86 2.47 2.45 2.46

The load on each wheel of an 80 kN (Standard Axle) load on a SADT axle group is (80 kN x 1.2)/4 = 24 kNper wheel. From Figure 9.6 of Austroads (1992) the allowable number of repetitions is therefore 40 x 106.Using this number of allowable repetitions (40 x 106), and the Erosion Factors for the other three axle grouptypes, it was possible to back-calculate, using Figure 9.6, the load on each axle group. The results are

presented in Table A2.

Fatigue AnalysisFor the fatigue distress type, a trial pavement comprising a 200 mm thick undowelled plain concrete basewithoutshoulders and having an effective subgrade CBR of 15% was selected. The design flexural strengthwas 4.25 MPa and a design LSF of 1.2 was used. Using Table 9.2 of Austroads (1992) the followingEquivalent Stresses, and Stress Ratio Factors (divide by the flexural strength of 4.25 MPa) for each axlegroup type were derived.

Axle Group SAST SADT TADT TRIDT

Equivalent Stresses 1.02 1.65 1.40 1.05

Stress Ratio Factor 0.24 0.39 0.33 0.25

The load on each wheel of an 80 kN (Standard Axle) load on a SADT axle group is (80 kN x 1.2)/4 = 24 kNper wheel. From Figure 9.4 of Austroads (1992) the allowable number of repetitions is therefore 10 x 106.Using this number of allowable repetitions (10 x 10 6) and the Stress Ratio Factor for the other three axlegroup types, it was possible to back-calculate, using Figure 9.4, the load on each axle group. The results are

presented in Table A2.

Examination of the above axle loads for the Austroads load equivalency factor of unity shows the much lowermasses for the TADT and TRIDT axle groups, as compared to those adopted by AASHTO (1993) (see Table

A3). Given that the AASHTO method equivalent loads for the TADT and TRIDT axle groups are lower thanthe Austroads (PCA) method by 20 to 30% mass on the axle groups, the Austroads axle load masses (atAustroads LEFs of 1.0) would produce between approximately 3 to 24 times the amount of damage than thoseof the AASHTO loads at an LEF of unity.



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Table A3Axle Group Load for Austroads LEF of 1 (Erosion) and Comparison with AASHTO Procedure

Erosion Fatigue

Axle Group SAST SADT TADT TRIDT SAST SADT TADT TRIDT

Austroads Equivalent Axle

Loads (kN)

80 80 165 244 67 80 191 385

Austroads LEFs 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

AASHTO LEFs (approx.) NA 1.00 2.6 4.2 NA 1.00 4.7 24.9

A.2.3 France

As discussed in Section 3.1.5, The method adopted by the Highways Directorate of France considers the

Aggressiveness of an Axle, which is based on the fatigue damage caused to the pavement.

Aggressiveness, A, corresponds to the damage caused by one passage of an axle load P, compared to thedamage due to one passage of the reference isolated axle load PO. Aggressiveness is determined using the

following relationship:

=PO

PkA

where A = Aggressiveness,

P = load on each axle of the axle group,

PO = reference axle; dual-wheel isolated [single] axle, weighing 130 kN.

= constant for concrete pavement is 5, and

k = constant for axle type for concrete slab pavement(single axle: 1.0; tandem axle: 12.0; triaxle: 113).

Using this relationship, the following loads for an LEFs equivalent to one Reference Axle were calculated asgiven in Table A2.

As the reference load for the French rigid pavement design procedure is different from that of Austroads andAASHTO, the equivalent axle loads for other axle groups cannot be compared. In addition, the Frenchmethod, as with the AASHTO and Austroads procedures, does not cater for changing axle spacings in multi-axle groups, or the use of super single wide tyres.



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Appendix BThe South African Procedure for Determining Group Equivalence Factor

(GEF)

Group Equivalence Factor (GEF) was defined as the ratio between the allowable loading (N ISO) under anisolated single axle of an axle group and the allowable loading (NG) under the group.

GEF =NISO/NG (B1)

The allowable loading under the group (NG) was determined using the following equation:

NG = NCR/(1+Fc) (B2)

Where

NCRis the number of repetitions of the critical axle (most damaging axle) of the group.

Fc is the contribution factor, which was developed to take into account the contribution of other minoraxles (less damaging axle) of the group to the critical axle

Fc was defined as:

Fc = nA

Where

nA is the number of axles of the group

is the ratio between the peak surface deflection of critical axle and the peak surface deflection of

minor axle



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BIBLIOGRAPHY

AASHTO (1993). AASHTO Guide for Design of Pavement Structures. American Association of StateHighway Transportation Officials, Washington, USA.

Austroads (1992). Pavement Design: A Guide to the Structural Design of Road Pavements. Austroads,Sydney.

Austroads (2001). 2001 Austroads Pavement Design (Final draft) For Public Comment. Austroads,Sydney.

Department of Transport, Great Britain (1993). Design Manual for Roads and Bridges. Volume 7:Pavement Design and Maintenance. Section 2, Part 1, HD 24/96, Revision dated February 1996.Department of Transport, UK.

Department of Transport, South Africa (1997). Rehabilitation Design of Flexible Pavements in SouthAfrica. RR 93/296 Book 1 of 2. Department of Transport, Pretoria, SA.

Foley, G.D. (2001)

appendix ear rb tr quad axle report

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