AP-R486 15 Influence of Multiple-Axle Group Loads

Research Report

AP-R486-15

Research Report

AP-R475-15

The Influence of Multiple-axle Group Loads on Flexible Pavement Design


Prepared by

Michael Moffatt

Publisher

Austroads Ltd.

Level 9, 287 Elizabeth Street

Sydney NSW 2000 Australia

Phone: +61 2 8265 3300

[email protected]

www.austroads.com.au

Project Manager

Graham Hennessy

Abstract

The current Austroads approach to assess the relative damaging

effects of different axle groups on road pavements is by comparison

of the peak static pavement deflection response under the axle

groups. The assumption that deflection is the most appropriate

indicator of pavement damage is open to question and is not

consistent with the use of strains to calculate the performance of

pavement materials.

In response, research conducted has determined that, with regard to

the fatigue damage of asphalt and cemented materials, the standard

load for an axle group type is dependent upon the thickness and

modulus of the asphalt and the underlying pavement structure.

As a result, it is proposed that the mechanistic design procedure for

flexible pavements not use the concept of standard loads, but rather

that the procedure determines the pavement damage resulting from

each axle load and each axle group within a traffic load distribution.

An examination of the implications of pavement design outcomes in

using this method determined that in general, reductions in both

asphalt and cemented material thicknesses of up to 50 mm would

result.

The research also determined that the currently used standard loads

for tandem, triaxle and quad-axle were appropriate for use with the

current empirical procedures for the design of granular pavements

with thin bituminous surfacings.

About Austroads

Austroads’ purpose is to:

promote improved Australian and New Zealand transport outcomes

provide expert technical input to national policy development on road and road transport issues

promote improved practice and capability by road agencies

promote consistency in road and road agency operations.

Austroads membership comprises the six state and two

territory road transport and traffic authorities, the

Commonwealth Department of Infrastructure and Regional

Development, the Australian Local Government Association,

and NZ Transport Agency. Austroads is governed by a Board

consisting of the chief executive officer (or an alternative

senior executive officer) of each of its eleven member

organisations:

Roads and Maritime Services New South Wales

Roads Corporation Victoria

Department of Transport and Main Roads Queensland

Main Roads Western Australia

Department of Planning, Transport and Infrastructure South Australia

Department of State Growth Tasmania

Department of Transport Northern Territory

Territory and Municipal Services Directorate, Australian Capital Territory

Commonwealth Department of Infrastructure and Regional Development

Australian Local Government Association

New Zealand Transport Agency.

The success of Austroads is derived from the collaboration of

member organisations and others in the road industry. It aims

to be the Australasian leader in providing high quality

information, advice and fostering research in the road

transport sector.

Keywords

Pavement design, materials, laboratory testing, accelerated loading

facility, multiple-axle group, axles, design traffic, asphalt, cemented

materials, granular materials

ISBN 978-1-925294-43-9

Austroads Project No. TT1614

Austroads Publication No. AP-R486-15

Publication date May 2015

Pages 268

© Austroads 2015

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.

This report has been prepared for Austroads as part of its work to promote improved Australian and New Zealand transport outcomes by

providing expert technical input on road and road transport issues.

Individual road agencies will determine their response to this report following consideration of their legislative or administrative

arrangements, available funding, as well as local circumstances and priorities.

Austroads believes this publication to be correct at the time of printing and does not accept responsibility for any consequences arising from

the use of information herein. Readers should rely on their own skill and judgement to apply information to particular issues.


Austroads 2015 | page i

Summary

Road network owners are being faced with the need to make predictions of the long-term effect of

heavy vehicle loading changes on their networks. Exploration of future mass-distance and

incremental pricing for heavy vehicles requires an understanding of the effects of different axle

group’s loads and types on pavement performance.

The current Austroads approach to assess the relative damaging effects of different axle groups on

road pavements is by comparison of the peak static pavement deflection response under the axle

groups. This ignores the contribution to pavement damage made by the axles in the group which do

not correspond with the peak response. The traditional assumption that the deflection response is the

most appropriate indicator of pavement damage is also open to question and is not consistent with

the Austroads mechanistic design procedures, in which strains rather than deflections are used to

calculate the performance of pavement materials.

In response, this research study investigated improved methods for assessing the pavement damage

caused by different multiple-axle group loads, and developed a framework that can be used to

quantify this pavement damage for use in Austroads flexible pavement design processes. The project

focus was on utilising performance data that had been collected by others, and in the collection of

new performance data related to the pavement design performance criteria considered in the current

Austroads pavement design process.

In order to examine whether improvements were necessary for the design of unbound granular

pavements, the Accelerated Loading Facility was used to assess the deformation of a typical,

full-scale, unbound granular pavement and subgrade. Whilst analysis was hampered by significant

moisture change during the testing period, it was possible to demonstrate that the current standard

load value used for triaxle groups were appropriate. This standard load value assumes that the

interaction between axles of a multiple-axle group do not affect the relative damage caused by the

same number of ungrouped axles. Thus, the finding was extended to demonstrate that the currently

used standard loads for tandem, triaxle and quad-axle were appropriate for use with the current

empirical procedures for the design of granular pavements with thin bituminous surfacings.

A laboratory-based study conducted in France provided the basis for an examination of the effect of

multiple-axle group loads on the fatigue of asphalt for pavement design purposes. That study

developed a model allowing the prediction of fatigue life of a sample as a function of the maximum

strain level resulting from the simulation of a single axle or multiple-axle group. The model does not

consider how the grouping of axles may affect the magnitude of the strain developed. This effect was

examined using response-to-load modelling, and it was found that the standard load for an axle group

is dependent upon the thickness and modulus of the asphalt and the underlying pavement structure.

A laboratory-based investigation of a cemented material, conducted as part of the Austroads project,

obtained similar findings. In contrast, the current Austroads mechanistic design procedure assumes

constant standard loads apply across all pavement configurations.

As a result, a potential design procedure was developed for the design of bound materials in flexible

pavements that determines the damage resulting from each axle load and each axle group within a

traffic load distribution. In principle, this is the same approach used in the Austroads procedure for the

design of rigid pavements, and its use for flexible pavements would align the design traffic

characterisation for the two types of pavement.


Austroads 2015 | page ii

Contents

1. Introduction .................................................................................................................................... 1

1.1 The Australasian Pavement Network ...................................................................................... 1

1.2 Traffic Loads ............................................................................................................................ 1

1.3 Report Structure ...................................................................................................................... 2

1.4 Previous Related Reports ........................................................................................................ 3

2. Australasian Practice .................................................................................................................... 4

2.1 Overview of Pavement Design Methods ................................................................................. 4

2.1.1 Design of Unbound Granular Pavements with Thin Surfacings ................................. 4

2.1.2 Mechanistic Design of Flexible Pavements ................................................................ 4

2.1.3 Rigid Pavement Design .............................................................................................. 6

2.2 Origins of Standard Axle Group Loads .................................................................................... 6

2.3 Assumed Interaction between Axles ....................................................................................... 8

2.4 Limitations of Current Practice ................................................................................................ 9

3. Review of Alternative Methods .................................................................................................. 11

3.1 Introduction ............................................................................................................................ 11

3.2 1993 AASHTO Guide ............................................................................................................ 11

3.3 French Design Manual ........................................................................................................... 13

3.4 Response to Load Methods ................................................................................................... 14

3.4.1 Relating Response to Damage ................................................................................. 14

3.4.2 Maximum Response Methods .................................................................................. 16

3.4.3 MEPDG ..................................................................................................................... 16

3.4.4 Multiple Peak Response Methods ............................................................................ 17

3.4.5 South African Pavement Engineering Manual (2003) .............................................. 17

3.4.6 Peak Mid-way Methods............................................................................................. 18

3.4.7 Integration Methods .................................................................................................. 19

3.5 Summary................................................................................................................................ 21

4. Review of Research..................................................................................................................... 23

4.1 General .................................................................................................................................. 23

4.2 Asphalt Fatigue Using Simulated Multiple-axle Loads: Michigan State University ............... 23

4.3 Effect of Different Wave Forms and Rest Periods on Fatigue: Chuo University Study ......... 27

4.4 Effect of Different Wave Forms on Fatigue: French Studies ................................................. 28

4.5 Effect of Different Wave Forms on Laboratory Fatigue: Homsi Study .................................. 32

4.6 Pavement Response to Multiple-axle Loads: BASt Study ..................................................... 35

4.7 Summary................................................................................................................................ 39

5. Outline of Project Work .............................................................................................................. 41

5.1 General .................................................................................................................................. 41

5.2 Rutting of Unbound Granular Pavements .............................................................................. 41

5.3 Asphalt Fatigue ...................................................................................................................... 42

5.4 Cemented Materials Fatigue.................................................................................................. 42

5.5 Pavement Design Processes................................................................................................. 43


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6. Rutting of Unbound Granular Materials .................................................................................... 44

6.1 General .................................................................................................................................. 44

6.2 Accelerated Loading Facility .................................................................................................. 45

6.2.1 Overview of ALF Prior to Modification ...................................................................... 45

6.2.2 Multiple-axle Modifications ........................................................................................ 46

6.3 Site, Pavement Composition and Construction ..................................................................... 49

6.3.1 Description of Site ..................................................................................................... 49

6.3.2 Pavement Composition ............................................................................................. 50

6.3.3 Pavement Construction............................................................................................. 54

6.4 Loading Applied During Testing Program .............................................................................. 57

6.4.1 Loading Applied ........................................................................................................ 57

6.4.2 Transverse Distribution ............................................................................................. 58

6.4.3 Line Marking ............................................................................................................. 59

6.4.4 Pavement Bedding-in................................................................................................ 60

6.5 Experiment Progression ........................................................................................................ 61

6.6 Acquired Data ........................................................................................................................ 62

6.6.1 General ..................................................................................................................... 62

6.6.2 Loading Applied ........................................................................................................ 62

6.6.3 Particle Size Distribution of Base Material ................................................................ 65

6.6.4 Density and Moisture Content of Base Material ....................................................... 65

6.6.5 Deformation of Imported Clay Subgrade Material .................................................... 66

6.6.6 Deformation of the Surface of the Pavement ........................................................... 67

6.6.7 Pavement Deflection Testing .................................................................................... 71

6.7 Preparation of Data for Analysis ............................................................................................ 72

6.7.1 Overall Deformation and Variation of Results .......................................................... 72

6.7.2 Variation in Deformation Performance ...................................................................... 73

6.7.3 Measured In Situ Material Properties ....................................................................... 74

6.7.4 Data to Reflect Pavement Properties ....................................................................... 78

6.7.5 Measure of Performance .......................................................................................... 83

6.8 Analysis Using Generalised Model ........................................................................................ 85

6.9 Analyses Using Axle Group Pairing ....................................................................................... 86

6.9.1 General ..................................................................................................................... 86

6.9.2 40 kN Single Axle and 80 kN Tandem Group ........................................................... 89

6.9.3 60 kN Tandem Group and 80 kN Tandem Group .................................................... 91

6.9.4 60 kN Tandem Group and 90 kN Triaxle Group ....................................................... 92

6.9.5 40 kN Single Axle and 90 kN Triaxle Group ............................................................. 92

6.10 Conclusions ........................................................................................................................... 95

7. Fatigue of Asphalt ....................................................................................................................... 98

7.1 Introduction ............................................................................................................................ 98

7.2 Response-to-load Model ........................................................................................................ 98

7.2.1 Model Selection ........................................................................................................ 98

7.2.2 FEM Mesh Generation .............................................................................................. 99

7.2.3 Analysis Parameters ............................................................................................... 102

7.2.4 Response Locations ............................................................................................... 103

7.3 3D-FEM Response-to-load Analyses .................................................................................. 103


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7.4 Analysis of 3D-FEM Response-to-load Results Using Homsi’s Damage Model ................. 105

7.4.1 Calculation of Homsi Parameters ........................................................................... 105

7.4.2 Calculation of Relative Fatigue Damage ................................................................ 105

7.4.3 Calculation of Standard Axle Loads ........................................................................ 106

7.4.4 Variations of Standard Axle Loads with Pavement Structure ................................. 106

7.5 Simplifying Homsi’s Model ................................................................................................... 110

7.6 Analysis of 3D-FEM Response-to-load Results Using Simplified Homsi Damage Model... 111

7.7 Adjustment of Simplified Homsi Model for Use with Austroads Fatigue Relationship ......... 114

7.7.1 Rearranging Simplified Homsi Model ..................................................................... 114

7.7.2 Maximum Peak Model ............................................................................................ 114

7.8 Generalising Model to Consider Strains Generated by Each Axle ...................................... 119

7.9 Analysis of 3D-FEM Response-to-load Results Using Summed Peaks Method ................ 119

7.10 Selection of Damage Calculation Method ........................................................................... 122

7.11 Damage Calculated Using Linear-elastic Response-to-load Model .................................... 123

7.12 Conclusions ......................................................................................................................... 128

8. Fatigue of Cemented Materials ................................................................................................ 130

8.1 General ................................................................................................................................ 130

8.2 Laboratory Flexural Test Methods ....................................................................................... 130

8.3 Sample Preparation ............................................................................................................. 131

8.4 Laboratory Test Equipment ................................................................................................. 135

8.4.1 General ................................................................................................................... 135

8.4.2 IPC Global Universal Testing System ..................................................................... 135

8.4.3 IPC Global Test Control Software ........................................................................... 136

8.4.4 Pulse Shape Generation ......................................................................................... 136

8.4.5 Control Software ..................................................................................................... 140

8.5 Alterations to Test Procedures and Equipment ................................................................... 141

8.5.1 General ................................................................................................................... 141

8.5.2 LVDT Frame Alterations ......................................................................................... 142

8.5.3 Test Geometry ........................................................................................................ 142

8.5.4 Sample Size ............................................................................................................ 143

8.5.5 Definition of Initial Modulus and Strain for Fatigue Testing .................................... 143

8.6 Data ..................................................................................................................................... 144

8.6.1 Test Sequence ........................................................................................................ 144

8.6.2 Flexural Modulus Data ............................................................................................ 145

8.6.3 Flexural Fatigue Data.............................................................................................. 146

8.7 Flexural Fatigue for Each Load Type .................................................................................. 147

8.8 Analysis Using Estimated Strain Reach 100 000 Cycles of Loading .................................. 150

8.8.1 Background ............................................................................................................. 150

8.8.2 Tolerable Strain ....................................................................................................... 151

8.8.3 Correcting Tolerable Strains for Varying Density Condition ................................... 152

8.8.4 Effect of Load Shape on Tolerable Strain ............................................................... 153

8.9 Summary.............................................................................................................................. 155


Austroads 2015 | page v

9. Framework to Incorporate Multiple-axle Responses in Flexible Pavement Design ........... 157

9.1 Empirical Design of Unbound Granular Pavements with Thin Bituminous Surfacing ......... 157

9.2 Mechanistic Design of Bound Materials .............................................................................. 157

9.2.1 Modelling Each Axle Group/Load Combination ...................................................... 157

9.2.2 Scaling Response-to-load Calculations for Different Load Levels ......................... 158

9.2.3 Excluding Superposition of Responses – Considering Isolated Axles ................... 158

10. Determination of Characteristic Values of Parameters for Multiple-axle Group Modelling

and Example Design Outcomes ............................................................................................... 160

10.1 Introduction .......................................................................................................................... 160

10.2 Design Traffic Distributions .................................................................................................. 160

10.3 Design Pavement Structures ............................................................................................... 160

10.4 Modelling Constituent Axles of Groups as Isolated Axles ................................................... 161

10.5 Modelling of Combined Multiple-axle Groups ...................................................................... 163

10.5.1 General ................................................................................................................... 163

10.5.2 Axle Spacing ........................................................................................................... 164

10.5.3 Effect of Superimposing Responses from Grouped Axles ..................................... 164

10.5.4 Comparison of Scaled and Calculated Responses ................................................ 165

10.5.5 Dynamic Load Considerations ................................................................................ 165

10.5.6 Significance of Design Traffic Distribution .............................................................. 169

10.6 Summary.............................................................................................................................. 176

11. Conclusions ............................................................................................................................... 178

11.1 General ................................................................................................................................ 178

11.2 Empirical Design of Unbound Granular Pavements with Thin Bituminous Surfacings ....... 178

11.3 Mechanistic Design of Bound Materials .............................................................................. 179

11.4 Design Reliability ................................................................................................................. 180

References ......................................................................................................................................... 181

Appendix A Mean Deformation After Bedding-In: Tabulated .................................................. 185

Appendix B Mean Deformation After Bedding-In: Plotted ....................................................... 190

Appendix C Pavement Deflection and Back-Calculated Moduli .............................................. 214

Appendix D Comparison of Deflection Data: Observed and Back-Calculated ...................... 220

Appendix E Method of Equivalent Thickness ........................................................................... 235

Appendix F Data Used in Load Pairing Analyses ..................................................................... 237

Appendix G Axle Loads in Multiple-Axle Groups that Cause the Same Damage

as a Standard Axle Determined From 3d-Fem Analyses and Using

Homsi’s Damage Model .......................................................................................... 242

Appendix H Cemented Material Flexural Modulus Test Results ............................................. 249

Appendix I Cemented Material Flexural Fatigue Test Results ............................................... 256

Appendix J Estimation of Tolerable Strain From Fatigue Test Results ................................. 260

Appendix K Axle Group/Load Distributions .............................................................................. 263


Austroads 2015 | page vi

Tables

Table 1.1: Project reports .................................................................................................................. 3 Table 2.1: Axle group loads which cause the same damage as a Standard Axle ............................ 5 Table 2.2: Load damage exponents for each damage type ............................................................. 5 Table 2.3: Scala’s axle group loads which cause the same damage as a Standard Axle ............... 8 Table 2.4: Axle group loads which cause the same damage as a Standard Axle ............................ 9 Table 3.1: Typical values for parameters K and used in French aggressiveness calculation ...... 14 Table 4.1: Fatigue testing matrix for the Michigan study ................................................................ 23 Table 4.2: Load equivalency factors calculated by the Michigan study .......................................... 25 Table 4.3: Effect of strain load shape on fatigue life in the French study ....................................... 30 Table 4.4: Number of wheel (i.e. axle) passes represented by signals in the French study .......... 31 Table 4.5: Homsi’s experimental plan and observed Nf = f() or each signal .................................. 33 Table 4.6: Homsi’s relative signal equivalent factors (RSEF) ......................................................... 34 Table 6.1: ALF specification (before multiple-axle upgrade) .......................................................... 45 Table 6.2: Specifications of the modified ALF................................................................................. 47 Table 6.3: Location of ALF experiment sites................................................................................... 52 Table 6.4: Axle group load levels for ALF experimental program ................................................... 58 Table 6.5: Initial pavement bedding-in process .............................................................................. 60 Table 6.6: Experiments conducted ................................................................................................. 61 Table 6.7: Back-calculation model parameters ............................................................................... 81 Table 6.8: Aggregated stiffness parameters – simple averages (arithmetic means)...................... 82 Table 6.9: Aggregate stiffness parameters (MET) .......................................................................... 82 Table 6.10: Proposed standard loads for dual-tyre axles for use with empirical design

procedure ....................................................................................................................... 97 Table 6.11: Proposed standard loads for single-tyre axles for use with empirical design

procedure ....................................................................................................................... 97 Table 7.1: Material thicknesses and model parameters used in 3D-FEM modelling ................... 102 Table 7.2: Material thicknesses and model parameters used in CIRCLY modelling .................... 124 Table 8.1: Description of load pulse shapes ................................................................................. 139 Table 8.2: Fatigue regression equations for each load shape ...................................................... 149 Table 8.3: Summary of tolerable strains for different load shapes ............................................... 153 Table 8.4: Comparison of mean corrected tolerable strains ......................................................... 154 Table 8.5: Relative damages between different load shapes ....................................................... 154 Table 10.1: Axle group/load distributions used in example calculations ........................................ 160 Table 10.2: Parameters used in asphalt pavement design cases .................................................. 161 Table 10.3: Parameters used in cemented material pavement design cases ................................ 161 Table 10.4: Minimum thicknesses of asphalt determined using current Austroads

and multiple-axle damage models (Pacific Motorway traffic distribution) .................... 162 Table 10.5: Minimum thicknesses of cemented material determined using current Austroads

and multiple-axle damage models (Pacific Motorway traffic distribution) .................... 163 Table 10.6: Axle spacings determined from WIM data ................................................................... 164 Table 10.7: Maximum axle load sharing coefficients determined from WIM data .......................... 167 Table 10.8: Minimum thicknesses of asphalt determined using current Austroads

and multiple-axle damage models (Pacific Motorway traffic distribution) .................... 167 Table 10.9: Minimum thicknesses of cemented material determined using current Austroads

and multiple-axle damage models (Pacific Motorway traffic distribution) .................... 168 Table 10.10: Minimum thicknesses of asphalt determined using current Austroads

and multiple-axle damage models (Pacific Highway traffic distribution) ...................... 170 Table 10.11: Minimum thicknesses of cemented material determined using current Austroads

and multiple-axle damage models (Pacific Highway traffic distribution) ...................... 170 Table 10.12: Minimum thicknesses of asphalt determined using current Austroads

and multiple-axle damage models (Monash Freeway traffic distribution).................... 171 Table 10.13: Minimum thicknesses of cemented material determined using current Austroads

and multiple-axle damage models (Monash Freeway traffic distribution).................... 171


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Table 10.14: Minimum thicknesses of asphalt determined using current Austroads and multiple-axle

damage models (Kwinana Freeway traffic distribution) ............................................... 172 Table 10.15: Minimum thicknesses of cemented material determined using current Austroads and

multiple-axle damage models (Kwinana Freeway traffic distribution) .......................... 172

Figures

Figure 2.1: Ratio of tandem to single load compared with ratio of deflections .................................. 7 Figure 3.1: Comparison of LEF values from 1993 AASHTO guide and current

Austroads (2012) guide with an LDE = 5 ......................................................................... 13 Figure 3.2: Comparison of LEF values for French design method and current

Austroads (2012) guide with an LDE = 5 ......................................................................... 14 Figure 3.3: Discrete and integration methods for calculating LEFs ................................................... 15 Figure 3.4: Strains generated by a quad-axle group ........................................................................ 17 Figure 3.5: Peak mid-way method using strain response for a five axle group ............................... 18 Figure 3.6: Zone of neglected tension in the peak mid-way method ............................................... 19 Figure 3.7: Stress-strain hysteresis loops for asphalt material ........................................................ 20 Figure 3.8: Area under initial strain response curve for simulated quad-axle group

in a controlled stress test ............................................................................................... 21 Figure 4.1: Levels of interaction between axles used in the Michigan study ................................... 24 Figure 4.2: Dissipated energy density fatigue curve from the Michigan study ................................. 24 Figure 4.3: Axle factors (AF) for different interaction levels calculated by the Michigan study ........ 26 Figure 4.4: Loading wave shapes used in the Chuo University study ............................................. 27 Figure 4.5: Relationship between rate of dissipated energy and load cycles determined

by the Chuo University study ......................................................................................... 28 Figure 4.6: Example complex strain pulse used in the French waveform study .............................. 29 Figure 4.7: Aggressiveness of signals in the French study .............................................................. 31 Figure 4.8: Definitions of Homsi’s strain shape parameters ............................................................ 32 Figure 4.9: Homsi’s multi-linear model predictions compared to the experimental results .............. 35 Figure 4.10: Truck passing over test pavements during BASt study ................................................. 36 Figure 4.11: Location of pavement instrumentation used in BASt study ........................................... 36 Figure 4.12: Geometry of a three axle prime mover and semi-trailer used in the BASt study ........... 37 Figure 4.13: Tensile strains measured at the bottom of the asphalt layer (transverse direction) ...... 38 Figure 4.14: Tensile strains measured at the bottom of the asphalt layer (longitudinal direction) ..... 39 Figure 6.1: The ALF machine within the research testing building .................................................. 44 Figure 6.2: Individual axle module ................................................................................................... 46 Figure 6.3: The ALF multiple-axle assembly (tandem axle configuration) ....................................... 46 Figure 6.4: Triaxle and tandem axle assembly configurations showing individual modules

and primary and secondary attachment plates .............................................................. 48 Figure 6.5: Pins allowing pivoting of multiple-axle attachment plate................................................ 48 Figure 6.6: Single axle assembly configuration................................................................................ 49 Figure 6.7: Indoor facility for the ALF (54 m long by 18 m wide) ..................................................... 49 Figure 6.8: Structure of test pavements ........................................................................................... 50 Figure 6.9: Layout of test pavement ................................................................................................. 53 Figure 6.10: Appearance of the research testing facility building during construction ....................... 54 Figure 6.11: Profiler removing clay from borrow pit ........................................................................... 55 Figure 6.12: Placement of imported clay subgrade ........................................................................... 55 Figure 6.13: Tipping and spreading for first lift of base ...................................................................... 56 Figure 6.14: Appearance of primed surface ....................................................................................... 57 Figure 6.15: Load wheels centred over experiment width ................................................................. 58 Figure 6.16: Transverse load distribution ........................................................................................... 59 Figure 6.17: Experiment site (12 m × 1 m) with offset line for FWD testing....................................... 59 Figure 6.18: Strain gauge mounted to stub axle ................................................................................ 63 Figure 6.19: Example of data gained during single triaxle trolley pass .............................................. 64 Figure 6.20: Typical diagram of valid chainages (between vertical red dotted lines) ........................ 65


Austroads 2015 | page viii

Figure 6.21: Trenching experiment 3502 ........................................................................................... 66 Figure 6.22: Pavement trench showing straight edge used for layer profile measurements

and benched subgrade .................................................................................................. 67 Figure 6.23: ALF profilometer............................................................................................................. 68 Figure 6.24: Typical transverse surface profile data set (single chainage displayed) ....................... 69 Figure 6.25: Typical mean deformation along the trafficked length of an ALF experiment ............... 69 Figure 6.26: Measurement of deformation and rut depth ................................................................... 70 Figure 6.27: FWD collecting data under ALF ..................................................................................... 71 Figure 6.28: Progression of (post-bedding-in) overall deformation for all experiments ..................... 72 Figure 6.29: Rainfall measured at Dandenong weather station ......................................................... 73 Figure 6.30: Density, moisture content and CBR of pavement materials – 40 kN single axle

experiments .................................................................................................................... 75 Figure 6.31: Density, moisture content and CBR of pavement materials – 60 kN tandem group

experiments .................................................................................................................... 76 Figure 6.32: Density, moisture content and CBR of pavement materials – 80 kN tandem group

experiments .................................................................................................................... 77 Figure 6.33: Density, moisture content and CBR of pavement materials – 90 kN triaxle group

experiments .................................................................................................................... 78 Figure 6.34: Pavement model used in back-calculation .................................................................... 81 Figure 6.35: Alternative measures of deformation performance ........................................................ 83 Figure 6.36: Distribution of Erock for each axle type ............................................................................. 86 Figure 6.37: Distribution of maximum deformation observed for each load type ............................... 88 Figure 6.38: Distribution of cycles required to reach 4 mm deformation for 40 kN single axle

and 80 kN tandem group data ....................................................................................... 89 Figure 6.39: Distribution of Erock and E4 for 40 kN single axle and 80 kN tandem group paired data . 91 Figure 6.40: Distribution of cycles required to reach 3 mm deformation for 60 kN and 80 kN

tandem groups data ....................................................................................................... 92 Figure 6.41: Distribution of cycles required to reach 4 mm deformation for 40 kN single axle

and 90 kN triaxle group data .......................................................................................... 93 Figure 6.42: Distribution of Erock for 40 kN single axle and 90 kN triaxle group paired data ............... 94 Figure 6.43: Number of 40 kN single axle and 90 kN triaxle group cycles required to reach

4 mm deformation as a function of the effective stiffness of the crushed rock (Erock) ..... 95 Figure 7.1: Calculation of radius and contact stress for circular load model of tyre loads ............. 100 Figure 7.2: Example 3D meshes for 100 mm asphalt and 200 mm granular base pavements

(exploded view) ............................................................................................................ 101 Figure 7.3: Zoomed view of 3D mesh for load area ....................................................................... 102 Figure 7.4: Asphalt strains were recorded along the dotted lines for this quad-axle group ........... 103 Figure 7.5: Examples of strains ...................................................................................................... 104 Figure 7.6: Example calculation of tyre loads in multiple-axle groups that causes the

same damage as a Standard Axle using Homsi’s damage model .............................. 106 Figure 7.7: Example summary of standard axle loads in multiple-axle groups that causes

the same damage as a Standard Axle using Homsi’s damage model ....................... 107 Figure 7.8: Range of axle-loads in multiple-axle groups that causes the same damage

as a Standard Axle using Homsi’s damage model ...................................................... 108 Figure 7.9: Range of group loads that causes the same damage as a Standard Axle

using Homsi’s damage model ...................................................................................... 109 Figure 7.10: Cumulative distribution of Homsi shape parameters in 3D-FEM modelled strain

responses for single axle with 80 kN axle load ............................................................ 110 Figure 7.11: Range of axle-loads in multiple-axle groups that causes the same damage as a

Standard Axle using the simplified Homsi damage model .......................................... 112 Figure 7.12: Range of group loads that causes the same damage as a Standard Axle using

the simplified Homsi damage model ............................................................................ 113 Figure 7.13: Range of axle loads that causes the same damage as a Standard Axle using

the maximum peak model ............................................................................................ 116 Figure 7.14: Range of group loads that causes the same damage as a Standard Axle using

the maximum peak model ............................................................................................ 117


Austroads 2015 | page ix

Figure 7.15: Comparison of standard axle loads determined using simplified Homsi

and maximum peak methods ....................................................................................... 118 Figure 7.16: Range of axle loads that causes the same damage as a Standard Axle

using the summed peaks model .................................................................................. 120 Figure 7.17: Range of group loads that causes the same damage as a Standard Axle

using the summed peaks model .................................................................................. 121 Figure 7.18: Comparison of standard axle loads determined using summed peaks and

maximum peak methods .............................................................................................. 122 Figure 7.19: Range of axle loads that causes the same damage as a Standard Axle

using the summed peaks model (CIRCLY responses) ................................................ 124 Figure 7.20: Range of group loads that causes the same damage as a Standard Axle

using the summed peaks model (CIRCLY responses) ................................................ 125 Figure 7.21: Comparison of standard axle loads determined using simplified Homsi

and maximum peak methods (CIRCLY responses) .................................................... 127 Figure 7.22: Comparison of standard axle loads determined using summed peaks

and maximum peak methods (CIRCLY responses) .................................................... 127 Figure 7.23: Comparison of standard axle loads determined using 3D-FEM and CIRCLY

modelling ...................................................................................................................... 128 Figure 8.1: Flexural beam roller supports and load rollers ............................................................. 131 Figure 8.2: Marking saw cut lines for sample extraction ................................................................ 132 Figure 8.3: Precise cutting of samples using a concrete saw ........................................................ 133 Figure 8.4: Extraction of cut samples from road bed ..................................................................... 133 Figure 8.5: Samples being packed in damp sand in storage bins ................................................. 134 Figure 8.6: Cutting samples to the required depth ......................................................................... 134 Figure 8.7: Loading frame .............................................................................................................. 135 Figure 8.8: Assumed relationship between load pulse shape and axle spacing ........................... 137 Figure 8.9: Assumed relationship between vehicle speed and load pulse width ........................... 137 Figure 8.10: Load pulse shapes showing rest periods used in fatigue testing ................................ 138 Figure 8.11: Interaction between axle peaks within load pulse shape ............................................. 139 Figure 8.12: Load pulse shapes ....................................................................................................... 140 Figure 8.13: Succession of LVDT support frames used .................................................................. 142 Figure 8.14: Load support roller jigs ................................................................................................. 143 Figure 8.15: Distribution of modulus of samples (haversine pulse) ................................................. 145 Figure 8.16: Relationship between flexural modulus and relative density of samples

(haversine pulse).......................................................................................................... 146 Figure 8.17: Flexural fatigue results for single axle load shape ....................................................... 147 Figure 8.18: Flexural fatigue results for tandem axle group load shapes with interactions

between axles of 40% and 80%................................................................................... 148 Figure 8.19: Flexural fatigue results for triaxle axle group load shapes with interactions

between axles of 40% and 80%.................................................................................. 148 Figure 8.20: Flexural fatigue results for quad-axle group load shapes with interactions

between axles of 40% and 80%................................................................................... 149 Figure 8.21: Flexural fatigue relationships expressed in terms of cycles (axle groups)

of loading and peaks (axles) of loading ....................................................................... 150 Figure 8.22: Relative damages between different load shapes as a function of axle ratio .............. 155 Figure 10.1: Distribution of maximum LSC in WIM data .................................................................... 166 Figure 10.2: Minimum thickness of 3000 MPa asphalt for different design traffic levels ................. 173 Figure 10.3: Minimum thickness of 5000 MPa asphalt for different design traffic levels ................. 174 Figure 10.4: Minimum thickness of 4000 MPa cemented material for different design

traffic levels .................................................................................................................. 175 Figure 10.5: Minimum thickness of lean mix concrete for different design traffic levels .................. 176


Austroads 2015 | page 1

1. Introduction

1.1 The Australasian Pavement Network

Australia and New Zealand have led the world for many years in the design and management of low cost

road pavements. This has allowed sealed road access to areas which otherwise would only be serviced by

gravel roads, and has reduced the total cost of construction and maintenance across the network. In

Australia, these roads carry about 80% of the total road freight task, and therefore play a huge role in

regional, state and national economies.

Despite major dependence on these roads, Australasian design, material specifications and construction

technologies for them are still mostly empirically based. In a world without other constraints, building roads

today the same way as built yesterday may be sustainable, but it does not assist road agencies facing

today’s challenges. These include an increasing scarcity of quality materials, rapidly changing vehicle

designs and loads, a desire to incorporate sustainable materials (including recycled and industrial waste

products), and the emerging pressures of climate change.

One of the largest challenges facing road network owners is the rapidly growing amount of freight carried

by road. Predictions of road freight doubling or more over a ten-year period have been made by various

government bodies. Additionally, there has been a recent trend towards more innovative heavy vehicle

designs, and network owners are being faced with the need to make predictions of the long-term effect of

these new vehicles on their networks. These pressures are placing increased focus on the way in which

pavement designers and asset managers estimate the performance of road pavements under different axle

loads.

1.2 Traffic Loads

Traditionally, pavement design was based on the number of ‘equivalent standard axles’ likely to traffic a

pavement during its design life. With changing traffic demands of pavements, concerns have arisen that

this method may be too simplistic. A great deal of research has been conducted in recent years examining

the relative damaging effects of different axle loads on Australasian pavement types (e.g. Austroads 2006a,

Yeo & Sharp 2006); however, this work has addressed the damage related to a single axle carrying

different loads and/or tyre types. A serious examination of the effects of axle group type on pavement

performance has not been undertaken, particularly for Australian/New Zealand pavement types. It is

difficult to evaluate the effects of different axle groups using in-service pavements because of the problems

associated with isolating the effects of a particular axle group in mixed traffic, and practical problems

associated with obtaining performance data on long-life structures.

The development of more accurate procedures for assessment of the impact of a spectrum of axle group

loads is fundamental to many issues facing the road transport industry, and will assist:

pavement designers through the development of improved procedures for the structural design of

Australian and New Zealand road pavements

in the selection of the most appropriate pavement type for the prevailing traffic conditions

asset managers to develop improved models for management of the road network at the network level

industry (vehicle designers and operators) in the development of more efficient heavy vehicles, which

will maximise payload without increasing the wear to established road infrastructure

policy makers and planners in the development of improved methods of addressing the most equitable

method of estimating future maintenance and rehabilitation costs, and a transparent method of

defraying these costs to all stakeholders.



The current Austroads pavement structural design methods for flexible and rigid pavements consider the

design traffic in different ways:

The rigid pavement design method considers the response of the candidate design pavement to

different load levels and group types (single, tandem, triaxle, etc.), and is based on analytical

modelling of those different load/group types.

The flexible pavement design method models the response of a pavement to a single axle load, and

provides means of translating different axle load/group combinations within the design traffic spectrum

to an equivalent count of repetitions of the single axle used in the pavement model.

As the analytical pavement modelling that underlies the rigid design method includes the direct

determination of pavement responses under multiple-axle groups and with varying pavement structure, it is

considered that the current procedure adequately addresses the different levels of damage caused by

grouped and ungrouped axles. As a result, the project did not examine multiple-axle effects on concrete

pavement design, and was limited to design flexible pavements only.

The current means of assessing the relative damaging effects of different axle groups (single, tandem,

triaxle, etc.) on road pavements is by comparison of the peak static pavement deflection response under

the axle groups. This approach ignores the contribution to pavement damage made by the axles in the

group that do not correspond with the peak response. Additionally, the traditional assumption that the

deflection response is the most appropriate indicator of pavement damage is open to question and is not

consistent with the Austroads mechanistic design procedures, in which maximum strains rather than

deflections are used to calculate the performance of pavement materials.

Despite the fundamental nature of this issue, little research work has examined these issues, and the little

international work that has been done has focussed on relatively thick asphalt pavements, not on pavement

types typical to Australia and New Zealand.

Austroads established projects TT1219 Influence of Multiple-axle Loads on Pavement Performance and

TT1614 Pavement Wear Effects of Heavy Vehicle Axle Groups to examine these issues further.

In general terms, the objective of this combined research study was to investigate – using a combination of

current research, laboratory characterisation and field trials – improved methods for assessing the

pavement damage caused by different multiple-axle group loads; and to develop a framework that can be

used to quantify this pavement damage for use in Austroads flexible pavement design processes.

Recognising that a severe lack of material pavement performance data was preventing the development of

a defendable framework, the project ambitiously sought to obtain performance data for common pavement

materials.

1.3 Report Structure

This report summarises the combined work undertaken by these Austroads projects. After the introductory

sections summarising current Austroads and international methods (Sections 2 to 4), the report presents an

outline of the project testing work plan in Section 5.

Section 6 is dedicated to the collection and analysis of performance data of an unbound granular pavement

under full-scale multiple-axle group loads applied with the Accelerated Loading Facility test system. This

work was focussed on the use of multiple-axle group loads in the Austroads empirical design process for

unbound granular pavements with thin bituminous surfacings.

Sections 7 and 8 consider, in turn, the two bound materials whose flexural fatigue performance is central to

the Austroads mechanistic design process. Section 7 considers asphalt and contains an analysis based

upon the findings of an extensive international laboratory-based research project. Section 8 documents a

similar laboratory-based assessment, undertaken by the Austroads project, of the performance of a

cemented material subjected to simulated multiple-axle loads.

In order to assess how the findings of these three main bodies of work would impact on the design of

flexible pavements if the findings were to be implemented into Austroads procedures, Section 9 documents

a series of design examples.



The report finishes with an overarching summary and conclusions, followed by extensive appendices to

supplement the information provided within the report body.

1.4 Previous Related Reports

During the conduct of the projects, a series of reports have been produced (Table 1.1). Some of these

reports provide more detailed documentation of data collected than is contained within this final report, and

some of the reports represent progress studies. One report documents an approach to work that was being

planned at one stage, but was subsequently not pursued. The following table provides references to each

of these reports, and notes whether the report is superseded by this document, or provides additional

information.

Table 1.1: Project reports

Reference Title Contents Status

Austroads (2011a)

The Influence of Multiple-axle Loads on Pavement Performance: Interim Findings.

Extensive interim report containing many sections common to this report.

Superseded

Austroads (2011b)

A Laboratory Study of the Influence of Multiple-axle Loads on the Performance of a Cement Treated Material – Interim Report.

Contains complete documentation on the laboratory program to assess cemented material performance. Contains raw data. Contains an inconclusive analysis that was expanded upon in this final report.

Current

Data collection method and reporting is more comprehensive than this report.

Analysis results are less comprehensive.

Austroads (2011c)

Testing Plan to Examine the Effects of Multiple-axle Loads on Asphalt Fatigue Using Four-point Beam Tests

Documents the development of a testing plan to undertake a separate laboratory-based research program examining asphalt flexural fatigue using Australian-based equipment and methods. The testing plan was not undertaken as the findings of international work were found to be comprehensive enough to not warrant replication.

Current

Contents not relevant to final project outcomes or conclusions.

Austroads (2011d)

The Influence of Multiple-axle Loads on the Performance of an Unbound Granular Pavement under Accelerated Loading: Construction of Test Pavements

Comprehensive documentation of construction of the test pavement used for Accelerated Loading Facility testing.

Current

Contains comprehensive reference information.

Austroads (2013)

The Influence of Multiple-axle Loads on the Performance of an Unbound Granular Pavement under Accelerated Loading: Interim Data Report

Contains comprehensive documentation of all data collected during the Accelerated Loading Facility loading of the unbound granular test pavement. Does include data processing, but does not contain any analysis.

Current

Contains comprehensive reference information.



2. Australasian Practice

2.1 Overview of Pavement Design Methods

The Austroads pavement design processes provide performance models to assess the damaging effects of

different axle loads on commonly used pavement materials (Austroads 2012a). The design processes

include three different design methods:

an empirical design method used for sprayed seal surfaced unbound granular pavements

a mechanistic method used for flexible pavements containing asphalt or cemented materials

a mechanistically-based analytical method used for rigid concrete pavements.

2.1.1 Design of Unbound Granular Pavements with Thin Surfacings

For a given thickness of granular pavement and strength of underlying subgrade, the empirical design

method uses a design chart to provide the allowable load repetitions before the terminal condition is

reached. Allowable load repetitions are expressed in terms of Equivalent Standard Axles (ESAs). The

terminal condition, considered to be an unacceptable degree of surface roughness and extent of rutting, is

not explicitly defined but probably corresponds with an average rut depth of 20 mm and a roughness level

approximately three times the initial level (Jameson 2013).

2.1.2 Mechanistic Design of Flexible Pavements

The mechanistic method is limited to the assessment of load-associated distresses, and considers three

different distress or damage types:

rutting and shape loss exhibited on the pavement surface

flexural fatigue of asphalt materials

flexural fatigue of cemented materials.

The method uses computer software to determine critical strain responses in pavement layers resulting

from the static application of a standard reference load, the Standard Axle. The Standard Axle is defined as

a single axle with dual tyres loaded with 80 kN. The performance models used in the design process relate

the computed strain levels resulting from a single (static) application of the Standard Axle to the number of

allowable repetitions of the load. The method uses the concept of a Standard Axle Repetition (SAR) as the

unit of damage due to a single pass of an axle.

Road pavements are subjected to a range of different axle group types, and a range of loads on those axle

types. In order to express the spectrum of different axle group load levels expected in the design traffic, the

design method uses Equation 1 to determine the number of Standard Axle Repetitions generated by a

given vehicle.

𝑆𝐴𝑅 = ∑ (𝐿𝑖

𝑆𝐿𝑖)

𝐿𝐷𝐸𝑚

𝑖=1

1

where

𝐿𝑖 = load carried by axle group type 𝑖(kN)

𝑆𝐿𝑖 = standard load for axle group type (Table 2.1)

𝐿𝐷𝐸 = load damage exponent – varies with distress type being considered (Table 2.2)

𝑚 = number of axle groups for the vehicle



Table 2.1 lists the standard loads for each axle group type. Each axle group type loaded to its standard

load is considered to cause the same amount of pavement damage as the Standard Axle.

Table 2.1: Axle group loads which cause the same damage as a Standard Axle

Axle group type Load (kN)

Single axle with single tyres (SAST) 53

Single axle with dual tyres (SADT) 80

Tandem axle with single tyres (TAST) 90

Tandem axle with dual tyres (TADT) 135

Triaxle with dual tyres (TRDT) 181

Quad-axle with dual tyres (QADT) 221

Note: A Standard Axle is an SADT axle with a load of 80 kN.

Source: Austroads (2012a).

The load damage exponent (𝐿𝐷𝐸) used in the design method varies with the damage type being

considered (Table 2.2). These load damage exponents are used to calculate the following allowable SARs

for each damage mode:

SAR4 – Standard Axle Repetitions calculated using an 𝐿𝐷𝐸 of 4:

This is used to assess the damage to sprayed seal surfaced unbound granular pavements. SAR4 is

commonly called Equivalent Standard Axles and is used as the unit of damage in the empirical design

method.


This is used to assess the flexural fatigue damage of asphalt materials within a flexible pavement

structure.


This is used to assess the rutting and loss of shape of flexible pavements.


This is used to assess the flexural fatigue damage of cemented materials within a flexible pavement

structure.

The mechanistic design method, using SAR7, can be used to design sprayed seal unbound granular

pavements, and will yield very similar results as the empirical method. The performance relationship used

in the mechanistic method for rutting and loss of shape distress was derived from the empirical method.

Table 2.2: Load damage exponents for each damage type

Design method Pavement type Type of damage Load damage exponent

Mechanistic Pavement containing one or more bound layers

Fatigue of asphalt 5

Fatigue of cemented material 12

Rutting and loss of surface shape 7

Empirical Empirical design chart for granular pavement with thin bituminous surfacing

Overall pavement damage 4



2.1.3 Rigid Pavement Design

The rigid pavement design procedure is based upon the procedure developed by the US Portland Cement

Association (PCA 1984). The procedure considers two causes of pavement distress:

Flexural fatigue resulting from the generation of repeated tensile stresses at the bottom of the base

slab due to application of traffic loads. The analysis considers the location of the wheelpaths relative to

the outer longitudinal (in the direction of travel) edge of the slab, as this is the location where the

generated stresses are most critical.

Erosion of the pavement foundation in regions under joints or cracks caused by the accumulated

action of wheel passages crossing the joints/cracks.

Finite element modelling (Packard & Ray 1986, Packard & Tayabji 1985, Heinrichs et al. 1988) was used to

determine the response of the slab and foundation to a range of wheel loads and axle-group combinations.

A wide range of slab thicknesses were modelled.

As it is considered (Vorobieff & Hodgkinson in Jameson 2013) that the rupture of a concrete slab is caused

by heavier loads in the spectrum of all wheel/axle loads, and that the stresses generated within the slab are

dependent upon the thickness of the slab, the use of generalised load equivalencies, as used in the flexible

design methods, is inappropriate. Therefore, the design method considers the damage caused by each

combination of axle load and axle-group within the design traffic spectrum.

As the analytical pavement modelling that underlies the rigid design method included the determination of

pavement responses under multiple-axle groups, and with varying pavement structure, it is considered that

the current procedure adequately addresses the different levels of damage caused by grouped and

ungrouped axles. As a result, the project did not examine multiple-axle effects on concrete pavement

design, and was limited to the design flexible pavements only.

2.2 Origins of Standard Axle Group Loads

The following summary of the origins of standard axle group loads used in flexible design processes (Table

2.1) is drawn from Potter’s (in Jameson 2013) detailed description. Potter’s notes were based upon

surviving records, his recollection of analyses undertaken, and the resolutions of technical meetings.

During the 1960s, several independent analyses of AASHO road test data provided estimates of the

relative damaging effects of dual-tyred single axles and dual-tyred tandem axles (AASHO 1962). As the

test pavements in the road test were comprised of relatively thick asphalt layers and were subject to freeze-

thaw cycles, it was considered inappropriate to directly use the results of these analyses for Australian

pavements due to their sprayed seal surfacing (or thin asphalt) and lack of freeze-thaw cycles. In addition,

the analyses did not provide insight into the damaging effects of both single-tyred single axles (steer axles)

and triaxles. Steer axles were considered to have caused little damage during the road test, and so were

not included in subsequent analyses, and triaxles were not included in the road test at all.

In order to determine standard load levels for each axle group type that were suitable for use in Australia,

Scala (1970b) undertook a field study, commencing in 1969. His work was based on the presumption,

considered to be reasonably supported by limited data from the AASHO test, that axle groups (type and

load) that caused equal maximum deflection of the pavement surface caused equal pavement damage.

Scala measured surface deflections caused by different axle group types and load levels on a small

number of sprayed seal and thin asphalt surfaced pavements in the Altona-Williamstown area of

Melbourne. Scala’s primary data and analyses were documented in a series of internal ARRB reports,

which Potter was unable to trace at the time he prepared his notes. Given the lack of primary

documentation, and the passage of many years, it is understandable that Potter was unable to be clear in

describing the means by which the surface displacement data was collected. He mentions use of both a

conventional Benkelman Beam and a ‘scaled up’ version. It would appear that a pad (approximately 50 mm

thick, made from industrial conveyor rubber belting) was placed on the pavement surface. The tip of the

Benkelman Beam(s) was placed in a transverse slit cut in the pad, i.e. the orientation of the Beam was

perpendicular to the travel path of the vehicle, and the peak surface deflection response was measured as

the axle group passed over the pad.



Some of Scala’s data and findings are reported in a conference paper (Scala 1970a). The only data from

the field study presented in the paper relates to dual-tyred single and tandem axles, and is in the form of a

plot of tandem axle deflection/single axle deflection versus tandem axle load/single axle load (Figure 2.1).

A wide range of deflection ratios is evident for each of the six load ratios tested. Each load ratio was tested

on a separate day of testing. Scala’s notes for three days of testing (shown as 11, 12 and 13 in Figure 2.1)

reveal that the data ‘may be affected by water penetration’.

Figure 2.1: Ratio of tandem to single load compared with ratio of deflections

Source: Scala (1970a).

Regarding the load level on a single-tyred single axle that produces the same maximum deflection as a

Standard Axle, Scala (1970a) states that ‘the equivalent load by deflection tests is about 11.6 kips (ed. 51.6

kN)’ and ‘in this paper, 12 kips (53.4 kN) is used mainly for ease of computation’.

In the paper, Scala provides two values for the load on a tandem axle group which produced the same

maximum deflection as the 18 kip (80 kN) loaded Standard Axle – 28.9 kip (128.6 kN) and 29.2 kip

(129.9 kN). The two values would appear to have been the values Scala determined from two separate

studies of surface deflections. Again, the paper does not present any data supporting these numbers. For

the remainder of the paper, Scala assumes that ‘a 30 kip tandem axle load gives a deflection of the same

magnitude as an 18 kip single axle (dual tyre) load’.

In the same paper, Scala’s only statement regarding the load on a triaxle group that produces the same

maximum deflection as a Standard Axle is that ‘it is expected that the three axle group with a load of

40.7 kip (181.0 kN) would be equivalent to a single axle of 18 kip (80.1 kN)’.

In an ARRB internal report that was written about five months after the paper described above was

published, Scala rounded his estimate for the load on a single-tyred axle that produces the same damage

as a Standard Axle to a neat 12 kip (53.4 kN) (Scala 1970b).

Potter records that, as part of the NAASRA Economics of Road Vehicle Limits (ERVL) study, Stevenson

(1976) used both of the Scala references discussed above and also conversations with Scala as a basis for

the values of load on each axle group considered to produce the same damage as the Standard Axle.

Scala’s final values used by Stevenson are shown in Table 2.3.



Table 2.3: Scala’s axle group loads which cause the same damage as a Standard Axle

Axle group Load

kip kN Tonnes

Single axle, single tyres (SAST) 12 53.4 5.4

Single axle, dual tyres (SADT) 18 80.1 8.2

Tandem axle, dual tyres (TADT) 30 133.4 13.6

Triaxle, dual tyres (TRDT) 40.7 181.0 18.5

The Interim Guide to Pavement Thickness Design (National Association of Australian State Road

Authorities 1979) used the load values but, Potter believed probably due to oversight, dropped

consideration of triaxles.

The NAASRA pavement design working group reviewing the interim procedures revisited the load values

prior to their publication (NAASRA 1987) as finalised procedures. Potter states that the working group

noted the difference between Scala’s 30 kip load of a dual-tyred tandem axle group and values reported by

AASHO (33.4 kip) and the Asphalt Institute (31.5 kip) cited in Scala (1970a). Potter also states that the

working group had noted that Scala (1977) had subsequently adopted a value of 13.7 t for tandem axles.

On these grounds, Potter states that the working group adopted a revised value for tandem axles of

135 kN. Whilst not disputing Potter’s statements, it should be noted that this adjustment is relatively minor

in effect (corresponding to a change in only 0.2 t of load), and that Scala’s use of 13.7 t in 1977 is simply a

reference to his earlier conference paper described above (Scala 1970a)1. The use of different conversion

factors between parameters and different unit systems may provide an alternative explanation for these

changes.

More significantly, the working group incorporated triaxles into the final procedures, and also implicitly

included a reference load level for twin steer axles by stating that ‘twin steer axles may be considered to be

equivalent to tandem axles (both with dual wheels) which are loaded to 1.5 times the load on the twin steer

axles’. This statement effectively translates into a load of 90 kN, a value explicitly stated, from 2004, in

subsequently published revisions of the pavement design process (Austroads 2012a). Although Potter

does not document the basis for this equivalency, it seems most likely that it was based upon equating the

maximum surface deflections under the axle group and the Standard Axle group determined using linear

elastic modelling.

Using a variety of theoretical procedures, Vuong (2002) estimated the load on a quad-axle that would

cause the same deflection as a Standard Axle. Based on this analysis, a value of 221 kN was used as the

reference load in the 2004 version of the pavement design procedures (Austroads 2004). Subsequent field

measurements undertaken on a road in the Port of Brisbane confirmed that this value caused the same

maximum surface deflection as a Standard Axle (Yeo et al. 2007). The testing used multi-depth

deflectometers installed within the structure of thin asphalt surfaced granular pavements to determine the

surface deflection under a Standard Axle, and both a triaxle and quad-axle group with various loads. As

with Scala’s field testing of the late 1960s, this testing was conducted at creep travelling speeds.

2.3 Assumed Interaction between Axles

If it were assumed that a multiple-axle group is comprised of n single axles (SADT) of equal load, acting

entirely independently of each other, the total load, L, on those n single axles that causes the same

pavement damage as an Equivalent Standard Axle (ESA) could be determined using Equation 2. Table 2.4

shows the results of this calculation for tandem, triaxle and quad-axle groups, and demonstrates that the

results are remarkably similar to those used in the Austroads design processes.

1 This confusion is not helped by Scala’s incorrect dating of his ARRB Conference paper in the references of his 1977 report. Scala gives a date of 1972 rather than the correct 1970 date.



1 = 𝑛 × (𝐿

𝑛⁄

80)

4

2

where

𝑛 = number of axles in the multiple-axle group (i.e. 2 for tandem, 3 for triaxle, etc.)

𝐿 = total load on axle group (kN)

Table 2.4: Axle group loads which cause the same damage as a Standard Axle


Austroads Equation 2

Single axle with dual tyres (SADT) 80 –

Tandem axle with dual tyres (TADT) 135 135

Triaxle with dual tyres (TRDT) 181 182

Quad-axle with dual tyres (QADT) 221 226

This implies that the loads used in the Austroads design processes implicitly assume that interaction

between the loads on each axle within a multiple-axle group does not occur, and that each axle of a

multiple-axle group can be considered to be equivalent to a single axle. That is, in terms of pavement

damage, there is no interaction between the axles in the group.

2.4 Limitations of Current Practice

The key assumption underlying the Australian method for determining loads on axle groups that cause

equal damage is that, any axle group that causes the same maximum surface deflection as a Standard

Axle causes the same damage as the Standard Axle. There are three potential areas where this

assumption is open to serious question.

Firstly, in equating damage based solely upon the maximum surface deflection response, the approach

ignores the number of axles within the group that may generate multiple occurrences of this maximum

deflection.

Secondly, the assumption that the deflection response is the most appropriate indicator of pavement

damage is open to question. By using the surface deflection response, the approach provides no insight

into the performance of the individual material layers of which the pavement is comprised, but rather treats

the pavement as a single entity. The mechanistic design process adopted in Australia and New Zealand

characterises the performance of pavement materials in terms of their response to strains and not

deflections. Hence, the use of deflection response is incompatible with the current design process. Other

mechanistic design procedures used internationally, similarly use either strain or stress responses or no

deflection.

Thirdly, surface deflection measurement field trials have been, for practical reasons, limited to creep speed

travel of the axle groups over the deflection sensors. The visco-elastic nature of some pavement materials,

as well as the development of pore pressures within unbound crushed rock and natural soil layers, would

be expected to be affected by the loading and unloading speed.



There is a dearth of data relating axle configuration to observed pavement performance. The AASHO road

test in the late 1950s represents the only significant pavement performance data set in which pavements

were subjected to different axle group load types and levels, in a manner that ensured that sections of

pavement were only subjected to a given load level and axle group type. The road test examined only

single and tandem axle groups, and used relatively thick pavements which were subject to freeze-thaw

cycles. All of these factors are particularly unrepresentative of Australian road pavements. Additionally, the

study expressed pavement performance in terms of the pavement serviceability index (PSI) and not on the

performance of individual pavement material layers. Incorporation of the general PSI measure of

performance into a mechanistic design framework is problematic, as the PSI does not allow any

explanatory link between pavement modelling responses and performance.



3. Review of Alternative Methods

3.1 Introduction

A review of international literature discussing the effect of multiple-axle groups on pavement performance

was conducted.

The concept of a load equivalency factor (𝐿𝐸𝐹) is a convenient means of expressing the damage caused to

a pavement from a given load on an axle group, relative to the damage caused by the Standard Axle

reference load (Equation 3).

The load equivalency for a series of axle groups is determined by multiplying the 𝐿𝐸𝐹 for each axle load

level/group combination by the number of occurrences of that combination in the series. A load on an axle

group providing an 𝐿𝐸𝐹 of unity is considered to cause the same damage as the Standard Axle.

𝐷𝑖 = 𝐿𝐸𝐹𝑖 × 𝐷𝑆𝐴 3

where

𝐿𝐸𝐹𝑖 = load equivalency factor for axle group 𝑖

𝐷𝑖 = damage caused by 𝑖

𝐷𝑆𝐴 = damage caused by Standard Axle load

Ideally, 𝐿𝐸𝐹 factors would be determined from observing pavement or material performance and directly

utilising pavement damage in Equation 3. An alternative approach is to use the response of pavements or

materials to load, in place of observed damage.

3.2 1993 AASHTO Guide

The American Association of State Highway and Transportation Officials (AASHTO) have developed two

distinctly different pavement design guides. The last official release of the original guide was in 1993, and

so the following discussion refers to this guide as the 1993 AASHTO guide. The new AASHTO guide

(AASHTO 2008) incorporates radical changes in design methods, and is widely known as the Mechanistic-

Empirical Pavement Design Guide (MEPDG). The MEPDG is discussed in Section 3.4.3.

The AASHTO 1993 method is predominantly used to design flexible pavement designs in the USA. It uses

𝐿𝐸𝐹s based on analysis of the AASHO road test (AASHO 1962) conducted in the late 1950s to early

1960s. The road test consisted of six loops of road, including a broad range of both flexible and rigid

pavement structures. The pavements were trafficked with test vehicles, and it was ensured that each lane

only received trafficking from a single type of vehicle (i.e. axle combination).

The flexible pavement structures were characterised in terms of their structural number (SN), and the

observed performance changes were expressed in terms of a change in the pavement serviceability index

(PSI). The performance data was observed and comparisons made between the same pavement

structures loaded with different axle configurations.

The 𝐿𝐸𝐹s used in the 1993 AASHTO guide processes were based on analysis of the performance of road

test pavements under dual-tyred single and tandem axle groups. Factors are also provided for triaxle

groups, however, these were not based on road test data (the road test did not include triaxle groups), but

rather on the assumption that one pass of a triaxle is equivalent to one pass each of a single and tandem

axle. Rilett and Hutchinson (1988) concluded that this assumption was not supported by field observations

or theoretical analysis. Steer axles were not considered to contribute to pavement wear during the road test

and, consequently, 𝐿𝐸𝐹s were not developed for this axle type (i.e. single-tyred single axle).



For a load level and axle group being considered, the relationship for determining the 𝐿𝐸𝐹 (Equation 4) is a

function of the structural number (SN) of the pavement being loaded and the terminal PSI value (i.e. the

serviceability of the pavement at the end of its design life).

A comparison of the 𝐿𝐸𝐹 values in the Austroads (2012a) guide with the 1993 AASHTO guide shows that

the AASHTO values are considerably lower. This is demonstrated for asphalt damage (𝐿𝐷𝐸 = 5) in the

example in Figure 3.1.

The performance data used to derive the 1993 AASHTO guide 𝐿𝐸𝐹 values was from the trafficking of

relatively thick asphalt pavements which were subjected to freeze-thaw cycles. Both of these factors are

especially unrepresentative of Australian road pavements, which are predominantly granular pavements in

non-freezing conditions. Additionally, the 𝐿𝐸𝐹 values were based upon pavement performance expressed

in terms of PSI, and not on the performance of individual pavement material layers. The incorporation of a

general PSI measure of performance into a mechanistic design framework is problematic, as the PSI does

not allow any explanatory link between pavement modelling responses and performance. The move to a

mechanistic design process has resulted in these old 𝐿𝐸𝐹 values not being adopted in the more recent

mechanistic design process used in the 2008 AASTHO Guide (Section 3.4.3).

1

𝐿𝐸𝐹= (

𝐿18 + 𝐿2𝑠

𝐿𝑥 + 𝐿2𝑥)

4.79

× (10

𝐺𝛽𝑥

10𝐺

𝛽18

) × (𝐿2𝑥)4.33

4

where

𝐿𝐸𝐹 = load equivalency factor for axle group at the load being evaluated

𝐿𝑥 = axle load being evaluated (kip)

𝐿18 = 18 kip (i.e. Standard Axle load)

𝐿2 = code for axle configuration

1 = single axle

2 = tandem axle

3 = triaxle

x = axle load equivalency factor being evaluated

s = Standard Axle (𝐿2𝑠 = 1)

𝐺 = log10 (4.2 − 𝑝𝑡

4.2 − 1.5)

𝑝𝑡 = terminal pavement serviceability index

𝛽 = 0.4 + (0.08(𝐿𝑥 + 𝐿2𝑥)3.23

(𝑆𝑁 + 1)5.19𝐿2𝑥3.23 )

𝑆𝑁 = structural number of the pavement



Figure 3.1: Comparison of LEF values from 1993 AASHTO guide and current Austroads (2012) guide

with an LDE = 5

Note: A typical terminal PSI value of two and pavement structural number of five was used in Equation 4 to generate the 1993 AASHTO guide values.

3.3 French Design Manual

The French pavement design manual (LCPC & SETRA 1997) contains a method for determining the

aggressiveness of each axle, whether isolated or within a multiple-axle group, using Equation 5. The

aggressiveness is the damage caused by one pass of an axle with load 𝑃 compared to the damage caused

by one pass of the reference axle of load 𝑃𝑂. A key factor in the relationship is the factor 𝐾, which is used

to consider the effect that grouping axles together has on the damage caused. The manual states that the

factor varies with pavement structure and material composition, and provides a table of average values

(Table 3.1).

𝐴 = 𝐾 (

𝑃

𝑃𝑂)

𝐿𝐷𝐸

5

where

𝐴 = aggressiveness of axle

𝐾 = factor used to take into account the axle group type (equals one for single axles)

𝐿𝐷𝐸 = load damage exponent

0.0

1.0

2.0

3.0

4.0

5.0

0 50 100 150 200 250 300 350

LEF

Group load (kN)

Austroads single

Austroads tandem

Austroads triaxle

AASHTO single

AASHTO tandem

AASHTO triaxle



Table 3.1: Typical values for parameters K and used in French aggressiveness calculation

Pavement type 𝜶 K

Single axle Tandem Triaxle

Flexible and bituminous pavements 5 1 0.75 1.1

Semi-rigid pavements 12 1 12 113

Concrete pavements

Slabs

Continuously reinforced concrete

12

12

1

1

12

unknown

113

unknown

Source LCPC & SETRA (1997).

Using the average 𝐾 values in Table 3.1, 𝐿𝐸𝐹 values can be calculated relative to a standard 80 kN

Standard Axle as used in Australia (the reference axle load in France is 130 kN). This is shown in

Figure 3.2 for a flexible pavement (i.e. 𝐿𝐷𝐸, 𝛼 equal to five). It can be seen that French values are lower

than Austroads ones, but not as low as those determined using the AASHTO 1993 method. It must be

remembered however, that the French method considers the value of the 𝐾 factor to be a function of both

the structure and composition of the pavement.

Figure 3.2: Comparison of LEF values for French design method and current Austroads (2012) guide

with an LDE = 5

The line for single axle 𝐿𝐸𝐹 values using the French method is the same as the Austroads line, as they both use a damage exponent of five.

3.4 Response to Load Methods

3.4.1 Relating Response to Damage

The concept of a load equivalency factor (𝐿𝐸𝐹) is also a convenient means of expressing the response of a

pavement to a given load on an axle group, relative to the response of the pavement to the application of a

Standard Axle reference load (Equation 6). The load equivalency for a series of axle groups is determined

by multiplying the 𝐿𝐸𝐹 for each axle load level/group combination by the number of occurrences of that

combination in the series.

0.0

1.0

2.0

3.0

4.0

5.0

0 50 100 150 200 250 300 350

LEF

Group load (kN)

Austroads single

Austroads tandem

Austroads triaxle

France tandem

France triaxle



The load on an axle group providing an 𝐿𝐸𝐹 of unity is considered to cause the same damage as the

Standard Axle. The underlying premise of this approach is that equal response equates to equal pavement

damage.

𝐿𝐸𝐹𝑖 = (𝑅𝑖

𝑅𝑆𝐴)

𝑛

6

where


𝑅𝑖 = pavement response to load 𝑖

𝑅𝑆𝐴 = pavement response to Standard Axle load

𝑛 = damage exponent for the response and mode of distress (i.e. 𝑛 = 𝐿𝐷𝐸)

Response to load methods fall into two distinct categories (Figure 3.3):

discrete methods – which characterise the response to load curve using only discrete values (typically

the magnitude of the peak and trough values of the response curve)

integration methods – which use the whole response to load curve.

Figure 3.3: Discrete and integration methods for calculating LEFs

Source: Hajek and Agarwal (1990).



3.4.2 Maximum Response Methods

Maximum response methods consider only the maximum response of the pavement to the axle group load

applied. For example, in Case a in Figure 3.3, a maximum response method would only consider the value

of D1 in determining the load equivalency factor. The Austroads method for relating load damage between

axle groups discussed in Section 2.1.3 is a maximum response method that uses the surface deflection

(response) of the pavement.

The 𝐿𝐸𝐹 using the maximum response method is calculated using Equation 7.

𝐿𝐸𝐹𝑖 = (𝑅𝑖

𝑅𝑆𝐴)

𝑛

7

where

𝐿𝐸𝐹𝑖 = load equivalency factor for axle group i




An alternative to using surface deflection in the method would be the use of maximum strain generated in a

pavement layer under an axle group. Any maximum strain generated under a given axle group and load

that matched the strain generated under a Standard Axle would be considered to cause the same damage

as the Standard Axle.

Using strain response instead of surface deflection has the advantage that the strain response can be

related directly to strain-based material performance models (e.g. the mechanistic Austroads design

process uses tensile strains as a key input in determining the fatigue performance of asphalt materials).

As noted above, the main limitation of maximum response methods is that they ignore the potentially

pavement damaging effects of response peaks other than the maximum one (e.g. D*2 in Case a in Figure

3.3).

3.4.3 MEPDG

The MEPDG (AASHTO 2008) is a fundamentally different design method to the AASHTO (1993) method.

Central to the method is modelling of the response of pavements to applied loads. It uses a maximum

response method to consider damage caused by multiple-axle groups.

In the context of this report, the MEPDG differs from the current Austroads mechanistic design procedure in

two fundamental ways:

The Austroads procedure considers that the load applied to a multiple-axle group that will cause the

same damage as the Standard Axle is independent of the structure of the pavement. The MEPDG

considers that the pavement structure has an effect on the loads that cause equivalent damage.

The Austroads procedure uses the strain responses of the candidate pavement structure loaded with a

Standard Axle to determine the number of allowable repetitions of this load. Different load levels and

axle group tyres are equated to determine the design repetitions of the standard axle. The MEPDG

models the response of each axle load and each axle group type within the design traffic spectrum,

and determines a level of damage associated with each of those combinations.

To determine the strain response under a multiple-axle group load, the strains resulting from each axle

within the group are superimposed as shown in Figure 3.4. The maximum strain within the resulting

combined group response is then used to determine the damage caused by that group and load.



Figure 3.4: Strains generated by a quad-axle group

Source: Applied Research Associates (2004).

3.4.4 Multiple Peak Response Methods

A refinement of the maximum peak response method is to consider the magnitude of the peak response

under each axle in the group (i.e. to consider both D1 and D*2 in Case a in Figure 3.3).

This multiple peak response method calculates the 𝐿𝐸𝐹 using Equation 8.

𝐿𝐸𝐹𝑖 = ∑ (𝑅1

𝑅𝑆𝐴)

𝑛𝑝

𝑖=1

8

where





𝑝 = number of peaks in the axle group response curve

An advantage of this method over the maximum peak response method is that it can distinguish between

Cases a and b in Figure 3.3, recognising the difference in magnitude of the minor peaks.

3.4.5 South African Pavement Engineering Manual (2003)

The current South African Pavement Engineering Manual (SAPEM) (South African National Roads

Agency 2013) contains a mechanistic procedure for the design of flexible pavements that is similar in

principle to the Austroads method. In characterising the damage caused by multiple-axle groups, the

SAPEM differs from Austroads and uses a variant of the multiple peak response method.

In principle, the process is similar to the MEPDG, wherein the damage resulting from each axle load and

group within the design spectrum is summed. However, whereas the MEPDG models a multiple-axle group

as a whole and determines the maximum resulting response, the mechanistic SAPEM method models the

group as separate isolated axles (i.e. with no superposition of responses from each axle) and determines

damage resulting from each axle. The guide acknowledges that this approach overestimates the damage

resulting from multiple-axle groups, but does not consider the overestimation to be significant.

Whilst the process considers the peak response associated with each axle within a group, it does not

consider the superposition of those responses, i.e. the grouping of the axles. Therefore, it is not a pure

example of a multiple-peak response method.



3.4.6 Peak Mid-way Methods

The peak mid-way method2 was originally used for analysis of the Canadian Vehicle Weights and

Dimensions Study (Christison 1986a, 1986b). The method uses the peak response under the lead axle (1

in Figure 3.5) and the difference between the peak and trough for remaining axles in the group (2, 3, 4

and 5 in Figure 3.5).

Figure 3.5: Peak mid-way method using strain response for a five axle group

Source: Chatti and Lee (2004).

The formula for calculating the LEF for an axle group using the peak mid-way method is shown in Equation 9.

𝐿𝐸𝐹𝑖 = (𝑅1

𝑅𝑆𝐴)

𝑛

+ ∑ (𝑅𝑖 − 𝑅𝑖−1

𝑚

𝑅𝑆𝐴)

𝑛𝑝

𝑖=2

9

where


𝑅1 = pavement response to 1st (lead) peak


𝑅𝑖 = pavement response to 𝑖th peak

𝑅𝑖𝑚 = pavement response mid-way (in trough) between peaks (𝑖 − 1) and 𝑖


𝑝 = number of peaks in the axle group response curve

A criticism of this method (Chatti & Lee 2004) is that for some strain responses to load shapes, such as

that shown in Figure 3.6, there is a zone of ‘neglected’ tension which is not considered in determination of

the 𝐿𝐸𝐹.

2 Given this name by Chatti and Lee (2004).



Figure 3.6: Zone of neglected tension in the peak mid-way method


3.4.7 Integration Methods

By considering the entire response to load curve, integration methods can include the duration of the load

response curve, which is not done by the methods that only consider peak responses, as well as the

magnitude of the response(s). Integration methods can distinguish between Cases a and b of Figure 3.3,

as can some discrete methods, but they can also distinguish between Cases a and c which have the same

peak responses but over different durations.

Dissipated energy method

The area within a stress-strain hysteresis loop (i.e. the loop created by plotting the loading and unloading

stress-strain characteristic of a material) represents the energy lost to the material during the loading

regime, and is termed the dissipated energy. A linear-elastic material has identical and linear loading and

unloading stress-strain curves. The loading of such a material creates zero dissipated energy.

Asphalts have demonstrated non-linear elastic behaviour, and exhibit significant stress-strain hysteresis

loops. Generalised stress-strain loops generated by a single and triaxle (tridem) axle group are shown for

an asphalt material in Figure 3.7. Loops for both longitudinal (i.e. in the direction of travel) and transverse

strain (perpendicular to the direction of travel) are shown.

Dissipated energy changes with long-term loading of materials, and so it is common practice to

characterise a material in terms of its initial dissipated energy behaviour.



Figure 3.7: Stress-strain hysteresis loops for asphalt material

Transverse stress-strain hysteresis loop

Longitudinal stress-strain hysteresis loop


The dissipated energy method for determining LEFs uses the calculation shown in Equation 10.

𝐿𝐸𝐹𝑖 = (𝑤𝑜,𝑖

𝑤𝑜,𝑆𝐴)

𝑛

10

where


𝑤𝑜,𝑖 = dissipated energy of axle group 𝑖 during initial cycles

𝑤𝑜,𝑆𝐴 = dissipated energy of Standard Axle during initial cycles


Use of the method within a pavement design approach, however, requires the computation of dissipated

energy for all axle load and group combinations in the design traffic spectrum. The Austroads design

process makes use of linear-elastic computational tools and calibrated performance relationships, and so is

unable to determine dissipated energy.

Strain area method

The strain area method is a simpler integration method than the dissipated energy method, and simply

uses the area under the initial strain curve generated by the axle group (Figure 3.8). Equation 11 is used to

determine 𝐿𝐸𝐹s using this method.



Figure 3.8: Area under initial strain response curve for simulated quad-axle group in a controlled

stress test

Source: Salama and Chatti (2006).

𝐿𝐸𝐹𝑖 = (𝐴𝑜,𝑖

𝐴0,𝑆𝐴)

𝑛

11

where


𝐴𝑜,𝑖 = area under strain curve for axle group 𝑖

𝐴𝑜,𝑆𝐴 = area under strain curve for Standard Axle


3.5 Summary

Different international pavement design systems consider relative damage factors for multiple-axle groups

in different ways.

The AASHTO guide (1993), which is based upon a large-scale field study and does not contain a

mechanistic model, determines that load equivalency factors are a function of the pavement’s structure.

This is in contrast to the Austroads approach which uses the same 𝐿𝐸𝐹 values across all pavement

materials and thicknesses. The AASHTO (1993) 𝐿𝐸𝐹 factors result in higher equivalent loads on multiple-

axle groups than the Austroads approach.

The French design method considers 𝐿𝐸𝐹s to be affected by pavement structure, but only provides

example average values for structures varying by material type, not by thickness. The French method

results in equivalent higher loads on multiple-axle groups than the Austroads method, but not as high as

the AASHTO (1993) method.

The current South African method models each axle as an isolated axle, and sums the damage determined

from the response-to-load modelling of the load on of each of the individual axles within the design traffic

spectrum. This is similar to the French method in modelling the pavement response to each load level, but

does not consider the effect that any interaction between the axles within a group will have on the damage

resulting from that group. It results in lower equivalent loads for a given pavement structure than the French

method.



Finally, the new AASHTO MEPDG (2008) method also considers that the structure affects load

equivalence. The method uses a response-to-load model to determine the response of each group and

load level. In contrast, in the South African approach, the response to multiple-axle group loads is modelled

directly rather than considering the group to be composed of a series of isolated axles with equal load.

However, the method only uses the maximum peak response from each group, and does not consider

responses from other peaks as affecting damage.

Alternative theoretical methods of characterising the response of a pavement to multiple-axle loads have

been developed, but little work has been undertaken to demonstrate the relevance of these

characterisations to the performance of pavement materials/structures.



4. Review of Research

4.1 General

A range of theoretical methods of characterising the response of a pavement to multiple-axle loads were

described in Section 3. However, the AASHO road test (AASHO 1962) represents the only significant

pavement performance data set in which pavements were subjected to different axle group load types and

levels in a manner that ensures that sections of pavement were only subjected to a given load level and

axle group type. A range of relevant smaller-scale response-to-load and laboratory tests have been

conducted, and are summarised here.

4.2 Asphalt Fatigue Using Simulated Multiple-axle Loads: Michigan

State University

The Pavement Research Center of Excellence at Michigan State University conducted a comprehensive

study of the effect of multiple-axle trucks on the distress of typical Michigan flexible and rigid pavements.

Chatti et al. (2009) documents the work conducted on flexible pavements, including a laboratory-based

asphalt fatigue study.

In the study, 31 asphalt samples were subjected to fatigue testing using the indirect tensile method, with a

series of load pulses simulating different axle groups. Fatigue tests were conducted for single, tandem,

triaxle, quad-axle and eight-axle groups. Three different levels of peak stress were applied in the study, and

three levels of axle interaction (Figure 4.1) were included.

Controlled load/stress testing was used, with the load pulse shapes being determined from theoretical

analysis of pavement structures. Only responses transverse to the direction of travel were simulated in the

laboratory testing. Examination of longitudinal responses would have required the development of both

tensile and compressive strains/stresses in the samples, which is impossible within an indirect tensile test.

A rest period equal to four times the length of the loading pulse was used, regardless of the number of axles

within the axle group. The length of the loading pulse varied between axle group simulations, with the single

axle pulse width having a load time of 0.1 seconds. With the addition of a 0.4 second rest time, this

corresponds to a loading frequency of 2 Hz. Multiple-axle group load tests would have had lower frequencies.

The testing matrix is shown in Table 4.1.

Table 4.1: Fatigue testing matrix for the Michigan study

Stress level Interaction level Number of axles

1 2 3 4 8

Low (30 kPa)

Low (25%) 2 tests – 2 tests – 2 tests

Medium (50%) – – – –

High (75%) – – – –

Medium (60 kPa)

Low (25%) 3 tests – 3 tests 3 tests 3 tests

Medium (50%) 3 tests – – –

High (75%) – – – 2 tests

High (120 kPa)

Low (25%) 2 tests 2 tests 2 tests – 2 tests

Medium (50%) – – – –

High (75%) – – – –

Source: Chatti et al. (2009).



Figure 4.1: Levels of interaction between axles used in the Michigan study

(a) Low interaction (25%) (b) Medium interaction (50%) (c) High interaction (75%)


The study examined a range of alternative analysis methods, and found that a fatigue relationship based

solely upon the dissipated energy density determined during the initial cycles of the test provided the best

fit to the laboratory data. Significantly, the study found that a single fatigue relationship could be used for all

axle groups, load levels and interaction levels. Figure 4.2 shows the determined function relating the number of load cycles to fatigue failure, 𝑁𝑓, to the initial dissipated energy density (DE) of the test, and

shows the remarkable fit of the function to the collected data. It would appear that the differences in test

parameters, and thus the differences in load pulse shape, were all reflected in the initial dissipated energy

density value.

It is important to note, however, the very short test durations used – the median test duration was less than

4000 cycles (and the upper quartile was approximately 7500 cycles).

Figure 4.2: Dissipated energy density fatigue curve from the Michigan study




Having developed a function relating the fatigue performance of asphalt to the initial dissipated energy

density of the material, the study then used computationally derived dissipated energy densities, using

finite layer analysis software, to explore the theoretical fatigue life of an asphalt material subject to a range

of different load levels, axle configurations and interaction levels. This data enabled the calculation

(Equation 12) of 𝐿𝐸𝐹s relating the damage caused by each combination of axle group type (with each axle

within a group presumed to have a 13 kip (58 kN) load) and interaction level to a standard 18 kip (80 kN)

single axle load. These load equivalency factors are shown in Table 4.2.

𝐿𝐸𝐹 =𝐷𝑎𝑚𝑎𝑔𝑒 (axle configuration)

𝐷𝑎𝑚𝑎𝑔𝑒 (18 kip standard axle)=

𝑁𝑓 (18 kip standard axle)

𝑁𝑓 (axle configuration)

12

where

𝐿𝐸𝐹 = load equivalency factor for the axle configuration being considered

𝐷𝑎𝑚𝑎𝑔𝑒 = damage caused by the axle configuration

𝑁𝑓 = number of cycles to fatigue failure

Table 4.2: Load equivalency factors calculated by the Michigan study

Test conditions 𝑵𝒇 𝑳𝑬𝑭

1 axle 18 kip (80 kN) 5388 1.00

1 axle 13 kip (58 kN) 7750 0.70

25% interaction

2 axles 489 1.10

3 axles 3876 1.39

4 axles 2889 1.87

5 axles 2377 2.27

7 axles 1893 2.85

8 axles 1707 3.16

50 % interaction

2 axles 5987 0.90

3 axles 4592 1.17

4 axles 3577 1.51

5 axles 2992 1.80

7 axles 2477 2.18

8 axles 2289 2.35

75% interaction

2 axles 5644 0.95

3 axles 4155 1.30

4 axles 3431 1.57

5 axles 3058 1.76

7 axles 2549 2.11

8 axles 2439 2.21




The Axle Factor (AF) is defined as the relative damage caused by an axle group compared to that of a

single axle carrying the same load as that carried on an individual axle within the group. For example,

Equation 13 shows determination of the AF for a 39 kip triaxle group. If, for a given multi-axle group, the AF

were to equal the number of axles within the group, then the grouping of the axles would have no effect on

the damage caused. Similarly, if the AF was lower than the number of axles within the group, then the

grouping of the axles would have reduced the damage caused. AF values computed in the Michigan study

are shown in Figure 4.3 for a range of different interaction levels. It can be seen that the study calculated

axle factors lower than the number of axles within the groups, reflecting the pavement-friendly benefit of

grouping axles together. It can also be seen, within the scale of the graph, that the effect of axle interaction

for tandem, triaxle and quad-axle groups is considerably less than for large axle groupings such as seven

and eight axles. The state of Michigan allows multi-axle groupings of up to eight axles.

𝐴𝐹 =𝐷𝑎𝑚𝑎𝑔𝑒 (39 kip triaxle)

𝐷𝑎𝑚𝑎𝑔𝑒 (13 kip single axle)=

𝑁𝑓 (13 kip single axle)

𝑁𝑓 (39 kip triaxle)

13

where

𝐴𝐹 = axle factor for the axle group being considered (in this case a 39 kip triaxle)

𝐷𝑎𝑚𝑎𝑔𝑒 = damage caused by the axle configuration

𝑁𝑓 = number of cycles to fatigue failure

Figure 4.3: Axle factors (AF) for different interaction levels calculated by the Michigan study


The study then went on to determine the best means of relating the loading/response pulse shape to the

observed fatigue lives and resulting axle factors, without the need to determine dissipated energy.



In summary, the study determined that the dissipated energy-based fatigue approach was found to be

unique for all axle configurations examined. This allowed a single relationship to be used to predict the

fatigue life of any other axle group, if the initial dissipated energy density caused by that axle group could

be determined. The study also found that both speed of loading and asphalt thickness (reflected in the

interaction level between axles within a group) did not have a significant effect on the axle factors

determined (changes in either of them did affect fatigue life, but not the relative damage caused).

However, the study had its limitations. Firstly, the fatigue test durations were extremely short. Additionally,

the use of indirect tensile testing meant that only tensile strains could be generated in laboratory samples,

preventing examination of the effect of alternations between tensile and compressive strains/stresses

experienced in the longitudinal direction (i.e. the direction of travel). A major recommendation of the study

by Chatti et al. (2009) was that:

…a different testing setup (flexural beam preferably) be used to check the consistency of the results

under different loading modes and stress states. The flexural beam test could allow for stress

reversals, which are relevant for longitudinal stresses and strains.

4.3 Effect of Different Wave Forms and Rest Periods on Fatigue:

Chuo University Study

At the University of Chuo in Tokyo, Kogo and Himeno (2008) conducted strain-controlled four-point bending

fatigue tests on beams made from a single dense graded asphalt mix using the following types of load

pulses (the shapes are shown in Figure 4.4):

continuous sinusoidal at 5 Hz

continuous triangular at 5 Hz

continuous twin peaks at 5 Hz

sinusoidal (loading time 0.2 s) with a 1 second rest period

sinusoidal (loading time 0.2 s) with a 10 second rest period.

Hence, in all cases, the length of loading was 0.2 seconds.

Figure 4.4: Loading wave shapes used in the Chuo University study

(a) Sinusoidal (b) Triangular (c) Twin peaks

Source: Kogo and Himeno (2008).



The study calculated the rate of dissipated energy change for each test with increasing number of load

cycles. This rate was determined during the long gradual damage phase of the fatigue test, i.e. after the

initial damage caused by early loading and before the sudden drop indicating approaching failure. For the

continuous loading tests, plotting the rates of dissipated energy change against the number of cycles

required to reach fatigue failure (Figure 4.5(a)) demonstrated that the loading pulse shape (not the duration

of load, as that was constant) did not have a significant effect on the fatigue life of the samples.

As shown in Figure 4.5(b), the tests incorporating a rest period did, however, demonstrate a different

fatigue relationship. Uniaxial fatigue tests conducted as part of a separate study also demonstrated a

different relationship between rate of dissipated energy change and fatigue life.

The study demonstrated the potential for dissipated energy change to predict fatigue performance

independently to the load pulse shape (but not necessarily width of load pulse). Significantly, the study

showed the considerable effect that rest periods during testing can have on fatigue performance.

Figure 4.5: Relationship between rate of dissipated energy and load cycles determined by the

Chuo University study

(a) Effect of load shape (b) Effect of rest period and loading type

Source: after Kogo and Himeno (2008).

4.4 Effect of Different Wave Forms on Fatigue: French Studies

Merbouh et al. (2007) conducted a series of controlled strain fatigue tests using synthetic load shapes. The

original paper is written in French. A summary of the test results is presented in Bodin et al. (2009).

The fatigue testing was conducted on laboratory-prepared trapezoidal samples comprised of a single

asphalt mix. The testing was conducted by generally following the requirements of the European Standard

EN12697-24:2012, originally developed in France. The equipment was modified to allow a numerical

generator to generate more complex strain shapes than the standard sinusoidal shape used in routine

tests.

In order to overcome creep of samples during fatigue testing, the standard tests make use of a sinusoidal

shape, moving the critical edge of the trapezoidal beam from tensile strain to compressive to tensile, etc.

The Merbouh et al. (2007) study extended this principle by applying complex shapes in a similar manner –

as had been done, although using four-point bending, by Kogo and Himeno (2008).



Figure 4.6 shows an example of the complex waveforms applied during the testing, and also introduces the

parameter 𝜆 to reflect ‘unloading’ between successive strain peaks. When 𝜆 = 0, there is no decrease of

the load between the two peaks, i.e. there is a single, long peak. When

𝜆 = 0.5, the displacement level between the peaks is zero, i.e. touching the x-axis in Figure 4.6. When 𝜆 =

1, the valley between the two adjacent peaks is equal in magnitude to the peak level, but opposite in sign,

i.e. the signal is fully reversed, as shown by the grey line in Figure 4.6, and is sinusoidal in shape with a

frequency of three times the multiple peak shape.

Figure 4.6: Example complex strain pulse used in the French waveform study

Source: Bodin et al. (2009).

Fatigue tests were conducted at a temperature of 20C, at different strain levels, using the standard

sinusoidal load shape, and double peak shapes with 𝜆 equal to 0, 0.25, 0.5, 0.75 and 1. The period of each

signal was fixed at 0.12 seconds (i.e. a frequency for the shape of 8.3 Hz). Strain levels were selected to

obtain fatigue lives between 104 and 5 × 105 cycles. The test results for each load shape were grouped and

linear interpolation was used to define the strain level that would equate to a fatigue life of 105 cycles, 휀5,

and the load damage exponent, 𝑝, in Equation 14. Table 4.3 lists the values of these parameters for each

shape reported by Bodin et al. (2009).

𝑁 = 105 (

휀𝑎

휀5)

𝑝

14

where

𝑁 = number of cycles to reach fatigue failure (i.e. modulus reduction to 50% of initial

modulus)

휀5 = strain level that will result in a fatigue life of 105 cycles

휀𝑎 = strain level applied in test

𝑝 = load damage exponent



Table 4.3: Effect of strain load shape on fatigue life in the French study

Type of signal No. tests 𝒑 𝜺𝟓 (μm/m)

Value 95% confidence interval

Sinusoidal 11 4.57 ± 0.75 380 (297 488)

𝜆 = 0 12 4.29 ± 1.36 323 (256 406)

𝜆 = 0.25 12 4.76 ± 0.90 324 (277 319)

𝜆 = 0.5 12 4.26 ± 1.43 319 (232 437)

𝜆 = 0.75 12 4.79 ± 1.89 321 (232 447)

𝜆 = 1 12 3.61 ± 0.94 243 (170 349)


Bodin et al. (2009) concluded that:

Influence of 𝜆:

– In the range from 0 to 0.75, the 𝜆 parameter had no significant effect on the fatigue performance.

– When 𝜆 was equal to 1, the fatigue performance noticeably dropped.

– This indicates that the amount of decrease in strain level that occurs between the two peaks of the

signal had no significant effect on the fatigue life, until such point as the decrease results in a

completely symmetrical sinusoidal signal.

Duration of peak load:

– The sinusoidal and 𝜆 = 0 shapes both had a single peak and a frequency of 8.3 Hz. The 𝜆 = 0

shape had a flat peak strain level, and therefore a longer period over which the peak load was

applied.

– There is a noticeable decrease in fatigue performance when the longer load 𝜆 = 0 shape was used

when compared to the sinusoidal loading.

Bodin et al. (2009) examined the aggressiveness of each shape. They defined the aggressiveness of a

shape having a period of 𝑇 seconds, as:

𝐺𝑇 =

1

𝑁𝑇

15

where

𝐺𝑇 = aggressiveness of the signal with period of 𝑇 seconds

𝑁𝑇 = number of cycles of the signal to fatigue failure

It can be seen that aggressiveness and the term damaging, which is used elsewhere within this report, are

synonymous.

In addition, Bodin et al. considered that the shapes simulated different number of wheel (i.e. axle) passes,

as listed in Table 4.4. Equation 15 could then be rewritten to express the aggressiveness of wheel passes,

as shown in Equation 16.



Table 4.4: Number of wheel (i.e. axle) passes represented by signals in the French study

Type of signal Period of the signal, 𝑻𝒔 Number of wheels, 𝒏𝒘

Sinusoidal 0.12 s 1

𝜆 = 0 0.12 s 1

𝜆 = 0.25 0.12 s 2

𝜆 = 0.5 0.12 s 2

𝜆 = 0.75 0.12 s 2

𝜆 = 1 0.12 s 3


𝐺𝑤 =

1

𝑁𝑇 × 𝑛𝑤

16

where

𝐺𝑤 = aggressiveness of a wheel pass within a signal with period of 𝑇 seconds

𝑁𝑇 = number of cycles of the signal to fatigue failure

𝑛𝑤 = number of wheels represented in the signal

Figure 4.7 presents the aggressiveness of the signals, normalised to the aggressiveness of the sinusoidal

loading, in terms of both the periods and the number of wheel passes within each shape. Figure 4.7(a)

shows that all of the two-peak shapes, except for the 𝜆 = 1 shape, have aggressiveness about two times

greater than the sinusoidal signal with the same period/frequency (8.33 Hz). The 𝜆 = 1 shape is

considerably more aggressive. As noted earlier, this shape is equivalent to a sinusoidal shape of three

times the frequency, i.e. 25 Hz.

Figure 4.7 (b) demonstrates that the aggressiveness of a wheel pass for the 𝜆 = 0.25 – 0.75 shapes is

close to unity, indicating that for these shapes, the two-peak area as aggressive as two single peaks. The

longer duration single-peak load shape, 𝜆 = 0 is twice as aggressive as the shorter duration sinusoidal

shape, and has approximately the same wheel aggressiveness as the 𝜆 = 1 shape.

Figure 4.7: Aggressiveness of signals in the French study

(a) Period (b) Wheel passes




4.5 Effect of Different Wave Forms on Laboratory Fatigue: Homsi

Study

As the basis of a doctoral thesis, Homsi (2011) undertook an extensive laboratory exercise examining the

effects of different load shapes on the flexural fatigue performance of a single asphalt mix. Her thesis is

written in French, and two English language journal papers also document the relevant work (Homsi et al.

2011, 2012).

To assist in defining the load shapes to investigate in the laboratory study, Homsi et al. (2011) describe the

collection of asphalt strain responses under multiple (half) axle loads applied using the Fatigue Carrousel

(a large circular accelerated pavement testing facility) operated by the Laboratoire Central des Ponts et

Chaussées (LCPC) in Nantes, France. Data was collected under single, tandem and triaxle groups on two

different pavement structures, one with 160 mm asphalt material and the other with 260 mm of asphalt. A

tyre load of 42.5 kN was applied to all tyres (the half axles used were all fitted with single tyres typical of

those used as trailer tyres on European semi-trailers). Responses were collected in directions parallel and

perpendicular to the direction of travel, at loading speeds between 4 and 50 km/h, and asphalt

temperatures between 4 and 38 °C. A total of 1700 loading signals were collected.

Principal components analyses (PCA) were then undertaken to determine which parameters could be best

used to characterise a strain response shape. A long list of candidate parameters were identified, and

response data collected from the Fatigue Carrousel exercise were analysed to determine which of the

candidate parameters were correlated with each other, and which were demonstrably independent. Both

longitudinal and transverse signals were analysed, and the list of parameters that were found to

independently characterise both signal types were:

maximum strain (휀)

number of peaks (𝑁𝑝)

duration of the shape divided by the number of peaks (�̅�)

area under the strain time shape, normalised by strain magnitude and divided by the duration (�̂�𝑛).

Figure 4.8 shows examples of these parameters for triaxle loading, i.e. 𝑁𝑝 = 3.

Figure 4.8: Definitions of Homsi’s strain shape parameters

(a) Longitudinal (b) Transverse



Homsi et al. (2012) documents the results of a laboratory study wherein samples of a single asphalt mix

were subjected to a series of controlled strain fatigue tests at 20 °C, using load shape signals representing

a range of the above shape parameters (Table 4.5). The same equipment used in the Merbouh et al.

(2007) testing program was used.

Single, tandem and triaxle groups were considered in the testing program, and three strain magnitudes

were used. The strains selected were high in comparison to both levels traditionally used in fatigue testing,

and to magnitudes experienced in situ under highway loading. The highest level used, 347 μm/m, matched

the upper limit of the equipment used. The lowest level, 165 μm/m, was selected to ensure that test

durations were not excessive (as only a single test was conducted at this strain level for each combination

of shape parameters). The mid-range value of 240 μm/m was selected to be half-way between the other

values when represented on a logarithmic scale. The magnitudes of peaks within a multi-axle shape were

made equal.

The values of 0.21 and 0.42 were selected for the �̂�𝑛 parameter, the first representing a longitudinal strain

signal (i.e. strain in the direction of travel), and the second representing a signal in the transverse direction

(i.e. strain perpendicular to travel). The response-to-load data collected using the Fatigue Carrousel was

analysed, and median values of �̂�𝑛 were selected for each strain direction. Two values for �̅� were selected,

0.105 and 0.25, representing a trafficking speed of between 20 and 150 km/h, depending upon the

thickness of the pavement structure.

At the two higher strain levels, three replicates of each combination of shape parameters were undertaken.

Due to the long duration of the test, only a single test was conducted at the lowest strain level. A total of 84

fatigue tests were conducted, with the number of cycles required to reach fatigue (a drop of modulus to

50% of its initial value) varying between 1500 to 1 million cycles. Long duration tests took up to 15 days to

complete. Homsi et al. (2012) records that a high amount of scatter was evident in the test results, but that

time restrictions prevented undertaking the six test beam replicates that would robustly be required using

EN12697-24:2012.

Table 4.5: Homsi’s experimental plan and observed Nf = f() or each signal

Signal 𝑵𝒑 �̂�𝒏 �̅� Period (s)

Frequency (Hz)

𝐥𝐨𝐠𝟏𝟎(𝑵𝒇) = 𝒂 𝐥𝐨𝐠𝟏𝟎(𝜺) + 𝒃

𝒂 𝒃

1 1 0.21(1) 0.105 0.28 3.57 –4.14 14.64

2 0.25 0.67 1.50 –3.63 13.64

3 0.42(2) 0.105 0.28 3.57 –3.54 13.54

4 0.25 0.67 1.50 –4.00 14.74

5 2 0.21 0.105 0.51 1.95 –4.85 16.10

6 0.25 1.22 0.82 –5.12 16.91

7 0.42 0.105 0.51 1.95 –4.30 15.12

8 0.25 1.22 0.82 –5.27 17.68

9 3 0.21 0.105 0.76 1.32 –4.71 15.49

10 0.25 1.80 0.56 –5.53 17.88

11 0.42 0.105 0.76 1.32 –3.65 13.23

12 0.25 1.80 0.56 –5.56 18.14

Strain level 165 240 and 347 μm/m

Replicates for each 𝑵𝒑, �̂�𝒏 and �̅� combination

240 and 347 μm/m : 3 replicates

165 μm/m : single test

1 Longitudinal signal 2 Transverse signal.

Source: Homsi et al. (2012).



The classic log-log fatigue relationship (see Equation 17) was fitted through the experimental data to yield

the results shown in Table 4.5. Using these relationships at a fixed peak strain level of 200 μm/m, Homsi calculated the damage (i.e. 1/𝑁𝑓) for each signal. Relative damages were then calculated to evaluate the

effect of each shape parameter, whilst holding all other parameters constant. Homsi called this ratio the

relative signal equivalent factor (RSEF). The results are shown here in Table 4.6.

𝑙𝑜𝑔10(𝑁𝑓) = 𝑎 𝑙𝑜𝑔10(휀) + 𝑏 17

where

𝑁𝑓 = number of cycles to achieve fatigue

휀 = peak strain level

Table 4.6: Homsi’s relative signal equivalent factors (RSEF)

Effect of 𝑵𝒑 Effect of �̂�𝒏 Effect of �̅�

𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒊 𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒋⁄ 𝑹𝑺𝑬𝑭 𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒊 𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒋⁄ 𝑹𝑺𝑬𝑭 𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒊 𝑫𝒔𝒊𝒈𝒏𝒂𝒍_𝒋⁄ 𝑹𝑺𝑬𝑭

𝐷5 𝐷1⁄ 1.49 𝐷1 𝐷3⁄ 1.91 𝐷1 𝐷2⁄ 1.49

𝐷6 𝐷2⁄ 1.44 𝐷2 𝐷4⁄ 1.77 𝐷3 𝐷4⁄ 1.39

𝐷7 𝐷3⁄ 1.47 𝐷5 𝐷7⁄ 1.93 𝐷5 𝐷6⁄ 1.54

𝐷8 𝐷4⁄ 0.96 𝐷6 𝐷8⁄ 2.66 𝐷7 𝐷8⁄ 2.13

𝐷9 𝐷1⁄ 2.89 𝐷9 𝐷11⁄ 1.51 𝐷9 𝐷10⁄ 3.19

𝐷10 𝐷2⁄ 1.36 𝐷10 𝐷12⁄ 1.55 𝐷11 𝐷12⁄ 3.27

𝐷11 𝐷3⁄ 3.66

𝐷12 𝐷4⁄ 1.55


The RSEF values in Table 4.6 indicate that, at the same peak strain level, the two-peak pulse shapes were

0.96 to 1.49 times more damaging than single-peak shapes, dependent upon the values of the parameters

of �̂�𝑛 and �̅�. Three-peak shapes were 1.36 to 3.66 times more damaging than the equivalent single-peak

shapes. Given that all bar one RSEF factor for the 𝑁𝑝 comparison were greater than one, Homsi et al.

concluded that multiple-peak configurations were more damaging than single-peak shapes when the strain

level and other shape parameters were held constant. However, the authors did not comment on the range

of damage factors obtained from this analysis.

When considering the effect of �̂�𝑛, it was concluded that an increase in �̂�𝑛 leads to an increase in fatigue

life, and therefore a decrease in damage. It should be noted that the distinction in value of this parameter in

the conducted experiments was also a distinction between strain shapes representative of those in the

longitudinal and transverse directions. In this context, the RSEF values indicate that, at the same strain

magnitude and duration, a longitudinal strain shape is more damaging than a transverse one.

Unfortunately, time restraints on the experimental work did not allow for testing of different values of �̂�𝑛 to

be used within each strain direction.

When considering the duration of the load pulse, the RSEF values obtained indicate that the lower the

value of �̅�, the higher the damage when strain magnitude and other shape parameters are held constant.

This could be interpreted to indicate that as trafficking speed increases, leading to decreasing values of �̅�,

the amount of damage incurred also increases. However, as noted by Homsi et al., in a pavement

structure, an increase in trafficking speed will also result in decreasing the magnitude of strain.

Homsi also developed a single multi-linear model to predict the number of cycles to reach fatigue failure as

a function of all of the shape parameters. This is shown here as Equation 18, with the significance of the

terms decreasing from left to right. A comparison of the model’s predictions compared to the experimental

data is presented in Figure 4.9.



Section 7.5 explores simplification of this model.

𝑙𝑜𝑔10(𝑁𝑓) = −4.58 𝑙𝑜𝑔10(휀)

− 0.84 𝑙𝑜𝑔10(𝑁𝑝) + 1.31 �̂�𝑛 + 1.76 �̅� + 15.22

18

where

𝑁𝑓 = number of cycles to achieve fatigue

휀 = peak strain level

𝑁𝑝 = number of peaks in strain signal

�̅� = duration of the shape divided by the number of peaks

�̂�𝑛 = area under the strain time shape, normalised by strain magnitude and divided by the

duration

Figure 4.9: Homsi’s multi-linear model predictions compared to the experimental results


4.6 Pavement Response to Multiple-axle Loads: BASt Study

Rabe (2008) documents a study conducted by the German Bundesanstalt fuer Strassenwesen (BASt)

where trucks of different configurations and weights were driven over a series of eight asphalt pavements

(Figure 4.10). Subbase materials for the pavements included gravel, crushed rock, lean mix concrete and

cemented sand. Total asphalt thicknesses for the pavements varied from 120 mm to 340 mm. The

pavements were specially constructed in an indoor facility, and were heavily instrumented with strain

gauges (in the asphalt layers), soil pressure cells (in the unbound layers) and temperature gauges, as

shown in Figure 4.11.



Figure 4.10: Truck passing over test pavements during BASt study

Source: Rabe (2008).

Figure 4.11: Location of pavement instrumentation used in BASt study

Note: Instruments shown (top to bottom) are: temperature sensor, H-bar strain gauge, soil pressure cell.

Source: Rabe (2008).

The following axle and tyre configurations were included, using a variety of different trucks:

single axle with single tyres

single axle with dual tyres

tandem group with single tyres

tandem group with dual tyres

tandem group with twin tyres on one axle and single tyres on the other

triaxle with single tyres

single axle with a 495 mm super single tyre (i.e. nominal width 495 mm).



Four different vehicle gross weight levels were used: 16, 28, 40 and 48 tonnes (the maximum permissible

gross weight in Germany is 40 tonnes). Tyre pressures were varied, and the speed of trafficking was varied

from 2 to 30 km/h. Lateral wander of the vehicles was also included in the study. A total of 2500 truck

passes were undertaken, and pavement response data was simultaneously collected from the pavement

instrumentation.

A huge volume of data was collected during the study, and was still being processed at the time of writing.

Of relevance to this Austroads research project is the strain data collected at the bottom of the asphalt

layers under single, tandem and triaxle groups. Of the trucks used in the study, the one shown in Figure

4.12 is of most relevance to the proposed laboratory study. The vehicle configuration would better reflect

Australian practice if dual-tyred axles had been used in the triaxle group (the use of single-tyred axles in

triaxle groups is standard practice in most European countries).

Figure 4.12: Geometry of a three axle prime mover and semi-trailer used in the BASt study

Figure 4.13 shows tensile strains generated by this truck travelling at 30 km/h, measured at the bottom of

the asphalt material in three pavement structures of varying asphalt thickness. The gross mass of the truck

was 40 tonnes, and the asphalt temperature at the time of testing was 11 °C. The strains plotted were

measured in the transverse direction, i.e. in the direction perpendicular to the direction of travel. The three

axle groups are clearly discernible in the response data. Of particular note are:

Increasing the thickness of the asphalt reduced the magnitude of the strains generated under all axle

groups.

Increasing the thickness of the asphalt increased the interaction between the axles of the tandem and

triaxle groups in the strain response (i.e. the depth of the ‘valley’ between peaks of the response – see

Figure 4.1).

Only tensile strains were generated in the transverse direction.

The visco-elastic response of asphalt meant that time was needed for the strains to relax to zero after

the axles had passed over the gauges – note the longer period needed for the strain to return to zero

after passage of the triaxle group compared to the tandem group (the time between passage of the

single steer axle and the tandem drive axle group was not sufficient for the strains to relax to zero).



Similarly, the peak strain generated by passage of the second axle of the tandem group was slightly

higher than the first, and this phenomenon was demonstrated successively by all three axles of the

triaxle group.

Under the thinnest pavement, the peak strain level reached was 120 microstrain.

Similarly, Figure 4.14 shows the tensile strains generated by the same truck in the longitudinal direction,

i.e. parallel to the direction of travel. The following observations are made:

Increasing the thickness of the asphalt also reduced the magnitude of the strains and increased the

interaction level between axles, as shown for the transverse strains.

Both compressive (i.e. negative in the figure) strains and tensile strains were generated.

Superposition of the three axles in the triaxle group resulted in a slightly lower peak strain generated

under the middle axle of the group.

For each of the three pavements tested, the peak longitudinal tensile strains generated by all three

axle groups were of a similar magnitude, whereas the peak transverse strains were different between

groups (this was most evident in the strains generated in the 120 mm asphalt pavement). The tandem

group, it should be remembered, had dual tyres whereas the other axles only had single tyres.

Under the thinnest pavement, the peak strain level reached was approximately 130 microstrain.

Figure 4.13: Tensile strains measured at the bottom of the asphalt layer (transverse direction)



Figure 4.14: Tensile strains measured at the bottom of the asphalt layer (longitudinal direction)

4.7 Summary

Simulation of the fatigue performance of asphalt has been examined in the laboratory, with three main

studies.

Salama and Chatti (2006) undertook fatigue testing using controlled stress and an indirect tensile

approach. They determined that a fatigue relationship based solely upon the dissipated energy density

determined during the initial cycles of the test provided the best fit to the laboratory data. The testing only

considered shapes representative of strains in the transverse direction (i.e. perpendicular to the direction of

traffic), and included a variable rest period between axle group cycles, with the rest period equal to four

times the length of the loading pulse. This means that the rest period increased significantly with increasing

number of axles within the group. The application of a performance model based upon dissipated energy is

not simple in a static response-to-load design framework such as that used in current Austroads design

procedures. Limitation of the data to transverse strains only is also of concern, especially in light of the

findings by Homsi et al. (2012) that longitudinal strains are more damaging. However, if these issues could

be resolved, direct application of this work into a pavement design context is considered to be severely

limited by the nature of the load levels used in the study. The loads applied were high in comparison to

highway loading, and the resulting fatigue tests did not last for many cycles. The median test duration was

less than 4000 cycles (and the upper quartile was approximately 7500 cycles).

The Bodin et al. (2009) study examined a data set collected by Merbouh et al. (2007) using two-point,

controlled strain, flexural fatigue testing. Test durations were considerably higher than used in the Salama

and Chatti study, between 104 and 5×105 cycles. The effect of the interaction between two axles within a

tandem group on fatigue life were examined and compared to the results obtained for a single axle. Rest

periods were not considered within the study. The experiment shapes used (where the minimum strain

magnitude between peaks was zero or greater) are similar to those obtained by Rabe (2008) in the

transverse direction. The Bodin et al. study indicated that these transverse shapes all produced

approximately the same fatigue life, regardless of the magnitude of the minimum strain level. These

experimental results do not indicate that the ‘zone of neglected tension’ has a significant effect on fatigue

performance. Additionally, they demonstrate that for transverse strain directions at least, the ‘peak mid-way

method’ does not better represent the fatigue life than simply considering the peak strain values.



The testing also included a shape where the minimum strain between peaks was –50% the magnitude of

the adjacent peak strains. This change from tensile to compressive strain within the pulse is more typical of

longitudinal strains. The study did not determine any appreciable difference in fatigue life for tests

conducted using this shape when compared to the results of tests conducted using ‘transverse’ direction

shapes at the same peak strain level. In all of these cases, the study found that the fatigue life for two-

peaked shapes was half that of the single-peak shape.

Homsi (2011) used a rational approach to determining shape parameters, whose effect on the flexural

fatigue of asphalt could be independently assessed in laboratory testing. Long duration flexural fatigue

testing using control strain was conducted at three peak strain levels yielding fatigue lives varying between

1.5×103 and 106 cycles. Transverse and longitudinal direction shapes were considered, and it was found

that longitudinal shapes caused more damage than transverse shapes at the same peak strain level. The

duration of the load shape was also found to affect fatigue life, with quick duration shapes causing more

damage. However, the two most significant factors found were the peak strain level applied, and the

number of peaks within the shape. The study had limitations. It was limited to a single asphalt mix, tested at

a single temperature. Whilst three replicates were used for all tests at the two higher strain levels

considered, no replicates were undertaken for the lowest strain level tests (these tests lasted up to 15

days). Homsi et al. (2012) acknowledged a high amount of scatter in the collected data, and noted that six

replicates for each test condition would be required for rigour. However, it is considered that the study

represents the most exhaustive performance-related study of the effect of (simulated) multiple-axles on the

(laboratory) fatigue life of asphalt.



5. Outline of Project Work

5.1 General

The review of alternative methods contained in Section 3 highlighted a number of frameworks used in

international design and for considering the damage caused by multiple-axle groups. A range of theoretical

frameworks were also discussed. However, only a very limited number of studies were identified that

examined the actual performance of pavement materials or structures when loaded with varying types of

multiple-axle groups.

Without data relating to the performance of materials and structures, it is difficult to determine which

theoretical framework is suitable for application for Australasian pavement design. Accordingly, the project

focus was on utilising the performance data that had been collected, and collecting new performance data

related to the pavement design performance criteria considered in the current Austroads pavement design

process:

deformation of unbound granular pavements with thin bituminous surfacings – for use with current

empirical, chart-based pavement design procedure

flexural fatigue of asphalt – for use with mechanistic design procedure

flexural fatigue of cemented materials – for use with mechanistic design procedure.

The following sections describe the overall approach taken by the project regarding these three materials

and design criteria. A separate section of the report is dedicated to each one.

5.2 Rutting of Unbound Granular Pavements

No performance data has previously been obtained on the effects of multiple-axle loading on the rutting of

unbound granular materials, neither full-scale trafficking, accelerated pavement testing nor laboratory-

based studies. As this material represents a very significant proportion of the Australian and New Zealand

road network, a significant proportion of the project’s effort was spent on obtaining a relevant set of

performance data.

The potential to use laboratory tests to simulate multiple-axle effects, similar in principle to the French

asphalt study discussed in Section 3.3, was explored. The currently available laboratory test for assessing

the deformation performance of granular materials is a repeat load triaxial (RLT) test. Considerable effort

has been spent over the last two decades in developing suitable RLT testing equipment and test protocols

to rank the performance of different unbound materials. However, the use of such equipment and protocols

was not used for this study for the following reasons:

The loading pulse applied to samples in the RLT equipment is slow and unable to replicate the

complex loading shape of a multiple-axle group.

Recent work conducted by Jameson et al. (Austroads 2010) to compare the ranking of materials using

RLT testing (using different equipment and methods) to the performance of materials under full-scale

accelerated testing using the Accelerated Loading Facility (ALF), has shown a poor match.

Accordingly, it was considered that laboratory testing of unbound granular pavement material was not

appropriate for the study. Instead, the ALF was used to assess the rutting of a typical, full-scale, unbound

granular pavement and subgrade. ALF can be used to simulate trafficking over the life of a pavement in a

very short time compared with on-road test sites.

Prior to this study, ALF could only simulate a (half) single axle. The machine was modified to allow the

application of tandem and triaxle (half) axle groups (the geometry of the ALF frame is insufficient to support

development of a quad-axle group).



A single test pavement, being an example of an unbound granular, light-to-moderately trafficked, rural

highway pavement and subgrade, was constructed and trafficked.

The experimental program focussed on the effect of the number of axles within an axle group on pavement

performance. Each test location was only trafficked by a given axle configuration and load level. The load

on each axle configuration was adjusted so as to ensure that the same load per axle was applied across

the axle groups.

Section 6 summarises this work, and provides analyses of the collected data.

5.3 Asphalt Fatigue

The French study undertaken by Homsi (2011), and described in Section 3.3, represents the most

exhaustive assessment of the flexural fatigue performance of asphalt when subjected to multiple-axle

loads. The study was laboratory-based. A pre-existing flexural fatigue test method was modified to include

simulations of multiple-axle loads, and the effect of different axle group loads on the resulting fatigue life of

the asphalt samples was observed.

Homsi et al. (2012) recognised that there was a high amount of scatter in the collected data. In determining

the best use of this work for the Austroads project, it was considered that:

the project scope would not allow for repeating the experimental work of Homsi with the addition of

more test replicates

additional tests conducted to supplement Homsi’s data set could not be meaningfully conducted

without access to the same laboratory equipment and, more significantly, the same asphalt mix

(including its age) used in the original study

the study does represent the best available data for the project.

Homsi developed a model allowing the prediction of fatigue life of a sample as a function of the maximum

strain level, the number of peak strains, and two strain shape factors, all resulting from the simulation of a

single axle or multiple-axle group. The model does not consider how the grouping of axles may affect the

magnitude of the strain developed.

In order to determine how grouping of loads affects the strain developed in asphalt material layers, a series

of pavement structures were modelled using two response-to-load models, and Homsi’s model was applied

to the resulting strains. Section 7 is dedicated to this work.

5.4 Cemented Materials Fatigue

The review of available literature did not find records of data relating the observed flexural fatigue

performance of cemented materials to the application of various multiple-axle loads. However, Yeo

(Austroads 2008a) has established and validated laboratory test processes for assessing the flexural

modulus and fatigue characteristics of cemented materials. This project modified these processes by

simulating a range of multiple-axle loads, and aimed to develop a separate strain-fatigue performance

relationship for each load shape.

The use of laboratory simulation of cemented material flexural fatigue performance is similar to the

approach taken by Homsi for asphalt.

Section 8 describes this work.



5.5 Pavement Design Processes

The ALF work concluded with a confirmation of current practice regarding the characterisation of multiple-

axle loads for empirical pavement design purposes. However, the analysis work for asphalt and the

laboratory study and analysis work for cemented materials both suggested a more rigorous means of

considering multiple-axle loads in the mechanistic pavement design procedure.

Section 9 examines whether this more rigorous approach has an appreciable effect on pavement design

outcomes (i.e. the critical material thicknesses that the pavement structural design process determines are

necessary for the design traffic). This work concluded that significant thickness reductions were possible for

both materials, if critical strains were determined under each axle group/load combination in the design

traffic load spectrum.



6. Rutting of Unbound Granular Materials

6.1 General

In order to obtain performance data, the Accelerated Loading Facility (ALF) was used to assess the

deformation of a sprayed seal surfaced unbound granular pavement and subgrade. ALF (Figure 6.1) can

be used to simulate trafficking over the life of a pavement in a very short time, compared with on-road test

sites. For this work, the machine was housed in a large (20 m × 54 m) building at the ALF research testing

facility located in the south eastern Melbourne suburb of Dandenong South.

A single test pavement, representing a typical unbound granular second-class rural highway pavement and

subgrade, was constructed and trafficked.

Figure 6.1: The ALF machine within the research testing building

Prior to this study, ALF could only simulate a (half) single axle. The machine was modified to allow the

application of tandem and triaxle (half) axle groups (the geometry of the ALF frame is insufficient to support

development of a quad-axle group).

With a view to minimising the likelihood of the testing program being compromised by the unforeseen

malfunction of the new multiple-axle components, a lengthy commissioning exercise was undertaken on a

length of pavement outside the testing shed. Once the components had demonstrated reasonable

reliability, which took considerably longer than anticipated, trafficking of the test pavement properly

commenced.



6.2 Accelerated Loading Facility

6.2.1 Overview of ALF Prior to Modification

The ALF is a full-scale pavement test system enabling the assessment of road pavement performance

within a short time scale. The Australian ALF (Figure 6.1) is owned and operated by ARRB Group. Four

other ALF systems have subsequently been built and these are owned and operated by the Chinese

Research Institute of Highways, the US Federal Highway Administration (which operates two ALF

machines), and the University of Louisiana at Baton Rouge.

ALF uses a directly-driven load trolley to apply rolling wheel loads in a single direction to the pavement

strips, at a constant speed, using a constant mass. The load is applied to the test pavement through a load

assembly trolley, consisting of a standard heavy vehicle hub and wheel assembly, chassis and weight bed.

This trolley tracks linearly, guided by rails mounted on a stationary main frame, and is driven by electric

motors mounted directly onto the wheel hub.

The wheel is lifted off the pavement at the end of each cycle and supported by the main frame on its return.

By loading in a single direction only, the ALF machine is able to simulate real-world trafficking conditions,

and the raised rails at the ends of the machine allow for conservation of the majority of the trolley’s kinetic

energy.

The load applied to the pavement can be varied from 40 kN to 90 kN in 10 kN increments, by adding ballast

weights to the trolley above the axle assembly.

The cycle time for each load is about 10 seconds, which corresponds to approximately 350 load cycles per

hour or, depending on the percentage of operating time, about 50 000 cycles per week (based on 22 hours

per day operation). ALF can be set up to apply loads using dual, single or super-single wheel types. The

loading can be channelised or applied over any transverse distribution pattern within a 1.2 m width. A

normal distribution of transverse locations covering a 1.0 m wide trafficked area is commonly used to

simulate typical traffic wander on a road.

Table 6.1: ALF specification (before multiple-axle upgrade)

Test wheels Dual tyres (11R22), 330 mm centre-to-centre

Mass of test wheel assembly 40 kN to 90 kN in 10 kN steps

Suspension for variable mass Air bag and shock absorbers

Power drive to wheel Two 11 kW electric geared motors, uni-directional operation, wheels off pavement on return

Transverse movement of test wheels

User programmable; typically a normal distribution about 0.9 m or 1.2 m wide between outer edges of the dual tyres

Test speed Nominally 17.5 km/h

Cycle time Approximately 10 seconds

Pavement test length Nominally 12 m

Site constraints Max. grade: 1%; max. crossfall: 3%

Operation Automatic control system and fail-safe operation

Portability Readily detachable and transportable

Overall length of ALF 26.3 m

Overall width of ALF 4.0 m (operating); 3.2 m (transport)

Overall height of ALF 5.7 m (operating); 4.4 m (transport)

Total mass of ALF Approximately 45 tonne



6.2.2 Multiple-axle Modifications

A key aspect of the modified machine is that the load trolley assembly uses identical and interchangeable

axle modules (Figure 6.2), which can be set up for single, tandem or triaxle group trafficking. Figure 6.3

shows an illustration of the new multiple-axle assembly for ALF (in a tandem axle configuration). To aid in

uniform loading of the pavement by each axle, the design incorporates separate swing arm suspensions,

including airbag and shock absorbers, for each axle, and a central pivot point attaching the assembly to the

main ALF loading trolley.

Figure 6.2: Individual axle module

Figure 6.3: The ALF multiple-axle assembly (tandem axle configuration)

Details of the modifications are beyond the scope of this report, but can be found in Austroads (2013). In

summary, the modifications were:

The main frame was lifted by 520 mm, allowing sufficient height for the new assemblies and

suspension components to operate within the suspension manufacturer’s specifications.

The main frame, return rails and all central webs were removed to allow the new wheel assembly

space to operate; and strengthening beams were added underneath the lower rails to compensate for

material removal.

The existing wheel assembly was removed and replaced with an attachment plate, allowing up to three

individual axle modules to be attached to the load trolley.

The load trolley membrane was stiffened to cope with the implications of the larger and heavier axle

assemblies.



Mass was removed from the load trolley membrane to compensate for the addition of mass in the

wheel assemblies, allowing the total minimum applied weight of single axle and tandem axle

configurations to be 40 kN and 60 kN, respectively.

The specifications of the modified machine are given in Table 6.2.

The triaxle and tandem assembly modules are bolted to a primary attachment plate, as shown in

Figure 6.4. This plate pivots around a secondary attachment plate though two large pins (Figure 6.5)

located symmetrically, relative to the axle positions of the modules. The secondary attachment plate is

bolted directly to the load trolley (not shown).

The reason for the pivot is two-fold, as it allows:

the ballast load from the assembly trolley to be transferred down through the centre of the assembly

plate and evenly applied to each axle

the trolley to remain level to the pavement surface, despite the surfacing progressively lowering due to

the pavement deformation that occurs over the course of the experiment.

Table 6.2: Specifications of the modified ALF

Test wheels Any dual, single, super-single or steer tyre and rim combination complying with ISO 10/335 PCD, 26.75 mm stud holes and 281.2 mm centre bore diameter

Rim offsets of up to 250 mm

Mass of load trolley 40 kN to 90 kN in 10 kN steps

Axle group assemblies Swing-arm mounted, 120 mm stub axle available in single, tandem and triaxle assemblies

Suspension for variable ballast mass

Standard BPW-Transpec air spring and standard heavy vehicle shock absorbers

Power drive to wheel Direct coupling drive onto wheel hub from swing-arm mounted single 22 kW SEW bevel gear/motor, powered by 3–phase 415V Toshiba AS-1 Variable Speed drive

Transverse movement of test wheels

Programmable in both pattern and frequency of movement. Typically uses a normal distribution, nominally either a 0.9, 1.0 or 1.2 m width between outer edges of the dual tyres

Test speed Incrementally variable up to 17.5 km/h

Cycle time Approximately 10 seconds at nominal operating speed

Pavement test length Single axle assembly: 11 m + 3 m lead-in/lead-out

Tandem axle assembly: 9.5 m + 4.5 m lead-in/lead-out

Triaxle assembly: 8 m + 7 m lead-in/lead-out

Site constraints Max. grade: 1%; max. crossfall: 1%

Operation Fully automatic control system and fail-safe operation provided by programmable logic controller. Wireless graphical user interface supporting remote access, integrated data logging and machine cardiology reports

Portability Readily detachable and transportable between sites. Self-powered intra-site jockey movement over relatively level ground, both forwards and reverse with 360 degree turning radius

Overall length of ALF 26.3 m

Overall width of ALF 4.0 m (operating); 3.2 m (transport)

Overall height of ALF 6.3 m (operating); 4.4 m (transport)

Total mass of ALF Approximately 45 tonne

Each axle module is individually sprung and damped, and the modules are attached to a pivoting

attachment plate, the geometry of which ensures that the overall self-weight of the assembly is shared

evenly across each axle. When operated in tandem or triaxle configurations, the drive motor is located on

one module and the remaining modules are free-wheeling, save for a flexible belt which runs between hub

lines of the dual wheels. This belt maintains rotational inertia of the freely spinning wheel sets, while the

load assembly is raised above the pavement on the return pass.



Figure 6.4: Triaxle and tandem axle assembly configurations showing individual modules and

primary and secondary attachment plates

Figure 6.5: Pins allowing pivoting of multiple-axle attachment plate

When operating as a single axle assembly, a lighter, non-pivoting attachment plate is used (Figure 6.6).



Figure 6.6: Single axle assembly configuration

6.3 Site, Pavement Composition and Construction

6.3.1 Description of Site

For the tests described in this report, the ALF was housed at the ARRB indoor research testing facility

(building 54 m in length and 18 m wide) at Dandenong South, Victoria (Figure 6.7).

The test pavement was constructed as detailed in Section 6.3.3. The size of the building, relative to the

size of the ALF machine, allows for 12 individual ALF experiment locations. An experimental layout plan of

the test pavement is shown in Figure 6.9.

Figure 6.7: Indoor facility for the ALF (54 m long by 18 m wide)



6.3.2 Pavement Composition

Test pavement structure

Available resources only allowed the test program to examine the effect of multiple-axle group loads on a

single pavement structure. The main factors affecting the selection of test pavement materials and

composition were:

The pavement would be an unbound granular pavement with a thin bituminous surfacing.

The pavement materials and thickness should be representative of a typical, not especially heavy duty,

state road.

As permanent deformation of the pavement was to be the performance measure used during the

experiments, it was important that at least moderate levels of deformation occur under the expected

ALF loading.

Deformation of the subgrade was to be considered in the experiments, so a weak-to-moderate

strength subgrade should be incorporated.

Uniformity of material quality, density and moisture content was considered important to the

experiment goals.

Figure 6.8 shows the pavement structure adopted for the test pavements. The crushed rock drainage layer

(which integrates with a drainage system that surrounds the test pavement area) and underlying clay

material were constructed some years ago to isolate any overlying pavement structure from variations in

the natural water table. Yeo documents their characteristics and construction in Austroads (2008b).

Based on the Austroads empirical design procedure (Austroads 2012a), the pavement structure would

have a design life of between 1.2 × 105 and 106 ESAs, depending upon the level of subgrade support

provided by the imported subgrade.

Figure 6.8: Structure of test pavements



Subgrade material selection

The previous trial conducted within the research testing building had used a cemented material subbase

overlying a sand subgrade (Austroads 2008c). For this research study, it was believed that the sand

subgrade would provide excessive support to an overlying crushed rock base, and the observed pavement

deformations would be too small to discern differences between axle group loads. Accordingly, it was

decided that a low-to-mid-strength clay subgrade would be more appropriate. Suitable clay was sourced

from within the ALF site area. This clay had been placed as imported subgrade for a previous ALF trial

conducted on a test area outside the current ALF testing shed (Moffatt et al. 1998).

Base material selection

The current ALF test facility is located in the Melbourne suburb of Dandenong South, which an area near

several large quarries producing crushed rock products for road pavements. There are several advantages

in using base material from one of these quarries when constructing a trial pavement:

the quarries are close to the test facility, resulting in low haulage costs

the proximity allows material to be pug-milled, hauled and placed within an hour, providing uniform

moisture condition of the placed material

the local quarries have process control systems to ensure uniform products.

For this trial, however, it was identified that a significant disadvantage would be the likely high-quality

material sourced being unrepresentative of many rural areas in Australia. Nevertheless, previous

experience with ALF trials has demonstrated that uniformity of pavement composition and construction is

critical to subsequent meaningful analysis. Accordingly, it was decided that local quarries would be used,

but that a search would be undertaken to select a material which, whilst uniform, was of representative

quality for the Australian rural network.

Ultimately, a 20 mm VicRoads (2013) Class 2 crushed rock product from the Boral quarry in Lysterfield (a

20 minute drive from the ALF site) was selected. A VicRoads Class 2 material is a base quality plant mixed

crushed rock material for use in unbound flexible pavements in locations where a very high standard of

surface preparation may not be required. VicRoads specifications do not have a minimum plasticity index

or a maximum permeability requirement for Class 2 materials (the plasticity index is specified to be

between 0 and 6%).

Layout of test pavement

A plan view of the pavement within the shed is shown in Figure 6.9, providing chainage (running along the

length of the shed) and offset distances (running along the width of the shed) measured relative to a

standard benchmark used in previous ALF trials. A 1% grade and crossfall is built into the site to enable

easy drainage.

The area provides 12 possible ALF experimental sites, each 12 m long by 1 m wide (Table 6.3). By pre-

determining these sites, care could be taken during the construction works to ensure that the pavement

constructed in these exact locations was the best that could be achieved. The numbering of the ALF

experiment sites followed established practice, and reflects that these pavements were to be tested as part

of the 35th ALF trial.

Near the conclusion of the loading program, additional experiment locations were defined between

previously tested experiments. As shown in Figure 6.9, the potential locations for these additional

experiment locations was limited by trench investigations in adjacent completed experiments.



Table 6.3: Location of ALF experiment sites

Experiment no. Chainage (m) Centreline offset (m)

3500 8–20 3.375

3501 20.5–32.5 3.375

3502 33–45 3.375

3503 8–20 7.125

3504 20.5–32.5 7.125

3505 33–45 7.125

3506 8–20 10.875

3507 20.5–32.5 10.875

3508 33–45 10.875

3509 8–20 14.625

3510 20.5–32.5 14.625

3511 33–45 14.625

3514 26.5–36.5 9.090



Figure 6.9: Layout of test pavement



6.3.3 Pavement Construction

General

Prior to placement of the new test pavement, pavements constructed and trafficked with ALF for a previous

trial had to be removed. The following sections provide a brief overview of the removal of the old

pavements and construction of the new pavement. Also included are pavement layer relative levels,

thicknesses, and relative densities measured during the construction works.

A separate report (Austroads 2011d) documents the construction of the test pavement in much greater

detail than the following summary, and includes a construction diary, descriptions of the plant used, and

photographs of all construction activities. The report also contains design notes for the sprayed seal

surfacing.

Temporary removal of wall panels

To assist in drying back the new pavements, a considerable number of wall panels were removed from the

shed prior to pavement construction. Panels at both ends of the shed were entirely removed to a height

approximately one metre below the bottom of the gable. This arrangement allowed the free flow of air

throughout the test shed, facilitating material dry back, and also provided easier access by pavement

construction equipment. Free-flowing air during construction also minimised the build-up of equipment

exhaust fumes within the shed. Figure 6.10 shows the appearance of the shed, with the wall panels

removed, during the construction exercise.

The wall panels were stored offsite in the warehouse of the shed fabrication firm engaged to remove the

panels, and were reinstated upon completion of the construction works (i.e. after placement of the final

surfacing).

Figure 6.10: Appearance of the research testing facility building during construction



Reclamation of clay subgrade material from Borrow Pit

A profiler was used to remove the clay material to be used as the imported subgrade from an old test area

adjacent to the ALF shed. The profiler did not encounter any trouble in removing the clay material. Trucks

were used to transport the clay to the floor of the excavated test area inside the ALF shed (Figure 6.12).

The clay was placed in two lifts, spread with a skid steer loader, and compacted with a padfoot roller and

smooth drum roller (Figure 6.12).

The use of the profiler to extract the clay resulted in a small clumpy material that proved to be very easy to

spread.

Figure 6.11: Profiler removing clay from borrow pit

Figure 6.12: Placement of imported clay subgrade

(a) Tipping reclaimed clay material onto floor of test

pavement area (b) Rolling clay subgrade with smooth drum roller



Placement of granular base layers

The 300 mm thick unbound crushed rock base layer was placed in two lifts on two separate days. The

material was pug-milled at its source quarry and transported to the ALF site, with a haulage time of

approximately 20 minutes.

The delivery trucks were backed to the end of the pavement and then driven forwards as they dropped their

loads onto the subgrade (Figure 6.13). The material was spread by skid steer loader and compacted with a

smooth drum roller. The surface of the first lift was lightly scarified before placement of the second lift to

improve the bond with the second lift.

After compaction of the second lift, a level check conducted showed that the pavement area was generally

between 0–10 mm too high, with two areas being 10–15 mm too low. A skid steer loader was again used to

conduct a final trim of the base, which was followed by a light rolling using a multi-tyred roller.

Figure 6.13: Tipping and spreading for first lift of base

Sprayed seal surface

As the main pavement condition parameter to be measured during the ALF experimental program was rut

development, it was considered important that the final pavement surfacing be rut/deformation resistant in

its own right. This would ensure that any observed surface deformation would be a true reflection of the

deformation of the underlying base and subgrade.

A prime followed by a double/double sprayed seal (14/7 mm) was selected in place of asphalt to remove

the possibility of asphalt deformation to surface shape changes during the ALF experiments.



Previous experience of placing a sprayed seal inside the ALF shed demonstrated that there was insufficient

exposure to sunlight to remove cutback from the binder. The previous ALF trial had, however, used a

polymer modified emulsion binder in place of a cutback. As noted by Holtrop and Moffatt (2008), the

performance of that seal under ALF loading had been excellent.

As had been the case with the previously successful seal, the spray seal design was conducted in

accordance with current Austroads sprayed seal design methods (Austroads 2006b). Detailed design notes

can be found in Austroads (2011d).

Before application of the prime, the surface of the pavement was lightly broomed. This removed a

significant amount of crust resulting in an open and bony surface. The application and absorption of the

prime appeared uniform, even though the underlying texture of the base was very open (Figure 6.14).

Placement of the seal was undertaken using standard full-scale equipment.

Figure 6.14: Appearance of primed surface

6.4 Loading Applied During Testing Program

6.4.1 Loading Applied

ALF loads the test pavement with half axles, and in this report, all loads relate to the load applied to the half

axles and need to be doubled to reflect the equivalent load on a full axle or axle group.

The experimental program focussed on the effect of a number of axles within an axle group on pavement

performance. Each test location was only trafficked by a given axle configuration and load level. The load

on each axle configuration was adjusted so as to ensure that the same load per axle was applied across

the axle groups.



Unfortunately, the self-weight of some of the assembly components meant that the lightest load that the

single axle assembly could apply was 40 kN. Maintaining this axle load level throughout the experimental

program would have meant that the tandem axle configuration would have used a load of 80 kN (which was

achievable) and the triaxle configuration would have had an unachievable 120 kN. The loadings shown in

Table 6.4 were used to overcome this limitation. The step change in loading level is undesirable, but

unavoidable.

Table 6.4: Axle group load levels for ALF experimental program

Axle group Total group load (kN) Load per axle (kN)

Single 40 40

Tandem 1 80 40

Tandem 2 60 30

Triaxle 90 30

6.4.2 Transverse Distribution

The ALF machine was designed to enable trafficking at different transverse locations within a wheel path

width of up to 1.2 m, to simulate traffic wander within a lane. For this trial, the ALF was programmed to

conduct randomised passes of the load wheels according to a normal distribution within a 1.0 m width.

As described below, the change in transverse location of the load wheels occurred frequently during the

bedding-in process; initially being every cycle, then every 25 cycles and finally, after the bedding-in process

was completed, every 50 cycles. This was to ensure a more even transverse distribution of loading during

the crucial initial stages of loading.

Because the load applied to the pavement is applied through dual wheels (Figure 6.15), there are two

locations within the width of the trafficked area that have the same maximum amount of load passes

applied – one for each wheel. These locations are located 165 mm each side of the centre of the dual

wheel assembly. The actual loading distribution that the pavement is subjected to over the course of an

experiment is depicted by the blue line shown in Figure 6.16.

Figure 6.15: Load wheels centred over experiment width



Figure 6.16: Transverse load distribution

6.4.3 Line Marking

After the test pavement was constructed, the locations of 12 possible experiment locations were marked.

The geometry of the shed only allowed 12 practical experiment locations. The geometry of the ALF

machine, and in particular the feet upon which it rests, tightly defined these locations. Since the experiment

locations were well-known before commencement of trafficking, the locations were clearly marked so that

any personnel conducting work on the site could avoid any activity that may compromise the conduct of a

future experiment.

Once trafficking of an experiment was under way, the markings were used as reference points in the

collection of data.

As described in Section 6.4.2, whilst the wander in the transverse position of loading followed a normal

distribution along the centreline of the experiment, the dual tyres used for loading meant that the lengths of

the experiment that received the most trafficking were located under each tyre, 165 mm either side of the

centreline.

The line under the left tyre (facing the direction of trafficking, i.e. looking towards the door) in Figure 6.9

was marked (Figure 6.17) to aid collection of falling weight deflectometer (FWD) data. After trafficking,

destructive forensic testing also took place along this line.

Figure 6.17: Experiment site (12 m × 1 m) with offset line for FWD testing



6.4.4 Pavement Bedding-in

As the test pavement was constructed in indoor laboratory-like conditions, the spray seal was not subjected

to normal traffic or environmental hardening that would normally take place following field placement.

Additionally, the unbound granular base layer would be expected to experience a bedding-in or

densification phase under normal in-service loading conditions.

To take account of this, a bedding-phase process at the commencement of loading was adopted to be

representative of in-service conditions. With the exception of experiment 3502, which used the 90 kN triaxle

configuration throughout all trafficking, each experiment utilised the 60 kN tandem axle configuration for the

duration of the bedding-in process. The bedding-in process is listed in Table 6.5.

This bedding-in process typically lasted for 48 hours. In order to provide a measure of the initial high rate of

pavement deformation, the transverse profilometer was used to collect deformation data (and texture data)

at frequent intervals during this time.

Table 6.5: Initial pavement bedding-in process

ALF loading cycles Activity

Prior to traffic loading

If the pavement surface temperature was below 20 °C, it was heated to this temperature and this was maintained for 24 hours to ensure the seal binder was sufficiently pliable to allow the aggregate in the seal to reorientate rather than have the seal break up during initial trafficking.

The entire experiment area was swept and vacuumed clean of any loose aggregate to enable accurate and uniform readings from sensors used to measure surface profile of the pavement.

Initial surface profile measurements were recorded using the transverse profilometer.

Texture depth was measured using the volumetric patch method and also with the transverse profilometer laser.

Falling weight deflectometer (FWD) measurements were taken.

Cycles 1–500 (tandem axle with 60 kN)

ALF was operated at a reduced speed (16 km/h) with transverse movements at every cycle.

ALF profilometer collected deformation and texture data at regular intervals.

Cycle 500 Entire experiment pavement was re-swept of any loose aggregate.

ALF profilometer collected deformation data (these initial readings were used as a datum in conjunction with subsequent repeat sets of data for pavement deformation calculations) and texture data.

Transverse straight edge photographs were taken at 2 m intervals along the length of the experiment (additional photographs were taken of any observed pavement abnormalities).

Cycles 500–10 000 (tandem axle with 60 kN)

ALF was operated at full speed (approximately 22 km/h) with transverse movements every 25 cycles.

ALF profilometer collected deformation and texture data at regular intervals.

Cycle 10 000 Entire experiment pavement was re-swept of any loose aggregate.

ALF profilometer collected deformation and texture data.


Dynamic load measurements of the loaded axles were recorded for a short period of trafficking.

Falling weight deflectometer (FWD) measurements were taken.


Bedding-in complete

Cycles 10 001+ (experiment axle group and load)

ALF was operated at full speed with transverse movements every 50 cycles.

ALF profilometer robot collected deformation and texture data at varying intervals.



6.5 Experiment Progression

Following completion of the bedding-in period, deformation data collection intervals changed from 1000

cycles to approximately 2000 cycles, and the interval gradually increased as the experiment progressed

towards a total cycle count of 50 000. After this point, data collection intervals were aimed to be

approximately 20 000 cycles, but depended on operator convenience and were selected to coincide with

machine maintenance intervals.

The decision to cease trafficking for an experiment was based upon judgement, considering the following

factors:

the amount of pavement deformation achieved

seal and pavement condition

time available and budgetary constraints.

Table 6.6 lists the experiments conducted. The experiment numbers used, e.g. 3502, correspond to the

location of the experiment (as shown in Figure 6.9) and not to the order in which they were conducted.

Detailed descriptions of the conduct of each experiment and all of the collected data are reported in

Austroads (2013).

Table 6.6: Experiments conducted

Experiment number

Date commenced Date completed Duration (days)

Assembly Load Total cycles

3502 Thursday 15 October 2009 Thursday 19 November 2009 35 Triaxle 90 kN 210 000

3508 Monday 7 December 2009 Saturday 6 February 2010 61 Tandem axle

60 kN 278 232

3505 Monday 15 March 2010 Monday 10 May 2010 56 Tandem axle

80 kN 291 000

3511 Sunday 23 May 2010 Wednesday 7 July 2010 45 Single axle 40 kN 298 400

3504 Tuesday 13 July 2010 Monday 13 September 2010 62 Triaxle 90 kN 310 000

3507 Monday 20 September 2010 Tuesday 16 November 2010 57 Single axle 40 kN 350 000

3503 Monday 22 November 2010 Monday 10 January 2011 49 Tandem axle

60 kN 322 600

3506 Saturday 19 February 2011 Tuesday 12 April 2011 52 Tandem axle

80 kN 370 000

3501 Monday 18 April 2011 Tuesday 14 June 2011 57 Triaxle 90 kN 390 000

3510 Thursday 23 June 2011 Sunday 17 July 2011 24 Single axle 40 kN 75 000

3500 Wednesday 3 August 2011 Friday 7 October 2011 66 Single axle 40 kN 350 000

3512 Wednesday 18 February 2012

Wednesday 2 March 2012 14 Tandem axle

80 kN 250 000

3514 Monday 19 March 2012 Monday 9 July 2012 113 Tandem axle

80 kN 230 000



6.6 Acquired Data

6.6.1 General

Before and during each ALF experiment, data was collected using non-destructive methods in order to

capture the change in deformation of the pavement resulting from the application of cycles, as well as

measuring the deterioration of surface texture. At the end of each experiment, more destructive methods of

pavement data collection were employed to explore the physical condition of the base and subgrade.

Austroads (2013) contains all data collected during the experimental program.

6.6.2 Loading Applied

To assess whether individual axles within the multiple-axle groups (tandem and triaxle) were loading the

pavement evenly, strain gauges were fitted to each of the assemblies’ stub axles (Figure 6.18). This

allowed a measure of the load applied to the pavement from each set of dual wheels to be determined.

Due to the bulk and relative fragility of the logging equipment, and the huge amounts of data that would

have been generated, dynamic load data was not collected continuously during trafficking; but rather it was

collected for a limited number of loading cycles at the start and end of each experiment, and at occasional

times in between.

Strain gauges could have been fitted to measure either bending strain or shear strain in the stub axles.

Bending strain magnitudes would have been much higher and shown a greater range than shear strains,

yielding a higher signal-to-noise ratio. However, as the stub axles act as cantilevers, any small changes in

the load distance due to bending would produce high fluctuations in the bending strains measured by the

fixed gauges. Shear strain measurements do not suffer this problem and so, despite the smaller magnitude

and range of results, it was decided to measure shear strains.

On each stub axle, four gauges were arranged as a Wheatstone bridge to limit the effects of temperature

variation on the measurement signal. Each time data was collected, the measurement equipment was set

up with a specific signal conditioner paired with each Wheatstone bridge, using the same logging channels,

plugs and sockets. The signal conditioners used had a fixed range of amplification, which proved to be

much more resistant to drift than signal conditioners with variable range amplification.

At the beginning and end of an experiment, each individual assembly was weighed statically in order to

calibrate the responses of the strain gauges to the load on the axles. Having obtained a calibration

relationship, small adjustments to the pressure in each air-spring were made, if needed, to set the

assembly group at equilibrium when stationary and loaded to the test load for the experiment. ALF was

then operated for approximately 50 cycles and the strain gauge outputs were logged using acquisition

equipment temporarily mounted onto the ALF loading trolley. Analysis of this data provided reassurance

that the individual axle assemblies were applying equivalent load to the pavement during trafficking, and

also assisted in assessing which areas of the pavement were not loaded evenly by all axle groups at the

start (trolley landing) and end (trolley take-off) of an ALF load cycle.



Figure 6.18: Strain gauge mounted to stub axle

The air-spring pressures were recorded during static calibration and used throughout the experiment as

reference pressures for conducting intermittent dynamic load checks without wheel-load scales.

Dynamic load data was collected at a rate of 50 samples per second (50 Hz) and required some filtering to

remove noise. Signal noise was present due to the physical vibrations of the ALF, the measurement

equipment, and also electro-magnetic signal interference from the variable speed drive (operating at 45 Hz).

At the conclusion of an experiment, the dynamic load data collected at the start and end of trafficking was

analysed in order to make a conservative decision about which pavement chainages were not subject to

full loading. Data at these locations could be marked as invalid, and could be excluded from any

subsequent analysis. Uneven loading of the pavement occurred as a result of lowering and lifting of the

load assembly during an ALF cycle. The extent of uneven loading fluctuated due to several factors:

variations made to the lift and lower trigger delays of the trolley lifting system to ensure

day-to-day smooth operation

the speed of the lift and lower movements, which were dependent upon the hydraulic system oil

temperature

the amount of ballast mass that was needed to contribute (with the trolley mass) to the total applied

load

the amount of deformation experienced by the pavement at different stages of an experiment.

Typical dynamic load data collected, for the triaxle assembly, is shown in Figure 6.19. Only chainages that

were subjected to trafficking by all wheels of the assembly group under stable and equivalent loading were

considered to be valid.



Figure 6.19: Example of data gained during single triaxle trolley pass

With the speed of the trolley logged, it was possible to determine the distance trafficked under full and even

loading for any cycle. Using the clearly visible location of the landing point, trafficked distance could be

matched to a chainage on the experiment pavement to within half a metre. Dynamic load data collected at

different stages of each experiment had varying touchdown and lift-off locations, and the length of travel

that occurred between touchdown and the axle group stabilising also varied, due to the factors described

above.

As a result of these variations, a conservative approach to assessing data validity was used. The dynamic

load data analysis determined the minimum range for valid data. Figure 6.20 schematically shows the

different phases of the loading cycle that could be determined by examining the load data. Having defined

the minimum even loading distance, experiment observation notes and pavement deformation results were

used to identify any further invalid chainages.



Figure 6.20: Typical diagram of valid chainages (between vertical red dotted lines)

6.6.3 Particle Size Distribution of Base Material

After trafficking of each experiment was completed, samples of base material extracted from both trafficked

and untrafficked areas were sieved and particle size distributions determined. At each location, samples

were extracted over two depths; the top 150 mm and the lower 150 mm of the base. The particle size

distribution data can be found in Austroads (2013) and, as noted in that report, the data did not indicate any

significant variation of particle size distribution between the trafficked and untrafficked areas, or with depth

within the base material. It can be concluded that aggregate particles did not significantly break down under

ALF trafficking. Therefore, surface deformation resulted from densification of pavement materials, and not

from breakdown of particles.

6.6.4 Density and Moisture Content of Base Material

Density testing was carried out during pavement construction as well as at the conclusion of each

experiment. In all cases, testing was conducted using a nuclear density meter (NDM) in direct transmission

mode, in which the probe containing the radioactive material is lowered into a prepared hole, and the

number of radiated particles reaching the gauge was counted.

Comprehensive density testing was conducted at the conclusion of each experiment. Readings were

collected along the centre ‘trafficked’ offset, as well as along two outer ‘untrafficked’ offsets. Testing was

conducted at metre intervals along the length of the experiment. Readings were taken with the probe

lowered to depths of 125 mm and 275 mm into the unbound granular base material.

To ensure accuracy, raw data collected from the nuclear density gauge was calibrated against third party

(NATA) accredited calibration datasheets for the particular nuclear gauge that was used. Samples of the

granular material were also extracted after testing, and the moisture content of the samples determined in

the laboratory. The raw count data was then reprocessed, using the laboratory-determined moisture

contents.

The full set of readings is presented in Austroads (2013). As documented in that report, a comparison of

the density readings taken in the trafficked areas with adjacent readings taken either side of the trafficked

area, demonstrated a consistent increase in density of the base course material for each experiment. This

supports the earlier conclusion (Section 6.6.2) that surface deformation resulted from solely densification of

pavement materials.



6.6.5 Deformation of Imported Clay Subgrade Material

After conclusion of most of the experiments, transverse trenches were cut across the trafficked areas. Two

trenches were cut for each experiment (Figure 6.21). Each trench exposed two faces of the pavement’s

depth profile.

The preparation of each trench involved the following activities:

marking out the area of the trench to be excavated (along the centreline of the experiment)

(dry) cutting through the sprayed seal with an abrasive saw

removal of the sprayed seal

excavation of the majority of the trench materials using a small mechanical excavator

manually excavating materials at the two faces of the trench

carefully exposing the subgrade material near the faces, creating a bench to clearly differentiate

between the subgrade and base.

To observe pavement deformation changes with depth within the pavement structure, the distance between

pavement layer boundaries (between sprayed seal, base and clay subgrade) was measured relative to an

overlying straight edge across the full width of the trench at 100 mm spacings (Figure 6.22).

The raw data is collated in Austroads (2013). Difficulty was encountered in clearly identifying the interface

between a granular material and a fine grained subgrade material, leading to an uncertainty of measure of

at least a few millimetres. Given the relatively low surface deformations, any contribution by subgrade

deformation would have been within this measurement uncertainly. Additionally, even though the imported

clay material was finished with smooth drum rolling, the presence of indentations made by pad foot rollers

was clearly evident in the trench profiles, adding increased uncertainty of measurement.

It was concluded that the data did not present evidence of deformation in the top surface of the clay

material.

Figure 6.21: Trenching experiment 3502



Figure 6.22: Pavement trench showing straight edge used for layer profile measurements and

benched subgrade

6.6.6 Deformation of the Surface of the Pavement

ALF profilometer

The new ALF profilometer is a four-wheeled device (Figure 6.23) that uses a 12V DC system to drive itself

along a set of longitudinal steel tracks, and is assembled parallel to the ALF experiment strip at the

beginning of trafficking. A driven toothed wheel mates with a hole pattern in the tracks, thus ensuring

accuracy of the device’s position relative to the tracks. The ALF profilometer uses an ultrasonic sensor to

measure the distance from the sensor to the pavement surface. The sensor is mounted to a carriage that

can be moved along the length of the profilometer frame. This allows the collection of transverse profile

data, or for precise positioning of the sensor to collect longitudinal profile data along a specified line.

The device uses rotary shaft encoders to measure the distance travelled in both the transverse and

longitudinal directions, relative to a physical home marker which is set up with the tracks at the beginning of

each ALF experiment.



Figure 6.23: ALF profilometer

Surface deformation calculation

Transverse profile data was collected progressively throughout each experiment so as to track the gradual

deformation of the pavement surface as a result of trafficking. Each transverse profile consisted of 130

height readings, measured with the ultrasonic sensor, taken at even intervals of 16.92 mm across the

loaded pavement area.

Processing of the data from each survey allowed subsequent data sets (from different stages of the

experiment) to be overlayed and compared to each other as well as the datum set of data. Figure 6.24

shows the typical transverse profile of a particular chainage within an ALF experiment, with each data

series representing a different stage of trafficking. The amount of vertical downwards movement of each

profile in Figure 6.24 is defined as the deformation relative to the original (datum) profile. The surface

profile recorded after 500 cycles of the bedding-in stage was used as the datum profile.



Figure 6.24: Typical transverse surface profile data set (single chainage displayed)

Whilst the transverse profiles are useful for observation of localised pavement deformations, to represent

the performance of the pavement over the whole experiment, a mean deformation value for the surface

profile at each chainage is required. The mean deformation for each chainage was defined as the mean of

the highest 60% of deformation values within the trafficked area. This was calculated during secondary

processing of the raw transverse profile data.

These mean deformation values can be used to create plots displaying the increasing deformation at each

chainage over the course of the experiment. An example is shown in Figure 6.25.

Figure 6.25: Typical mean deformation along the trafficked length of an ALF experiment



In order to represent deformation of the entire pavement length within an experiment, after a given number

of loading cycles, the overall deformation was defined as the average of the mean deformations for each

chainage, excluding locations:

at the start and end of the experiment where the pavement was not subject to even loading

where isolated damage to the seal had occurred as a result of normal trafficking

where isolated surface or pavement damage had occurred as a result of an incident unrelated to

normal trafficking.

All deformation data collected during the experiments is documented in Austroads (2013).

Difference between deformation and rutting

Rut depth is usually defined as the maximum distance below a straight edge, of specified length, placed on

the road surface. Traditionally, ALF experimental data is presented as vertical deformation rather than

rutting. Figure 6.26 illustrates the difference between these two parameters. Deformation is used instead of

rutting as significant heave can occur just outside the area trafficked with ALF – and this may be

exaggerated compared to that which may occur when normal wide traffic wander is applied. Any unusual

heave would exaggerate the rut depth, whereas this heave does not affect the vertical deformation results.

It should be noted that as deformation represents only downwards movement of the pavement, it is

generally less than the equivalent rut depth value. The magnitude is dependent upon the amount of heave

produced on the test pavement(s). Excessive heave was not observed in the experiments described in this

report.

Figure 6.26: Measurement of deformation and rut depth

Post bedding-in deformation

As noted above, the profile measurements taken after 500 cycles of ALF loading was used as the datum

for calculating deformation. These readings were taken within the bedding-in period, wherein the pavement

was trafficked with 10 000 cycles of a 60 kN tandem group load. All deformation data in this report

represents post-bedding-in deformation. This was simply calculated using Equation 19.



𝑑𝑛′ = 𝑑𝑛+10000 − 𝑑10000 19

where

𝑑𝑛′ =

mean deformation at a location that occurred as a result of 𝑛 cycles of load being

applied after bedding-in

𝑑𝑛+10000 = mean deformation at a location that occurred as a result of 10 000 cycles of

bedding-in and 𝑛 cycles after bedding-in

𝑑10000 = mean deformation at a location that occurred as a result of 10 000 cycles of

bedding-in

The analyses in this report ignores the progression of deformation during the bedding-in period, and

focusses solely on the deformations that resulted from the differing axle group loads that were applied after

the bedding-in period. This data is tabulated in Appendix A.

6.6.7 Pavement Deflection Testing

At the beginning and end of the bedding-in period, and at the end of each experiment, pavement deflection

was measured using a falling weight deflectometer (FWD). FWD drops were conducted every metre along

the marked line described in Section 6.4.3. As the ALF machine was not located directly above the

experiment locations, FWD testing prior to, and at the end of, each experiment was able to encapsulate

some extra chainages as ‘lead-in’ for each experiment strip. However, because of the geometric

constraints of the ALF machine and FWD, it was not possible to collect this lead-in data when ALF was

placed over the experiment. FWD testing of the experiment area could, however, take place (Figure 6.27).

All FWD data is presented in Austroads (2013).

The FWD data used in the analyses in this report were the data collected at the end of the bedding-in

period, i.e. after 10 000 cycles of 60 kN tandem load applications. This FWD data is contained in

Appendix B; along with the results of back-calculation analyses (see Section 6.7.4).

Figure 6.27: FWD collecting data under ALF



6.7 Preparation of Data for Analysis

6.7.1 Overall Deformation and Variation of Results

As described in Section 6.6.6, the average deformation readings taken at each longitudinal chainage within

an experiment is termed the ‘overall deformation’. Figure 6.28 plots the progression of this overall

deformation for each experiment, categorising the experiments by the type of loading applied.

In some of the experiments, it can be seen that the magnitude of overall deformation did not smoothly change

with increasing application of loading cycles: this is particularly evident in Figure 6.28 (d). This fluctuation in

overall deformation is simply explained. Prior to presenting the deformation data listed in Appendix A, the raw

data presented in Austroads (2013) were examined to ensure that inconsistent readings were identified and

removed. For each chainage, the progression of deformation with increasing loading cycles was plotted, and

visual examination was used to identify readings which were inconsistent with readings taken at adjacent

cycle counts. This means that deformation data for a given chainage might not be available for all cycle

counts. As the overall deformation parameter is simply an average of valid deformation data for all chainages,

it can be seen that the inclusion of data at a specific chainage in one cycle count, and its exclusion in the

subsequent cycle count, could lead to the fluctuations evident in Figure 6.28. This indicates the necessity to

examine the deformation progression data at a chainage-by-chainage level, and not as a simple aggregate

average such as the overall deformation parameter.

Figure 6.28: Progression of (post-bedding-in) overall deformation for all experiments

(a) 40 kN single axle (b) 60 kN tandem group

(c) 80 kN tandem group (d) 90 kN triaxle group



6.7.2 Variation in Deformation Performance

Another, more significant issue that is highlighted by Figure 6.28 is the widely different performance

exhibited by the different experiment locations to the same loading. As described in Section 6.6.2, the load

applied to the pavement structure was checked at the start and conclusion of each experiment, and so the

variation in performance cannot be explained by unexpected variation in the loading. The pavement

structure was relatively uniform in construction thickness, as evident by the data presented Appendix C,

and so the only factors that could explain the variation in pavement performance were changes in the

properties of the materials. As the pavement materials and substructure were unbound materials, without

the presence of bituminous materials, variation of material stiffness or deformation resistance with

variations in ambient temperature can be excluded from consideration. Variations in moisture content within

the pavement structure, and over the time period in which the experiments were conducted, is considered

the most likely explanation for variable deformation performance.

The test pavement area was enclosed by a sub-surface drainage system, installed in November 2004. In

the intervening years, tests of pavement structures have not been affected by changing moisture conditions

of the pavement or subgrade materials. It had been presumed that the drainage system was functioning

appropriately. However, rainfall records from the nearby Bureau of Meteorology weather station

(Figure 6.29) indicate that the annual rainfall was considerably higher during the conduct of the

experiments than had occurred previously. This was also evident from anecdotal evidence as the creek

that runs adjacent to the facility had previously had very little to no flow, but in recent times had contained

running water. Given that the rainfall levels were unprecedented during the timeframe of testing conducted

at the site, it is conceivable that the installed drainage system was not sufficient to prevent groundwater

changes in the test area.

It is, therefore, considered likely that changes in moisture content of the crushed rock base and/or the

imported clay subgrade material could have occurred both within the total pavement area and the

timeframe of testing.

Figure 6.29: Rainfall measured at Dandenong weather station



6.7.3 Measured In Situ Material Properties

In order to determine whether any changes in material properties could have occurred as a result of the

moisture changes, the following data (Austroads 2013) collected immediately after the conclusion of each

experiment, were examined:

Dry density measurements taken using a nuclear density meter, used in direct transmission mode,

collected every metre along each experiment in the trafficked area and either side of it.

Moisture content data recorded with a nuclear density meter, used in back-scatter mode, collected

every metre along each experiment in the trafficked area and either side of it (moisture contents

recorded using back-scatter mode are considered to only reflect the top 50–80 mm of material).

In situ California Bearing Ratio (CBR) data estimated, from dynamic cone penetrometer (DCP) tests

conducted every metre along the trafficked area and either side of it using the established Austroads

(2012a) method.

The density data was collected with two probe depths at 150 and 275 mm. The 150 mm data represents

the density of the top of the crushed rock base, and the density of the bottom of the base was determined

using Equation 20.

All of these data are plotted, grouped by load type, in Figure 6.30 to Figure 6.33.

𝜌𝐿 =

275 × 𝜌275 − 150 × 𝜌150

275 − 150

20

where

𝜌𝐿 = dry density of bottom of crushed rock (t/m3)

𝜌275 = dry density recorded with probe at depth of 275 mm

𝜌150 = dry density recorded with probe at depth of 150 mm

Figure 6.30 shows that experiments 3500 and 3511 had similar crushed rock densities (both top and

bottom) and similar moisture contents, and so differences in density cannot explain the wide difference in

performance between these two experiments shown in Figure 6.28 (a). Experiment 3507 had slightly higher

top density and slightly lower bottom density than 3500, and lower moisture content, and yet they had

similar deformation performance. The stark difference in performance demonstrated by experiment 3511 is

best reflected in the considerably lower CBR of the imported clay material.

Figure 6.33 shows a lower base bottom density, higher base moisture content and lower CBR of the clay

as the most likely explanation of the higher deformations observed for experiment 3501 than for experiment

3504.

Whilst similar assessments could be made for other experiments, the above example comparisons have

already highlighted that none of the examined parameters can solely explain variations in performance.

Additionally, as the data plotted in Figure 6.30 to Figure 6.33 demonstrates there is a considerable variation

in material properties within many of the experimental test sections.

Given the range of variation in properties and observed performance, the analytical use of a single average

overall deformation measure and average property data for each experiment runs the risk of assigning

average deformation and average property data that did not truly occur at any location within the

experimental length. Rigorous analysis of the data would require that the performance of each point within

an experiment be considered with the material and pavement properties at that point, rather than the use of

data averaged over the entire length. This is the approach used in this report.



Figure 6.30: Density, moisture content and CBR of pavement materials – 40 kN single axle

experiments

(a) Density of top of crushed rock (b) Density of bottom of crushed rock

(c) Moisture content of crushed rock (d) CBR of imported clay



Figure 6.31: Density, moisture content and CBR of pavement materials – 60 kN tandem group

experiments





Figure 6.32: Density, moisture content and CBR of pavement materials – 80 kN tandem group

experiments





Figure 6.33: Density, moisture content and CBR of pavement materials – 90 kN triaxle group

experiments



6.7.4 Data to Reflect Pavement Properties

Available data

Variation in four types of data could be used to help explain variation in observed pavement deformation:

variation in load applied

variation thickness of pavement layers

variation in density of crushed rock and clay materials

variation in moisture content of crushed rock and clay materials.



As discussed in Section 6.6.2, the dynamic loading applied was assessed at the start and conclusion of

each experiment, and the length of pavement that was subject to even loading identified. This analysis

report only contains data collected within these evenly loaded areas. The static mass of the applied load,

and the load applied by each axle within an axle group, was also checked using vehicle enforcement

scales. It is considered that the only variation in load that occurred during data collection was those

deliberately made between experiments.

The thickness of the crushed rock base and imported clay subgrade were collected during pavement

construction, and were observed to vary to a small degree within each experimental length, and to a higher

degree between experiments (Austroads 2011d, 2013).

In situ dry density data was collected using a nuclear density meter, for the crushed rock base material at

every metre within each experiment. As discussed above, the data allowed separation of the top 150 mm of

crushed rock base from the lower component.

As well as collecting density data, the same equipment also collected an estimate of the moisture condition

of the crushed rock base every metre along the experimental lengths. However, as noted above, it is

generally recognised that moisture contents recorded using back-scatter mode are considered to only

reflect moisture conditions of the top 50–80 mm of material. As such, the moisture condition data does not

allow insight into the moisture condition of the majority of the depth of crushed rock base. Assessment of

the moisture condition of the imported clay subgrade is also not possible from this data set.

Dynamic cone penetrometer tests were conducted within the imported clay subgrade every metre along the

test lengths, and the collected data was used to estimate the California Bearing Ratio (CBR) of the clay.

It was postulated in Section 6.7.2 that variation in moisture condition was a major variance factor within and

between experiments. Figure 6.30 to Figure 6.33 indicate that the moisture condition of the top of the base

did in fact vary considerably. Additionally, these figures show that the CBR of the clay varied dramatically.

Whilst some of this variance maybe the result of varying density of materials resulting from the construction

processes, moisture condition must also have varied. However, the moisture content information available

for the crushed rock base material is limited to a relatively small proportion of that material’s thickness, and

a similar data set does not exist for the clay subgrade3, or the underlying pavement structure.

In order to provide some insight into the variation in pavement behaviour not allowed by these data sets,

pavement deflection data collected with a falling weight deflectometer (FWD) was examined. FWD

readings were taken at the end of the bedding-in period (i.e. at 𝑑𝑛′ = 0 in Equation 19), and at the

conclusion of trafficking for each experiment. Readings were taken at load levels of 500 kPa and 700 kPa.

The deflection bowls measured were used to back-calculate the stiffness of the pavement materials, and

these stiffness were then used in subsequent analysis.

Back-calculation of pavement moduli

Of the available FWD data sets, back-calculation was conducted with the 500 kPa data collected at the end

of the bedding-in process. The reasons for excluding the other data sets were:

700 kPa data – excluded because many deflection readings recorded exceeded the range of the

deflection sensors (the 500 kPa readings were all within scale)

experiment conclusion data – excluded as the end of experiments was not uniformly defined, and in

some cases, was selected on the basis of operational issues.

3 Some selected samples of crushed rock material and clay subgrade were extracted and, via oven drying, their moisture contents were established in the laboratory. However, the data set is not extensive, with only two or three locations within each experiment. This data set is reported in Austroads (2013).



The computer program EfromD3 (developed from EfromD2, Vuong 1991) was used to estimate the moduli

of materials within the pavement structure. This program uses the linear-elastic software CIRCLY (MINCAD

Systems 2009) as its pavement response model, but incorporates processes to approximate the non-linear

behaviour exhibited by unbound pavement materials. Similar with most back-calculation programs,

EfromD3 uses pavement layer thicknesses and surface deflections as inputs to estimate the moduli of

pavement layers. The surface deflections calculated using the estimated moduli are compared to the

measured deflections, and this comparison is used as an assessment of the goodness of fit.

The pavement model structure adopted for the back-calculation analyses is shown in Figure 6.34, and the

model parameters are listed in Table 6.7. Key aspects of the model used are:

The crushed rock and imported clay layers were sub-divided into three sub-layers, as initial testing with

only a single layer for each material, or two sub-layers each, did not yield good fits to the deflection

data – it is conjectured that three sub-layers were necessary due to the highly non-linear variation in

modulus that likely occurred in these materials as a result of varying amounts of moisture infiltration.

The thicknesses of the lower sub-layer of the crushed rock and imported clay layers were determined

by subtracting the fixed sub-layer thicknesses from the measured total thickness of the layer at the

location at which each deflection point was measured.

The thickness base and clay layers for experiment 3514 were (linearly) interpolated from

measurements taken at adjacent locations – as the location of this experiment was not originally

planned, the exact thickness data was not collected during pavement construction.

The thickness data for the half-metre chainages (e.g. chainages 2.5 m, 3.5 m, etc.) for experiments

3500 and 3501 were interpolated from measurements taken at adjacent locations – thickness data was

collected at one metre spacings during construction, and FWD data was available at half-metre

spacings.

The thickness data for the whole-metre chainages (e.g. chainages 2.0 m, 3.0 m, etc.) for experiment

3504 were interpolated, as there was a half-metre shift in the planned testing location and the one

actually undertaken.

The 75 mm crushed rock drainage layer was incorporated into the lime stabilised clay subgrade, and

the resulting consolidated layer was considered to have a uniform thickness of 375 mm.

The sprayed seal surfacing was considered to have not played a structural role in the pavement

structure and it was simply ignored in the analyses.



Figure 6.34: Pavement model used in back-calculation

Table 6.7: Back-calculation model parameters

Layer Material Thickness (mm)

Seed 𝑬𝒗 (MPa)

Minimum 𝑬𝒗 (MPa)

Maximum 𝑬𝒗 (MPa)

Anisotropy 𝑬𝒗 𝑬𝒉⁄

Poisson’s ratio

𝝂𝒗 = 𝝂𝒉

1 Rock base 100 200 150 1000 2 0.35

2 Rock base 100 200 50 700 2 0.35

3 Rock base Total–200 200 50 700 2 0.35

4 Imported clay 125 20 10 120 2 0.45

5 Imported clay 125 20 10 120 2 0.45

6 Imported clay Total – 250 20 10 120 2 0.45

7 Stabilised clay 375 200 50 300 2 0.35

8 Natural clay Semi-infinite 100 100 200 2 0.45

Note: Thickness of lowest sub-layer for crushed rock base and imported clay subgrade was the measured thickness less the two fixed thicknesses of the overlying sub-layers.

Appendix C contains the thickness and FWD data used in the back-calculation analyses, and also the

vertical modulus values calculated by the back-analyses (denoted 𝐸1 to 𝐸8), with the subscripts reflecting

the layer numbers listed in Table 6.7. Plots of the measured FWD deflection bowl and the calculated bowl

resulting from the back-calculation analyses are listed for every data location in Appendix D. It can be seen

from these plots that the shape of the deflection bowls, and the absolute magnitude of the maximum

deflections, varied considerably within the experimental test area, and also, in some cases, within

experiment locations. The back-calculation analyses would appear to have matched the observed bowls

well.



Aggregated stiffness parameters

In addition to the back-calculated moduli, some additional parameters were defined to provide aggregated

back-calculated moduli values at a given location. The first set of these aggregated parameters, simple

averages, are listed in Table 6.8.

Table 6.8: Aggregated stiffness parameters – simple averages (arithmetic means)

Parameter Description Calculation

𝐸𝑏𝑎𝑠𝑒 The average modulus of the crushed rock base (𝐸1 + 𝐸2 + 𝐸3)

3

𝐸𝑐𝑙𝑎𝑦 The average modulus of the imported clay (𝐸4 + 𝐸5 + 𝐸6)

3

𝐸𝑠𝑔 The average modulus of underlying support layers (lime stabilised clay and natural clay)

(𝐸7 + 𝐸8)

2

𝐸𝑛 Back-calculated modulus of layer 𝑛 in pavement model (Figure 6.34)

An additional set of aggregate parameters were calculated using Odemark’s method of equivalent

thickness (MET) approach (Ullidtz 1998, see Table 6.9). The derivation of the general form of the equation

used is described in Appendix E. The following assumptions were used in generating these parameters:

the Poisson’s ratio of all merged layers were considered to be the same

the correction factor, 𝑓, used by some applications of MET was ignored – this is a simple multiplier in

the equation, and as the aggregate parameters were to be used in regression analyses, the factor

would effectively be absorbed into the coefficient for the parameter when used in the regression model

the contribution of the natural clay material was ignored in the determination of 𝐸𝑠𝑢𝑝𝑝𝑜𝑟𝑡 and 𝐸𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒

(as defined in Table 6.9) – this layer is semi-infinite in the model and cannot easily be considered in

the MET calculations, and the back-calculated values for this parameter were not considered to be

varying to the same degree as moduli for overlying layers.

Unlike the simple averages used in the parameters in Table 6.8, these MET-based parameters take

consideration of the thickness of the various component sub-layers in determining an aggregate stiffness.

Table 6.9: Aggregate stiffness parameters (MET)

Parameter Description Calculation

𝐸𝑟𝑜𝑐𝑘 The overall modulus of the crushed rock base

(𝑡1 ⋅ 𝐸1

1 3⁄+ 𝑡2 ⋅ 𝐸2

1 3⁄+ 𝑡3 ⋅ 𝐸3

1 3⁄

𝑡1 + 𝑡2 + 𝑡3)

3

𝐸𝑏𝑎𝑠𝑒_𝑙𝑜𝑤 The overall modulus of lower two sub-layers of the crushed rock base

(𝑡2 ⋅ 𝐸2

1 3⁄+ 𝑡3 ⋅ 𝐸3

1 3⁄

𝑡2 + 𝑡3)

3

𝐸𝑖𝑚𝑝_𝑠𝑔 The overall modulus of the imported clay subgrade

(𝑡4 ⋅ 𝐸4

1 3⁄+ 𝑡5 ⋅ 𝐸5

1 3⁄+ 𝑡6 ⋅ 𝐸6

1 3⁄

𝑡4 + 𝑡5 + 𝑡6)

3

𝐸𝑠𝑢𝑝𝑝𝑜𝑟𝑡 The overall modulus of the imported clay and lime stabilised clay

(𝑡4 ⋅ 𝐸4

1 3⁄+ 𝑡5 ⋅ 𝐸5

1 3⁄+ 𝑡6 ⋅ 𝐸6

1 3⁄+ +𝑡7 ⋅ 𝐸7

1 3⁄

𝑡4 + 𝑡5 + 𝑡6 + 𝑡7)

3

𝐸𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒 The overall modulus of all pavement layers (except the natural clay)

(𝑡1 ⋅ 𝐸1

1 3⁄+ 𝑡2 ⋅ 𝐸2

1 3⁄+ 𝑡3 ⋅ 𝐸3

1 3⁄+ 𝑡4 ⋅ 𝐸4

1 3⁄+ 𝑡5 ⋅ 𝐸5

1 3⁄+ 𝑡6 ⋅ 𝐸6

1 3⁄+ +𝑡7 ⋅ 𝐸7

1 3⁄

𝑡1 + 𝑡2 + 𝑡3 + 𝑡4 + 𝑡5 + 𝑡6 + 𝑡7)

3

𝐸𝑛 Back-calculated modulus of layer 𝑛 in pavement model (Figure 6.34)



6.7.5 Measure of Performance

Section 6.7.2 simplistically presented the deformation data collected as overall deformation, i.e. a single

measure is used to represent the deformation of an entire experimental length. As noted in Section 6.7.3,

rigorous data really requires that the performance of each measurement point within an experiment be

considered with the material and pavement properties at that point, rather than the use of data averaged

over the entire length. Before conducting any detailed analysis, the alternative parameters to reflect

deformation performance were investigated. Four different parameters were considered, each of which

would be calculated at each individual data point (i.e. chainage) within each experiment location:

1. Cycles to reach a given level of deformation.

As shown in Figure 6.35 (a), a given level of deformation is established, and the number of cycles

of the applied load needed to reach that level of deformation is obtained.

2. Long-term cycle rate

This parameter represents the long-term rate at which the cycles of the applied load need to be

applied to obtain an incremental increase in deformation (Figure 6.35 (b)).

3. Deformation at a given number of cycles

This parameter (Figure 6.35 (c)) is effectively the converse of the first parameter. In this case, a

given number of applied load cycles is defined and the deformation level at that number of cycles is

determined.

4. Long-term deformation rate

Similarly, this parameter (Figure 6.35 (d)) is the effective converse of the second parameter. It

represents the long-term rate at which deformation increases with increased application of load

cycles.

The aim of the experimental program and analyses was to determine the number of load cycles required by

different axle groups to produce the same level of damage. This is in keeping with the use of axle

equivalencies in a pavement design context – different axle group types and load magnitudes are

converted into a number of equivalent axle repetitions of a Standard Axle based on equivalent pavement

damage occurring. As the focus of the analyses was to be on the number of cycles of load to reach

equivalent damage levels, only the first two parameters in the list above were explored in detail. For the

sake of brevity, the two parameters were given simple names:

cycle count – the number of cycles of load applied, post-bedding-in, to reach the selected deformation

level

cycle rate – the long-term rate of application of load cycles needed to increment the deformation level

by one millimetre.

Figure 6.35: Alternative measures of deformation performance

(a) Cycles to reach deformation level (b) Long-term cycle rate (cycles/deformation change)



(c) Deformation at specific number of cycles (d) Long-term deformation rate (deformation/cycle)

In order to calculate cycle rate for all data locations in a consistent manner, a curve was fitted through the

cycles versus deformation data. A range of different functions were explored, and ultimately a simple log-

linear model was selected:

𝑙𝑜𝑔10 𝑦 = 𝑎𝑥 + 𝑏 21

where

𝑦 = cycles of loading (after bedding-in) (x1000 cycles)

𝑥 = mean deformation (after bedding-in) (mm)

𝑎, 𝑏 = constants

Cycle rate was calculated as the slope of a straight line fitted through the last 150 000 cycles of cycles

versus deformation data. A graphical check was made to ensure that this straight line did not encroach into

the region of the data where the slope was rapidly changing. Subsequent analyses demonstrated that the

cycle rate parameter was extremely sensitive to minor fluctuations in the underlying data, and it proved

impossible to reliably link this parameter to changes in the pavement material properties. Unsuccessful

analyses using this parameter have not been included in this report.

The following analyses focus on relating cycle count at selected deformation levels, to material properties.

The curves fitted using Equation 21 are plotted, and the equations are listed for each chainage location and

experiment in Appendix B. The plots also include the marks on the curves showing a deformation level of

three and four millimetres (except for those cases where either or both estimates are beyond the scale of

the plots). These deformation levels were two levels used in the analyses discussed in the next section.



6.8 Analysis Using Generalised Model

Whilst the progress of deformation was recorded at half-metre intervals within each experiment location,

the back-calculated moduli data was only available, in most cases, at metre intervals. This resulted in a

substantial reduction in the size of the combined data set.

Initially a generalised analysis was considered, wherein the number of cycles required to reach a specified

deformation level was a function of a combination of some, or all, of the following general data types:

the total load and number of axles in the load group

select deflection responses of the bedded-in pavement, e.g. D0, D200, D600, D900, etc.

aggregate stiffness parameters.

It became apparent, however, that it was not possible to develop a generalised model able to encapsulate

the combined data set of all experiments. Whilst there was variation between many of the factors listed

above, the amount that each overlapped was not consistent across the four different group/loads applied.

By way of an example, Figure 6.36 represents the distribution of the aggregate variable 𝐸𝑟𝑜𝑐𝑘 (the stiffness

of the crushed rock base) for each data location4. It can be seen clearly in the figure that, for example, half

of the chainages tested with the 60 kN tandem group had values of 𝐸𝑟𝑜𝑐𝑘 that were outside the range of

values encountered by the other three group/loads.

Even if a generalised model could have been developed using statistical regression techniques, it would

have been impossible to evaluate the model with fixed values for the dependent variables that were

representative of the variables values actually observed for all load types.

4 𝐸𝑟𝑜𝑐𝑘 was selected for this example as it was found to be the most common dominant factor in subsequent analysis (Section 6.9).



Figure 6.36: Distribution of Erock for each axle type

6.9 Analyses Using Axle Group Pairing

6.9.1 General

Given the above mentioned variability of test pavement properties, the detailed analyses focussed on data

from pairs of lead group types, attempting to understand the relationship between them, rather than

attempting the development of a generalised model. Four pairings were examined:



60 kN tandem group and 80 kN tandem group

This would allow an isolated assessment of the effect of axle group load on pavement deformation.

40 kN single axle and 80 kN tandem group

This would allow an examination of the effect of different axle numbers, with each axle loaded the

same, on pavement deformation.

60 kN tandem group and 90 kN triaxle group

This would allow an additional examination of the effect of different axle numbers, with each axle

loaded the same, on pavement deformation.

40 kN single axle and 90 kN triaxle group

This pairing represents loads that are considered to be equivalent using the current design

assumptions (i.e. the axles would act independently).

For each pair, the analysis approach used the following steps:

1. Select the data for the load group pair being considered.

2. For each test location (i.e. chainage), use a log-linear function to determine deformation as a function

of cycles of applied load – checking the quality of the fitted curve by plotting it against the raw data

(Appendix B).

3. Using Figure 6.37, identify the maximum deformation level that was achieved by the majority of the

data locations, for both load types. The maximum deformation level was chosen in order to reduce the

effect of measurement and uncertainty.

4. Discard those test locations where the observed maximum deformation was less than the selected

deformation level (step 3) – the number of cases was relatively small due to the selection process

used in step 3.

5. Using the fitted curves from step 2, calculate, for each test location, the cycle count that matched the

deformation level selected in step 3.

6. Discard those test locations where the deformation level selected in step 3 represented less than 30%

of the observed maximum deformation – the intention being to exclude those locations where a very

high deformation was observed in comparison to the deformation level selected (since, in these cases,

the selected deformation level was obtained after extremely short numbers of cycles).

7. Establish a baseline model form for each of the two load types. (cycle count) = 𝑎 + 𝑏(𝐷0). This model

was considered to be the simplest form of model, in as much as it used a single parameter to

represent pavement strength, and that it used a directly measured parameter and not a derived one.

8. Using a range of back-calculated moduli and aggregate stiffness parameters, attempt to develop a

model that improved the prediction of cycle count than that provided by the baseline model. Care was

taken during these analyses to ensure that the significance of additional parameters was statistically

valid, and that over-fitting of the model did not occur. With relatively few data points, models with fewer

parameters that offered only slightly poorer fits to data were accepted in preference to models with

slightly better fits but additional parameters. In order for the difference in performance under the two

load types to be examined, the models developed for the two load conditions would be need to be

compared with each other. For this comparison to be made, it would be highly desirable that the

models for each load type have similar parameters.

9. Having determined an improved model form in step 8, set it as the new baseline model and repeat

step 8 until no further model improvement is possible.

10. Examine the range of values for each of the parameters used in both load type models, and select

representative value(s) for those parameters that could be seen to be common across data sets for

both load types.

11. Use the model parameter values determined in step 10 to determine the cycle count to reach the

established deformation levels, and compare the results.



Figure 6.37: Distribution of maximum deformation observed for each load type



6.9.2 40 kN Single Axle and 80 kN Tandem Group

From Figure 6.37, it can be seen that the majority of data points for both experiments loaded with the 40 kN

single axle load and the 80 kN tandem group reached a deformation level of 4 mm or more. Accordingly,

4 mm was selected as the deformation level for the analysis. The cycles required to reach this 4 mm

deformation level were determined using the process described in Section 6.9.1, and the distribution of

these cycle count estimates is shown in Figure 6.38. The data is clearly scattered, and at a significant

number of test locations, for both load types, less than 50 000 cycles of loading were required to reach

4 mm of deformation, yet at other locations, in excess of 150 000 cycles were required. Some of the

locations loaded with the 80 kN tandem group required 250 000 or more cycles to reach this deformation

level.

Figure 6.38: Distribution of cycles required to reach 4 mm deformation for 40 kN single axle and

80 kN tandem group data

Regression models were developed to find those pavement material parameters which, when varied, could

explain the range of performance data obtained. Equation 22 was the model that was found to best fit the

40 kN single axle data. The model relates the number of cycles needed to reach the 4 mm deformation

level to the effective modulus of the crushed rock base, 𝐸𝑟𝑜𝑐𝑘 , determined using the MET method. Slightly improved R2 values could be found for models that contained an additional term, notably 𝐸𝑠𝑢𝑝𝑝𝑜𝑟𝑡; however,

analysis determined that the additional terms were not statistically significant.



𝑁40𝑆𝐼,4 𝑚𝑚 = −149407 + 1187𝐸𝑟𝑜𝑐𝑘 22

where

𝑁40𝑆𝐼,4 𝑚𝑚 = number of cycles of the 40 kN single axle to reach 4 mm of deformation

𝐸𝑟𝑜𝑐𝑘 = the overall modulus of the crushed rock base (definition in Table 6.9) (MPa)

Adjusted R2: 0.88

F-statistic: 121.7 on two variables and 16 degrees of freedom

p-value: 6.879 × 10-9

The model for the 80 kN tandem group data, Equation 23, uses the back-calculated modulus of the top

125 mm of imported clay subgrade (𝐸4) as the sole explanatory parameter for the variation in number of

cycles needed. A softening of the top of the clay material could well have resulted from water infiltration

and poor drainage of some of the experimental sections, as discussed in Section 6.7.1. As noted above, it

was considered to be beneficial if the two models had similar parameters, in order to make comparisons

between the two load cases easier. However, in this case, this was not possible. Attempts at using either

𝐸𝑟𝑜𝑐𝑘 as a variable in modelling 80 kN tandem data, or using 𝐸4 with 40 kN single data, failed to produce

models of any statistical significance.

𝑁80𝑇𝐴,4 𝑚𝑚 = −153895 + 15792𝐸4 23

where

𝑁80𝑇𝐴,4 𝑚𝑚 = number of cycles of the 80 kN tandem group to reach 4 mm of deformation

𝐸4 = the back-calculated modulus of the top 125 mm of imported clay (Table 6.7)

(MPa)

Adjusted R2: 0.93

F-statistic: 151.3 on one variable and 11 degrees of freedom

p-value: 9.019 × 10-8

The variation in the two explanatory parameters used in the models is shown in Figure 6.39. This figure

also includes shaded regions denoting the area enclosed by the upper and lower quartiles of each

parameter. The narrow range of variation in the 𝐸𝑟𝑜𝑐𝑘 parameter for the 80 kN tandem data is evident, as is

the wider range of variation in 𝐸4 for the same data. Represented in this fashion, it is clear why the models

differed in their parameters. Two distinct clusters of data are evident: locations with high 𝐸4 values and

locations with low values. These also correspond with high and low values for𝐸𝑟𝑜𝑐𝑘.

It is also evident that, for the locations with values of both parameters, almost all of the 80 kN tandem

group data shows a stiffer crushed rock base than the 40 kN single axle data. There would appear to be a

differentiation between the pavement conditions trafficked by the two load types, making confident direct

comparison of performance results impossible.

Another cluster of data showed a better matching of the pavement parameters across the two load types,

albeit with a wider spread in the 80 kN tandem data. This data cluster corresponds with locations that did

not require many load cycles to reach 4 mm deformation. As seen in Figure 6.38, all of the 40 kN single

axle data locations required 25 000 or less cycles to reach this level of deformation. Similarly, all but two of

the 80 kN tandem group data locations required similar numbers of cycles. Comparison between the two

load types at such low counts of load cycles is considered of little value, as small variations in pavement

behaviour would result in large differences in small cycle count numbers, swamping any meaningful

assessments to the difference in performance attributable to different loading conditions.



Unfortunately, variation in pavement material and subgrade moduli between the two data sets makes an

assessment of the difference in performance attributable to load type impossible.

Figure 6.39: Distribution of Erock and E4 for 40 kN single axle and 80 kN tandem group paired data

Note: Shaded regions represent regions between lower quartile and upper quartile of observations.

6.9.3 60 kN Tandem Group and 80 kN Tandem Group

An examination of Figure 6.37 shows that the test locations loaded with the 60 kN tandem group exhibited

very little deformation. Of the 16 locations at which valid data was obtained, only eight locations showed

deformation exceeding 3 mm. These locations were the same locations that form the lower grouping of

𝐸𝑟𝑜𝑐𝑘 data shown in Figure 6.36. The cluster of locations around 325 MPa in the same figure are the same

locations that did not reach any meaningful level of deformation at all. In attempting to compare the

difference in performance that could be attributed to changing the load level on the tandem axle group from

60 to 80 kN, a deformation level of 3 mm was selected. Figure 6.40 shows the distribution of the number of

cycles to reach this deformation level for the two load levels.



Figure 6.40: Distribution of cycles required to reach 3 mm deformation for 60 kN and 80 kN

tandem groups data

Modelling was undertaken to find parameters that would explain the spread of data evident for each load

type in Figure 6.40. A valid model could not be found for the small 60 kN tandem group data set. As there

was variation of parameters between cases, but no consistent parameter or combination of parameters, the

lack of an acceptable model is considered to be a result of the small data set.

A model was found to best match the 80 kN tandem axle data. It had a single term, 𝐸4, which is the same

term used to model the same data locations, but to a deformation level of 4 mm (Section 6.9.2). The model

is not reported here, as without any matching model for the 60 kN data set, the model is of no practical use.

6.9.4 60 kN Tandem Group and 90 kN Triaxle Group

As with the prior load pairing, the lack of 60 kN tandem group data prevented any direct comparison

between the 60 kN tandem and 90 kN triaxle groups.

6.9.5 40 kN Single Axle and 90 kN Triaxle Group

A successful comparison was made comparing damage caused by loading with the 40 kN single axle and

the 90 kN triaxle group. This comparison is significant in that, as discussed in Section 2.3, if it is presumed

that each axle in an axle group acts independently (i.e. there is no damage increase or decrease caused

per axle as a result of grouping them together), then this pair of loading types should cause the same

damage per cycle of loading (i.e. one pass of the 90 kN triaxle causing the same damage as one pass of

the 40 kN single axle).

Figure 6.37 demonstrates that the majority of data locations for both load types reached a deformation level

of 4 mm or more. Therefore, 4 mm was selected as the deformation level for the analysis. The loading

cycles required to reach this deformation level were determined, and the distribution of these is shown in

Figure 6.41.



Figure 6.41: Distribution of cycles required to reach 4 mm deformation for 40 kN single axle and

90 kN triaxle group data

A regression model relating the number of cycles of 40 kN single axle load needed to reach the 4 mm

deformation level to the effective modulus of the crushed rock base, 𝐸𝑟𝑜𝑐𝑘 , had already been developed

(Equation 22). A similar model was determined for the 90 kN triaxle load, shown in Equation 24. Trials

testing whether incorporating additional parameters would improve the fit of the model determined that any

additional parameters were statistically insignificant, and that an improvement in the model could not be

made in any case.

𝑁90𝑇𝑅,4 𝑚𝑚 = −217722 + 1607𝐸𝑟𝑜𝑐𝑘 24

where

𝑁90𝑇𝑅,4 𝑚𝑚 = number of cycles of the 90 kN triaxle group to reach 4 mm of deformation

𝐸𝑟𝑜𝑐𝑘 = the overall modulus of the crushed rock base (definition in Table 6.9) (MPa)

Adjusted R2: 0.87

F-statistic: 62.43 on 1 variable and 8 degrees of freedom

p-value: 4.77 × 10-5



Figure 6.42: Distribution of Erock for 40 kN single axle and 90 kN triaxle group paired data

Fortunately, models for both load types shared a common and single parameter, 𝐸𝑟𝑜𝑐𝑘 . Figure 6.42 shows

the distribution of this parameter for the data locations for both load types. It can be seen that there is an

overlap of this parameter for the two load types between 140 and 250 MPa.

The number of load cycles needed to reach the 4 mm deformation level are plotted as a function of 𝐸𝑟𝑜𝑐𝑘 ,

using Equations 22 and 24, in Figure 6.43. It can be seen that for low values of 𝐸𝑟𝑜𝑐𝑘 , very few cycles of

either load type were required to reach the 4 mm deformation level, and there is little difference between

the cycles required by either load group to cause the same damage. As the modulus of the base increases,

however, the regression models slowly separate, with more cycles of the 90 kN triaxle group required to

cause the same damage as the 40 kN single axle.

Expressing the difference between the numbers of cycles required to reach the same deformation level as

a ratio results in the load equivalency factor (𝐿𝐸𝐹) in Equation 25.



Figure 6.43: Number of 40 kN single axle and 90 kN triaxle group cycles required to reach 4 mm

deformation as a function of the effective stiffness of the crushed rock (Erock)

𝑁40 𝑘𝑁 𝑠𝑖𝑛𝑔𝑙𝑒 = 𝐿𝐸𝐹 × 𝑁90 𝑘𝑁 𝑡𝑟𝑖𝑎𝑥𝑙𝑒 25

where

𝑁40 𝑘𝑁 𝑠𝑖𝑛𝑔𝑙𝑒 estimated number of cycles of the 40 kN single axle needed to reach 4 mm

deformation level

𝑁90 𝑘𝑁 𝑡𝑟𝑖𝑎𝑥𝑙𝑒 estimated number of cycles of the 90 kN triaxle group needed to reach 4 mm

deformation level

𝐿𝐸𝐹 = load equivalency factor, i.e. the factor which relates the equivalent number of

load applications to achieve the same level of damage

For locations that needed a minimum of 50 000 cycles of ALF loading to reach the 4 mm deformation level,

the 𝐿𝐸𝐹 factor varied from 0.8 (at high effective stiffness) to 1.0 (at low effective stiffness) across the range

of experimental data.

However, appreciating the spread of data points plotted in Figure 6.43, it is difficult to conclude that there is

a substantial difference between the data sets, and that both load groups caused the same amount of

deformation.

6.10 Conclusions

Whilst the experimental results indicated that an 𝐿𝐸𝐹 of 0.8 applied to the majority of pavement locations

tested – indicating that 20% less cycles of an 180 kN triaxle were required than the single 80 kN Standard

Axle to achieve the same level of deformation – the scatter of the data does not allow sufficient confidence

to translate this finding directly into design practice. Variations in moisture content within the pavement

structure, and over the time period in which the experiments were conducted, is considered the most likely

explanation for range of the scatter in the collected deformation data.



The experimental results cannot be reasonably considered to provide enough evidence that the currently

used standard load for triaxles of 181 kN (full axle) is inappropriate.

The small difference in 𝐿𝐸𝐹 to current practice (0.8 cf. 1.0) is insignificant in comparison to the variation in

experimental results and the variety of assumptions made in the analysis.

Accepting that the 𝐿𝐷𝐸 was four, and that the standard load for the (full) triaxle group was 181 kN, it can be

concluded that the interaction between axles does not affect deformation damage, and that the axles can

be considered to each contribute to the overall damage in isolation to each other (Section 2.3). No

interaction would be expected if most of the deformation occurred in the top 100 mm of the crushed rock

base. Higher interaction between the axles would be expected lower in the pavement structure. As

discussed in Section 6.6.5, deformation of the top of the imported clay subgrade was not observed in any

test locations, including those comprising weaker structures.

Accepting that no significant interaction between axle occurs, the standard load for a multiple-axle group,

that is the load on the group that will result in the same deformation damage as a single axle with dual tyres

and a load of 80 kN, can be calculated using Equation 26.

1 = 𝑛 × (𝐿

𝑛⁄

80)

4

or 𝐿 = 80 × 𝑛 × (1

𝑛)

1/4

26

where

𝑛 = number of dual-tyred axles in the multiple-axle group (i.e. 2 for tandem, 3 for

triaxle, etc.)

𝐿 = standard load on the axle group with dual tyres (kN)

Equation 26 relates the damage caused by multiple axles with dual tyres to the damage caused by a single

axle with dual tyres. A similar function, Equation 27, can be used to do the same for single tyres – using the

current standard loads for single axles with different tyre widths.

1 = 𝑛 × (𝐿

𝑛⁄

𝐿𝑆𝐴𝑆𝑇)

4

or 𝐿 = 𝐿𝑆𝐴𝑆𝑇 × 𝑛 × (1

𝑛)

1

4

27

where

𝑛 = number of single-tyred axles in the multiple-axle group (i.e. 2 for tandem, 3 for

triaxle, etc.)

𝐿 = standard load on the axle group with single tyres (kN)

𝐿𝑆𝐴𝑆𝑇 = standard load on a single axle; depends upon nominal tyre section width:

53 kN for width less than 375 mm

58 kN for width at least 375 mm but less than 450 mm

71 kN for width 450 mm or more

It is concluded that the ALF testing and analysis confirmed the suitability of current practice for equating the

damage of axle groups for use in the empirical design procedure. It is proposed that Equations 26 and 27

be used in the future to determine the standard loads for multiple-axle groups. This would result in little

change for all currently listed axle groups, except quad-axles, for which a slight increase in standard load

would occur. Standard loads for a series of multiple-axle groups are listed in Table 6.10 and Table 6.11.



Table 6.10: Proposed standard loads for dual-tyre axles for use with empirical design procedure


Current Proposed

Single axle with dual tyres (SADT) 80 –

Tandem axle with dual tyres (TADT) 135 135

Triaxle with dual tyres (TRDT) 181 182

Quad-axle with dual tyres (QADT) 221 226

Table 6.11: Proposed standard loads for single-tyre axles for use with empirical design procedure

Axle group type Nominal tyre section width Load (kN)

Current Proposed

Single axle with single tyres (SAST) Less than 375 mm 53 –

At least 375 mm but less than 450 mm 58 –

450 mm or more 71 –

Tandem axle with single tyres (TAST) Less than 375 mm 90 89

At least 375 mm but less than 450 mm 98 98

450 mm or more 120 119

Triaxle with single tyres (TRST) Less than 375 mm 121 121


450 mm or more – 162

Quad-axle with single tyres (QAST) Less than 375 mm 150 150


450 mm or more – 201



7. Fatigue of Asphalt

7.1 Introduction

The search of international literature described in Section 3.3 concluded that the work undertaken by

Homsi (2011) represents the most exhaustive assessment of flexural fatigue performance of asphalt when

subjected to multiple-axle loads.

Homsi’s model (Equation 18) allows the prediction of fatigue life of a sample as a function of the maximum

strain level, the number of peak strains, and two strain shape factors, all resulting from the simulation of a

single axle or multiple-axle group. The model does not consider how the grouping of axles may affect the

magnitude of the strain developed.

In order to determine how grouping of loads affects the strain developed in asphalt layers, this section of

the report describes how Homsi’s model was applied to strains determined from response to load modelling

of a series of pavement structures.

7.2 Response-to-load Model

7.2.1 Model Selection

A three-dimensional finite element method (3D-FEM) was selected as the basis of the response-to-load

model, for the following reasons:

FEM modelling is able to cater for the non-linear behaviour of unbound pavement and subgrade

materials.

3D-FEM modelling is able to represent the simultaneous application of multiple loads, rather than

relying on post-processing to linearly superimpose responses to individual loads. This allows modelling

of the complex stress state that occurs horizontally within a non-linear material, and therefore, as the

modulus of a non-linear material is a function of stress, the stiffness variation of the material can be

modelled.

Austroads (2012b) documents the development of a 2D-FEM response-to-load model and software,

adopting Uzan’s (1992) universal model (Equation 28) for non-linear materials.



𝐸 = 𝑘1 [

𝜃

𝑝𝑎]

𝑘2

[𝜏𝑜𝑐𝑡

𝑝𝑎]

𝑘3

28

where

𝐸 = elastic modulus (MPa)

𝜃 = mean normal stress (kPa)

= 𝜎𝑥 + 𝜎𝑦 + 𝜎𝑧

3

for standard triaxial compression loading with confining stress 𝜎𝑐, and deviatoric

stress 𝜎𝑑:

𝜃 =3𝜎𝑐 + 𝜎𝑑

3

𝜏𝑜𝑐𝑡 = {1

9[(𝜎𝑥 − 𝜎𝑦)

2+ (𝜎𝑦 − 𝜎𝑧)

2+ (𝜎𝑥 − 𝜎𝑧)2] +

2

3[𝜏𝑥𝑦

2 + 𝜏𝑦𝑧2 + 𝜏𝑥𝑧

2 ]}0.5

for standard triaxial compression loading:

𝜏𝑜𝑐𝑡 =√2

3𝜎𝑑

𝑝𝑎 = atmospheric pressure (normalising factor), assumed as 100 kPa

𝑘1, 𝑘2, 𝑘3 = material parameters normally subjected to the following constraints:

𝑘1 > 0; 𝑘2 ≥ 0; 𝑘3 ≤ 0; 𝑘2 + 𝑘3 ≤ 1.0, 𝑘1 (MPa)

In order to undertake 3D-FEM analysis, the Cast3M software package was selected, as a 3D model was

not developed in the previous Austroads project. Developed over the last two decades by the French

Commissariat à l’énérgie atomique (CEA), Cast3M is freely available for research purposes and has a

large user base who have ensured that it is extensively validated and robust. The universal model was

programmed into Cast3M as an additional material model.

7.2.2 FEM Mesh Generation

A script file, written using the Cast3M command language, was developed to automate the generation of a

3D pavement mesh based on user inputs of pavement thicknesses and materials, and axle group and load

definitions.

Before undertaking FEM analyses, the mesh generation aspect of the script was validated by comparing

the results of pure linear-elastic analyses conducting using Cast3M and CIRCLY.

The analysis required modelling pavement responses to tyre loads from 4 to 24 kN. The FEM mesh

modelled the loads as a circular load of constant stress. Jameson (2013) had previously developed a

process for modelling circular contact patches for various loads on a standard 11R22.5 tyre. This was used

to estimate the contact stress and load radius for each tyre load. The process, shown graphically in

Figure 7.1, uses an equation based on data reported by Bonaquist (1992) which was adjusted to reflect the

differences between gross contact area and net contact area, to predict the contact area for tyre loads less

than 20 kN. At 20 kN, the radius was assumed to be 92.13 mm with a contact stress of 750 kPa to match

current Austroads design values. A series of linear interpolations are used at fixed points to determine the

radius and stress for tyre loads in excess of 20 kN.



Figure 7.1: Calculation of radius and contact stress for circular load model of tyre loads

In order to reduce analysis time, the 3D pavement mesh used geometric symmetry that exists in both the

longitudinal and transverse directions of an axle group. Example meshes, with the different pavement

layers (asphalt, granular and subgrade) graphically separated, are shown in Figure 7.2. A detailed view of

the mesh representing the load is shown in Figure 7.3.



Figure 7.2: Example 3D meshes for 100 mm asphalt and 200 mm granular base pavements

(exploded view)

(a) Single axle

(b) Tandem axle group

(c) Triaxle group

(d) Quad-axle group



Figure 7.3: Zoomed view of 3D mesh for load area

7.2.3 Analysis Parameters

A three-layer pavement was modelled for all cases: asphalt base, unbound granular subbase and

subgrade. The materials used for each of these layers and their thicknesses were varied to create a wide

range of pavement configurations, as shown in Table 7.1. The characterisations of the two subbase and

two subgrade materials were taken from the presumptive values listed in Austroads (2012b).

Table 7.1: Material thicknesses and model parameters used in 3D-FEM modelling

Parameter Values

Asphalt model 1000 MPa 𝐸 = 1000 MPa, ν = 0.4, ρ = 2.1 t/m3

3000 MPa 𝐸 = 3000 MPa, ν = 0.4, ρ = 2.1 t/m3

5000 MPa 𝐸 = 5000 MPa, ν = 0.4, ρ = 2.1 t/m3

Asphalt thickness

50, 100, 200, 300 mm

Granular model High quality crushed rock

𝑘1 = 250 MPa, 𝑘2 = 1.0, 𝑘3 = –0.25, RCS = 40 kPa, ρ = 2.2 t/m3, ν = 0.35

Lower subbase 𝑘1 = 150 MPa, 𝑘2 = 0.8, 𝑘3 = –0.25, RCS = 40 kPa, ρ = 2.2 t/m3, ν = 0.35

Granular thickness

200, 400, 600 mm

Subgrade model

Highly plastic clay (CBR 3%)

𝑘1 = 15 MPa, 𝑘2 = 0, 𝑘3 = –0.5, RCS = 0 kPa, ρ = 1.6 t/m3, ν = 0.45

Sand (CBR 15%) 𝑘1 = 85 MPa, 𝑘2 = 0.15, 𝑘3 = –0.35, RCS = 0 kPa, ρ = 2.0 t/m3, ν = 0.35

Note: ν = Poisson’s ratio, ρ = density, RCS = residual compaction stress, 𝑘1– 𝑘3 = constants of Uzan’s stress-dependency model.



The response-to-load of each pavement was calculated under single, tandem, triaxle and quad-axle

groups. Axle spacing for tandem, triaxle and quad-axle groups was fixed at 1.25 m. All axles were modelled

as dual tyre axles with 330 mm spacings, centre-to-centre, between the tyres. The length of the axles was

fixed at 1800 mm from centre-to-centre of the dual tyres. These individual axle dimensions were selected to

match the Standard Axle definition used by Austroads.

A range of load levels were applied to the axle groups. The loads were applied as variations to a tyre load

and in 2 kN increments.

7.2.4 Response Locations

Strain responses in the direction of travel (longitudinal) and perpendicular to the travel direction

(transverse) were calculated at the bottom of the asphalt layer, and were reported along longitudinal lines

under the innermost tyre and between the dual tyres, as demonstrated by the dotted lines in Figure 7.4.

Within these shapes, the peak strains occurring under each axle in the modelled group were also recorded.

Figure 7.4: Asphalt strains were recorded along the dotted lines for this quad-axle group

7.3 3D-FEM Response-to-load Analyses

Three-dimensional FEM response-to-load analyses were conducted for the 144 pavement structures

represented in Table 7.1. With four axle group types considered, a total of 576 analyses were conducted

for each tyre load level considered. Initially, four tyre load levels were analysed – 14, 16, 18 and 20 kN –

resulting in a total of 2304 analyses. For many pavement structures, load levels lower than 14 kN, always

decreasing in increments of 2 kN, were modelled in order to determine the tyre load for multiple-axle

groups that caused the same damage as a Standard Axle (i.e. a single axle with a tyre load of 20 kN). The

final number of analyses conducted exceeded 3100.

Analysis times varied with computing power used and with the number of axles being modelled in an axle

group. Typical analysis times using a 2.66 GHz Intel Core i7 running a 64 bit Unix operating system,

ranged from two minutes for a single axle analysis to 40 minutes for a quad-axle analysis.

Examples of strain outputs from the 3D-FEM analyses are presented Figure 7.5. The examples show

extreme asphalt thicknesses, whilst keeping the remainder of the pavement structure and load level

constant. The strains were extracted underneath the innermost tyre of the axles.

A key characteristic of shapes of strain pulses in the longitudinal direction (Figure 7.5(a) and (b)) is the

successive regions of compressive-tensile-compressive strain associated with each axle. In general, the

super-positioning of one area of compression generated by an axle, with an area of tension generated by

an adjacent axle, results in a reduction in the overall strain level in that area. Strains in the transverse

direction (Figure 7.5(c) and (d)) do not exhibit significant areas of compressive strain, and so the super-

positioning of strains generated by adjacent axles results in higher strain levels.



For thin structures (Figure 7.5(a) and (c)), it can be seen that there is little impact on peak strain levels (in

either direction) from adjacent axles. With thicker asphalt structures (Figure 7.5(b) and (d)), it can be seen

that the grouping of axles leads to more significant differences in peak strains. With the effect of

superimposing compressive strains with tensile strains, longitudinal strain peaks generally reduce with

increasing number of axles, and transverse direction strains generally increase.

A key feature of the strain shapes shown in Figure 7.5 are the unequal peak strain levels for each axle

within a triaxle or quad-axle group. Homsi’s laboratory study was conducted with all strain peaks within an

axle group having the same magnitude. Strains at the bottom of thin asphalt layers would best reflect this

condition.

Figure 7.5: Examples of strains

(a) 50 mm asphalt – longitudinal strain

(b ) 300 mm asphalt – longitudinal strain

(c) 50 mm asphalt – transverse strain

(d) 300 mm asphalt – transverse strain

Note: Asphalt model: 3000 MPa/granular model: high quality crushed rock/granular thickness: 400 mm/subgrade model: highly plastic clay/tyre load level: 14 kN.

For all of the pavement configurations, axle group tyres and load levels, the highest magnitude strains

always occurred in the longitudinal direction. The location of these peaks strains varied, dependent upon

pavement configuration and load level, from beneath the axle tyres to between the dual tyres.



7.4 Analysis of 3D-FEM Response-to-load Results Using Homsi’s

Damage Model

7.4.1 Calculation of Homsi Parameters

For each 3D-FEM modelled pavement structure and group/load condition, the strains described in

Section 7.2.4 were extracted. For each of these strain shapes, Homsi’s shape parameters (Section 4.5)

were determined.

Homsi’s strain signals represent the rise and fall of strains within a load group as a function of time. The

3D-FEM response-to-load model was a static model and, therefore, reflected the strain shapes under the

axle group as a function of distance. A key parameter of Homsi’s model is the duration of the strain shape,

�̅� (Figure 4.8). This parameter could be expected to vary with the speed of travel of an axle group, and also

with the depth within a pavement structure at which the strain shape is located. In order to translate the

distance-domain modelled strain shapes into the time-domain shapes considered by Homsi’s model, the

possible effect of pavement structure on �̅� was ignored, and a single distance-to-time translation was

made. In order to ensure that the majority of �̅� values determined from the response-to-load results fell

within the range used by Homsi in developing her model, a travel speed of 22 km/h was selected.

As described below, the impact of ignoring the effect of pavement structure on the distance-to-time-domain

translation was greatly minimised by the use of relative damages rather than absolute damages in further

analysis and in drawing conclusions.

Having determined �̅�, the remaining Homsi parameters were calculated for each strain shape as follows:

휀 as the maximum tensile strain peak (set to zero if the entire strain shape was compressive)

𝑁𝑝 as the number of peaks in the strain shape – equal to the number of axles in the group

�̂�𝑛 as the area under the strain shape, divided by 휀 and by �̅�.

7.4.2 Calculation of Relative Fatigue Damage

Having determined the shape parameters for each strain location, Homsi’s multi-linear model, Equation 18,

was used to estimate the number of allowable loadings of each axle group type and load level on each of

the 144 pavement configurations before flexural fatigue of the asphalt occurs. The damage caused by the

group/load combination on each pavement was then determined as the inverse of the minimum number of

allowable loadings determined for each strain location. Finally, the relative damage caused in comparison

to that caused by the 80 kN single Standard Axle was determined using Equation 29.

𝑅𝐷𝑔,𝑙 =

𝐷𝑔,𝑙

𝐷𝑆𝐴

29

where

𝑅𝐷𝑔,𝑙 = relative damage caused by axle group, 𝑔, with load 𝑙 kN

𝐷𝑔,𝑙 = damage caused by axle group, 𝑔, with load 𝑙 kN

𝐷𝑆𝐴 = damage caused by the Standard Axle, i.e. a single axle with 80 kN load

In addition to allowing easy comparison of damages caused by different axle groups and loads for given

pavement structures, the relative damage parameter also significantly reduces the effects of ignoring the

pavement structure when translating from the distance to the time-domain. As the effect that pavement

structure, acting alone, has on the translation for a single axle can be reasonably assumed to be the same

as for other axle groups, the absolute value of the relative damage can be considered to be reasonably

unaffected by the influence of structure on the translation.



7.4.3 Calculation of Standard Axle Loads

Having obtained relative damages for each group/load/pavement combination, the load on a multiple-axle

group that would cause the same damage as the Standard Axle was determined for each pavement

configuration. This standard load corresponds to the load on the axle group that creates a relative damage

equal to one. The standard loads were determined by linearly interpolating the relative asphalt damages

resulting from variations in tyre load.

As noted in Section 7.2.3, the 3D-FEM analyses were conducted using 2 kN increments of tyre-load

varying between 14 and 20 kN. In many cases, this range of tyre loads did not allow interpolation of

standard loads, and so additional 3D-FEM analyses were conducted to ensure that interpolation could

occur within a 2 kN range. Figure 7.6 shows graphical examples of this interpolation for the same

pavement configurations used in Figure 7.5.

Figure 7.6: Example calculation of tyre loads in multiple-axle groups that causes the same damage

as a Standard Axle using Homsi’s damage model

(a) Asphalt thickness = 50 mm (b) Asphalt thickness = 300 mm

Notes: Asphalt model: 3000 MPa/granular model: high quality crushed rock/granular thickness: 400 mm/subgrade model: highly plastic clay.

N1,20 represents the allowable Standard Axle loading before asphalt fatigue, as determined by the current Austroads design process (i.e. linear-elastic modelling and use of the Austroads fatigue performance relationship).

7.4.4 Variations of Standard Axle Loads with Pavement Structure

By way of example, Figure 7.7 presents a summary of the standard axle loads as a function of asphalt

thickness for pavements with the same underlying structure as used in Figure 7.6 for all three multiple-axle

groups. The figure also includes the allowable loading determined using current Austroads procedures for

both asphalt and subgrade performance criteria. Appendix G contains the complete set of these figures.

At very thin asphalt thicknesses, the standard load is considerably lower than for thicker asphalt layers, and

varies significantly with thickness. At higher asphalt thicknesses (greater than 200 mm), the effect of

asphalt thickness on standard load reduces in significance.



Figure 7.7: Example summary of standard axle loads in multiple-axle groups that causes the same

damage as a Standard Axle using Homsi’s damage model

Note: Asphalt model: 3000 MPa/granular model: high quality crushed rock/granular thickness: 400 mm/subgrade model: highly plastic clay.

A comparison between figures within Appendix G could be made to see the effect that other pavement

structure parameters, such as granular thickness or subgrade model, had on the determination of standard

load. Figure 7.8 shows the range of determined standard axle loads that result from variations with

pavement structure. The individual bars within the figure represent the range of standard loads obtained by

varying granular thickness and granular and subgrade models. Each bar represents a specific asphalt

thickness, and a separate chart represents variations in asphalt modulus. The dotted horizontal lines in the

figure represent the standard axle loads currently used in the Austroads design procedure. Figure 7.9

shows the same data but in terms of the standard group load.

From these figures, it can be clearly seen that standard load for an axle group is dependent upon more

than just the thickness of asphalt. The underlying structure also plays a role, and that role is more

significant at lower asphalt thicknesses than at higher ones, as evidenced by the larger range of standard

loads for 50 mm thicknesses of asphalt in comparison to higher thicknesses. Additionally, the derived

standard loads for 50 mm asphalt structures are all lower than the standard loads used in the current

Austroads design processes (shown as dotted lines). For asphalt thicknesses of 100 mm or greater, the

standard load for all structures is above the current Austroads values for all cases except for some 100 mm

thick asphalt cases with a low stiffness of 1000 MPa. As noted earlier, 1000 MPa represents a minimum

expected asphalt modulus, and would coincide with high temperatures and/or slow loading speeds.



Figure 7.8: Range of axle-loads in multiple-axle groups that causes the same damage as a

Standard Axle using Homsi’s damage model

(a) Asphalt model: 1000 MPa

(b) Asphalt model: 3000 MPa

(c) Asphalt model: 5000 MPa



Figure 7.9: Range of group loads that causes the same damage as a Standard Axle using Homsi’s

damage model






7.5 Simplifying Homsi’s Model

Homsi’s model was developed using two discrete values of the areas of strain parameter, �̂�𝑛 (0.21, 0.42),

and two values for duration of pulse parameter, �̅� (0.105, 0.25) used in the laboratory testing (Section 4.5).

Figure 7.10 shows the cumulative range of these shape parameters for the critical strain locations and

directions determined using the 3D-FEM model under a Standard Axle load. In all cases, the magnitude of

the peak strain was greater for the longitudinal direction than the transverse. Homsi’s model also

determined that the damage resulting from longitudinal strains was greater than the transverse ones. The

figure also shows, as vertical lines, the discrete values for these parameters used in Homsi’s experimental

study.

Figure 7.10: Cumulative distribution of Homsi shape parameters in 3D-FEM modelled strain

responses for single axle with 80 kN axle load

Figure 7.10 shows that the two discrete values of �̂�𝑛 used by Homsi to develop the model, 0.21 and 0.42,

bracket approximately 80% of the values of �̂�𝑛 calculated from the 3D-FEM modelled strain responses.

However, as noted earlier, the significant difference between the values used by Homsi was that �̂�𝑛 = 0.21

represented a longitudinal strain shape and �̂�𝑛 = 0.42 represented a transverse one. The experimental plan

did not include variations of �̂�𝑛 within a strain direction. This may mean that the �̂�𝑛 term in Homsi’s model,

Equation 18, largely considers the effect of strain direction (Figure 4.8) on fatigue life, rather than a more

comprehensive quantification of pulse shape.

Accordingly, this may have led to inaccuracies in standard loads determined in Section 7.4.4. By using

fixed values of �̂�𝑛 of 0.21 and 0.42 for longitudinal and transverse strain directions, respectively, Homsi’s

model (Equation 18) can be split into separate models for each strain direction, as shown in Equation 30.

These two models indicate that, all other factors being equal, longitudinal strains are 1.88 times more

damaging than transverse strains of the same peak magnitude. When isolating the effect on experimental

results of the two different �̂�𝑛 values, one for each strain direction, Homsi determined (see Table 4.6) that

longitudinal strains were 1.51 to 2.66 times more damaging than transverse strains, with an average of

1.89.



𝑙𝑜𝑔10(𝑁𝑓) = −4.58 𝑙𝑜𝑔10(휀)

− 0.84 𝑙𝑜𝑔10(𝑁𝑝) + 1.76 �̅� + 15.4951

(a) 30

𝑙𝑜𝑔10(𝑁𝑓) = −4.58 𝑙𝑜𝑔10(휀)

− 0.84 𝑙𝑜𝑔10(𝑁𝑝) + 1.76 �̅� + 15.7702

(b)

where

𝑁𝑓 = number of cycles of axle group pulse shape to achieve fatigue

휀 = peak strain level of the pulse shape

𝑁𝑝 = number of peaks in the pulse shape (i.e. number of axles in the simulated group)

�̅� = duration of the shape divided by the number of peaks

(a) applies for strains in the longitudinal direction

(b) applies for strains in the transverse direction

The �̅� parameter was included in the Homsi study with the goal of better understanding how the duration of

loading affects fatigue life. As the parameter is normalised by the number of peaks in the strain shape, the

intended effect of the parameter was to be independent of the number of axles. As indicated by Table 4.6,

the two different values of �̅� used in the experimental study had an isolated effect on fatigue life by a factor

of between 1.39 and 3.27. As indicated in Figure 7.10, a considerably wider range of the �̅� parameter was

extracted from the 3D-FEM modelled pavements than the values used as the basis for Homsi’s model.

Whilst not disputing the likely significant effect that loading duration has on fatigue life, it is considered that

examining such an effect is beyond the direct scope of this report. Homsi’s study of the effect of duration on

fatigue life was not exhaustive, and it is considered that scope exists for other studies to examine the effect

on fatigue life. Such studies should consider both the effect that speed of loading has upon the pavement

surface, and also effect that the thickness and stiffness composition of the pavement structure have on

duration or width of strain shapes.

Accordingly, it was decided to eliminate �̅� from Equation 30 by using a constant value of 0.1775,

representing the average of the two values used in Homsi’s experimental data. The resulting simplified

Homsi model is shown in Equation 31.

𝑙𝑜𝑔10(𝑁𝑓) = −4.58 𝑙𝑜𝑔10(휀) − 0.84 𝑙𝑜𝑔10(𝑁𝑝) + 15.8075 (a) 31

𝑙𝑜𝑔10(𝑁𝑓) = −4.58 𝑙𝑜𝑔10(휀) − 0.84 𝑙𝑜𝑔10(𝑁𝑝) + 16.0826 (b)

where


휀 = peak strain level of the pulse shape

𝑁𝑝 = number of peaks in the pulse shape (i.e. number of axles in the simulated group)

(a) applies for strains in the longitudinal direction

(b) applies for strains in the transverse direction

7.6 Analysis of 3D-FEM Response-to-load Results Using Simplified

Homsi Damage Model

The strains calculated from the 3D-FEM modelling were reprocessed to estimate fatigue life using this

simplified version of Homsi’s performance model (Equation 31).



Based on this modelling and following the process described in Section 7.4, Figure 7.11 shows the range of

determined standard axle loads that result from variations with pavement structure. Similarly, Figure 7.12

shows the results in terms of standard group loads. In comparison to the results obtained using the full

Homsi model in Figure 7.8 and Figure 7.9, it can be seen that the simplified model yields standard loads

that are slightly less dependent upon pavement structure. Significantly, at the high asphalt modulus of

5000 MPa, the reduction in variation of load with structure is more pronounced than at lower asphalt

moduli. A check of the �̂�𝑛 and �̅� parameters used in the full Homsi models, extracted from these

pavements, indicated that they were considerably different to the discrete values used in Homsi’s

experimental work.

Despite the slight reduction in standard load dependence upon pavement structure, the observations made

with regard to the full Homsi model still hold; namely:

the standard load for an axle group is dependent on the thickness and modulus of the asphalt layer,

and the underlying structure

the standard loads for 50 mm asphalt structures show greater dependence on underlying pavement

structure than structures with higher thicknesses of asphalt

for asphalt thicknesses of 100 mm or greater, the standard load for all structures is above the current

Austroads values for all cases, except for some 100 mm thick asphalt cases with a low stiffness of

1000 MPa.

Figure 7.11: Range of axle-loads in multiple-axle groups that causes the same damage as a

Standard Axle using the simplified Homsi damage model






Figure 7.12: Range of group loads that causes the same damage as a Standard Axle using the

simplified Homsi damage model






7.7 Adjustment of Simplified Homsi Model for Use with Austroads

Fatigue Relationship

7.7.1 Rearranging Simplified Homsi Model

The simplified Homsi model (Equation 31) can be rearranged as shown in Equation 32.

𝑁𝑓 =

1

𝑛0.84(

𝑘

휀𝑚𝑎𝑥)

4.58

32

where


𝑛 = number of peaks in the pulse shape (i.e. number of axles in the simulated group)

휀𝑚𝑎𝑥 = peak strain level of the pulse shape

𝑘 = constant

= 2828 for longitudinal strains

= 3257 for transverse strains

Two aspects of the model coefficients are noted:

the load damage exponent of the model, 4.58, is similar to the value of 5 used in the current Austroads

design process

the number of axles within the group is raised to a power that is close to unity.

7.7.2 Maximum Peak Model

The current Austroads asphalt fatigue performance model can be expressed as shown in Equation 33. This

model only considers the damage caused by a single axle. If it were assumed that each axle within a

multiple-axle group acted independently of each other, other than the superposition effect in altering the

strain level, then a simple expansion of this model to consider multiple-axle groups would be as shown in

Equation 34. For sake of reference, this model is called the maximum peak method.



𝑁𝑓 = (

𝑘

휀𝑚𝑎𝑥)

5

33

where

𝑁𝑓 = number of single axle passes to achieve fatigue

휀𝑚𝑎𝑥 = maximum tensile strain generated by the single axle

𝑘 = constant (dependent upon asphalt stiffness and binder content)

𝑁𝑓 =

1

𝑛(

𝑘

휀𝑚𝑎𝑥)

5

34

where

𝑁𝑓 = number of single axle passes to achieve fatigue

𝑛 = number of axles in axle group

휀𝑚𝑎𝑥 = maximum tensile strain generated by axle group

𝑘 = constant

The coefficients of this model are similar to those in the simplified Homsi model. In order to see whether the

maximum peak model differs significantly from the simplified Homsi model, the results of the 3D-FEM

analyses were re-processed and the damage caused by each axle group and load level determined using

Equation 34. Again, longitudinal strains dominated the calculated damages.

Figure 7.13 shows the range of determined standard axle loads that result from variations with pavement

structure, and Figure 7.14 shows the results in terms of standard group loads. The results are very similar

to those obtained using the simplified Homsi damage model.



Figure 7.13: Range of axle loads that causes the same damage as a Standard Axle using the

maximum peak model







maximum peak model




The loads on individual axles within a group that cause the same damage as the Standard Axle determined

using the two damage calculation methods are compared in Figure 7.15. All 3D-FEM modelled pavement

configurations and all three axle groups are included within the figure. The two methods can be seen to

produce almost identical results.



As the two exponents in the simplified Homsi model were slightly increased (0.84 to 1, and 4.58 to 5) in the

formation of the maximum peak model, it is understandable that the maximum peak model produces

slightly lower standard group loads (i.e. it is slightly more conservative).

Figure 7.15: Comparison of standard axle loads determined using simplified Homsi and

maximum peak methods

Asphalt thickness = 50 mm Asphalt thickness > 50 mm

2 axles

3 axles

4 axles



7.8 Generalising Model to Consider Strains Generated by Each Axle

A significant factor in the Homsi experimental work, and therefore the resulting models, is that testing was

conducted with each strain peak within a multiple-axle group having the same magnitude. As demonstrated

in Section 7.3, the 3D-FEM modelled strains that result from superimposing equally loaded axles within an

axle group do not necessarily have equal magnitude peaks. In applying Homsi’s model to the results of 3D-

FEM analyses, only the maximum peak strain was considered. Similarly, the maximum peak method

described in Section 7.7.2 does not consider potential differences in peak strain magnitudes.

To date, models have been expressed in terms of the number of repetitions of the axle group that will lead to fatigue failure, 𝑁𝑓. This term is cumbersome when considering the contribution that each axle within a

group makes to the overall allowable repetitions of the group. A simpler parameter is the damage caused

by each axle of the group. The damage caused by a single pass of an axle is the inverse of the number of

allowable loadings of that axle. These axle damages can simply be summed to yield the damage cause by

the group. The number of allowable loadings of the group is the inverse of the group damage.

Equation 35 expresses the maximum peak model (Section 7.7.2) in terms of damage rather than allowable

loading, and also generalises the form of the model, whereby the damage associated with each axle peak

within the group is considered in its own right rather than simply assuming that each axle peak is equal to

the maximum peak (as done in the maximum peak method).

As an individual axle peak strain within a group cannot exceed the maximum peak strain within the group, it

follows that damages calculated using the summed peaks model will be equal or lower than damages

calculated using the maximum peak method.

𝐷𝑛 = ∑ (

휀𝑖

𝑘)

5𝑛

𝑖=1

35

where

𝐷𝑛 = damage caused by an axle group with 𝑛 axles

𝑛 = number of axles in the axle group

휀𝑖 = tensile strain under axle 𝑖 within the group

𝑘 = constant

7.9 Analysis of 3D-FEM Response-to-load Results Using Summed

Peaks Method

The 3D-FEM analyses were re-processed and the damage caused by each axle group and load level

determined using Equation 35. Figure 7.16 shows the range of determined standard axle loads that result

from variations with pavement structure, and Figure 7.17 shows the results in terms of standard group

loads.

The results are very similar to those obtained using the maximum peak method. The loads on individual

axles within a group that cause the same damage as the Standard Axle determined using the two damage

calculation methods are compared in Figure 7.18. Superposition of two axles within a tandem group always

generates two equal magnitude strain peaks, and so there is no difference between the maximum peak

and summed peaks methods for tandem groups. However, superposition can result in different peaks for

triaxle and quad-axle groups, with the difference in peak magnitudes being a function of the asphalt

thickness, stiffness and underlying pavement structure. The maximum difference in equivalent axle loads

between the two methods for the modelled pavements was found to be 5% for triaxle and 6% for quad-axle

groups.




summed peaks model







summed peaks model






Figure 7.18: Comparison of standard axle loads determined using summed peaks and maximum

peak methods

7.10 Selection of Damage Calculation Method

Four models for estimating the damage caused by multiple-axle groups have been examined in the

previous sections:

Homsi multi-linear model (Section 7.4)

simplified Homsi model (Sections 7.5 and 7.6)

maximum peak method (Section 7.7)

summed peaks method (Sections 7.8 and 7.9).

For the reasons outlined in Section 7.5, Homsi’s multi-linear model can reasonably be simplified into a

model relating cycles of loading to reach flexural fatigue to maximum strain level and the number of peaks

of tensile strain. The simplified Homsi model comprises separate relationships for strains in the longitudinal

and transverse directions. For the same number of peaks and same maximum strain level, longitudinal

strains are considered by the model to be 1.9 times more damaging than transverse direction strains.

Direct application of either the full or simplified Homsi models for pavement design purposes is hampered

by the use of a single asphalt mix in the development of the models. In a pavement design context, the lack

of means of discerning between the fatigue properties of alternative asphalt mixes and binder types is

problematic.

However, Section 7.7.2 demonstrated that results almost identical to those obtained from the Homsi

simplified model could be achieved by using a modification of the simplified Homsi model

– the maximum peak method (Equation 34). This method would allow use of the current Austroads asphalt

fatigue performance model, or indeed any future performance model, wherein the constant 𝑘 in the model

is dependent upon properties of the asphalt mix. This method is, therefore, seen to be better suited to the

pavement design context.



Section 7.8 introduced the summed peaks method (Equation 35) as a means of recognising that the

individual peaks within a multiple-axle group do not necessarily have equal magnitudes. In Homsi’s original

experimental work, strain peaks had been set to be equal within an axle group. The maximum peak

method, with its very high correlation to the Homsi models, also assumes equal magnitude peaks. By

considering the damage associated with each axle peak with an axle group in its own right, the summed

peaks method is considered to be an improvement to the maximum peak method.

It should be noted that Homsi’s finding that longitudinal direction strains were more than 1.9 times

damaging than transverse strains for the same strain magnitude, was not directly considered in the

modelling work discussed in this section. As noted earlier, for all the modelled pavements, the strain

responses in the longitudinal direction had higher magnitudes than the strains in the transverse direction.

This meant that by comparison of strain magnitudes alone, longitudinal strains dominated damage

calculations. The fact that at the same strain magnitude, longitudinal strains appear to be more damaging

than transverse ones, did not affect which strain responses were more critical – longitudinal ones had

already been determined to be so. As the analyses ultimately compared damage relative to the damage

caused by a Standard Axle, the inclusion of the 1.9 factor would have been present in both determination of

the damage of the multiple-axle group and the Standard Axle, and so would have been cancelled out and

played no role in the calculation of relative damage.

It should be noted that as longitudinal strain magnitudes exceed transverse ones in all the pavements

analysed, current application of the Austroads fatigue performance relationship is based upon longitudinal

strains. In this context, Homsi’s finding could be expressed as saying that transverse direction strains are

less damaging than longitudinal ones, and that this finding has no impact on pavement design as

longitudinal strains are known to be of greater magnitude in any case.

As noted in Section 3.5, Bodin et al. (2009) did not see a demonstrable difference in fatigue tests

conducted using strain signals similar to longitudinal and transverse shapes. Reconciling these two findings

is beyond the scope of this project.

For both of these reasons, it is proposed that Homsi’s finding that longitudinal strains are more damaging

than transverse strains, should not be incorporated into the Austroads design procedure. It should be

remembered that if any specific response-to-load model were to determine higher magnitude transverse

direction strains than longitudinal ones, then this decision would result in a more conservative design.

Regarding the damage calculation method, it is considered that the above analyses have demonstrated

that the summed peaks method (Equation 35) represents the best means of considering the asphalt fatigue

damage caused by individual axles within multiple-axle groups within the Austroads pavement design

context.

7.11 Damage Calculated Using Linear-elastic Response-to-load Model

A 3D-FEM model was used to demonstrate the effect of multiple-axle superposition on the magnitude of

strain peaks as it was able to consider the non-linear behaviour of unbound pavement and subgrade

materials, and it was also able to represent the simultaneous application of multiple loads rather than

relying on post-processing to linearly superimpose responses to individual loads. This allowed modelling of

the complex stress state that occurs horizontally within a non-linear material, and therefore, also modelling

of the stiffness variation of the material.

However, the current Austroads (2012a) pavement design procedure does not use a 3D-FEM response-to-

load model, but rather a linear-elastic model (with cross-anisotropic modelling of unbound granular and

subgrade materials). In order to determine how well linear-elastic modelling reflects dependence of

standard axle loads on pavement structure, the pavement modelling analyses conducted with 3D-FEM

were repeated using linear-elastic modelling using CIRCLY analysis software (MINCAD Systems 2009).

The pavement model parameters shown in Table 7.2 were used, and the Austroads design procedures

were used to sublayer the granular material into five sublayers, with the modulus of the sublayers being

dependent on both the overlaying asphalt cover and underlying subgrade support.



Table 7.2: Material thicknesses and model parameters used in CIRCLY modelling

Parameter Values

Asphalt model 1000 MPa asphalt 𝐸 = 1000 MPa, ν = 0.4

3000 MPa asphalt 𝐸 = 3000 MPa, ν = 0.4

5000 MPa asphalt 𝐸 = 5000 MPa, ν = 0.4

Asphalt thickness 50, 100, 200, 300 mm

Granular model High quality crushed rock Maximum vertical modulus: 500 MPa

Lower subbase Maximum vertical modulus: 350 MPa

Granular thickness 200, 400, 600 mm

Subgrade model Highly plastic clay (CBR 3%) Vertical modulus: 30 MPa

Sand (CBR 15%) Vertical modulus: 150 MPa

Critical asphalt strains were extracted for each pavement analysed, and the damage caused by each axle

group and load level determined using the summed peaks method (Equation 35). Figure 7.19 shows the

range of determined standard axle loads that result from variations with pavement structure, and

Figure 7.20 shows the results in terms of standard group loads.

As with the results from 3D-FEM modelling, the results show a marked dependence of standard axle/group

loads on the pavement structure. For a given asphalt thickness, the effect of pavement structure is slightly

higher for the CIRCLY analyses than the 3D-FEM ones.


summed peaks model (CIRCLY responses)







summed peaks model (CIRCLY responses)






Both the maximum peak method and the simplified Homsi model were also used to determine the standard

axle/group loads. Figure 7.21 compares the standard axle loads determined using the simplified Homsi and

the maximum peak method. As with the 3D-FEM modelling, there is a very clear correlation between the

two methods.

Two regions in the figure demonstrate areas where the two approaches differed in outcome. Both of these

differences occurred as a consequence of differences in critical strain direction. In the 3D-FEM modelling,

the maximum strains in the longitudinal direction were in excess of those in the transverse direction.

However, the linear-elastic CIRCLY analysis did have some cases where the transverse strain became

critical.

The points in Figure 7.21 that are significantly below the line of equality correspond with the results where

the magnitude of transverse direction strains were found to be higher than the longitudinal ones in

modelling the Standard Axle (i.e. the 80 kN loaded single axle) using the maximum peak method. When

loaded with multiple-axle groups and analysed using the maximum peak method, the longitudinal direction

was dominant. Similarly, when using the simplified Homsi method, longitudinal strains were dominant for

these pavements. The pavements in question had low asphalt thickness and stiffness.

The points that are significantly above the line of equality reflect the results of a few very thick and stiff

asphalt pavement structures overlying weak substructures. In these cases, the simplified Homsi model for

some quad-axle loading cases was based on transverse strains, whilst the Standard Axle load cases used

longitudinal strains. The relative damages determined from CIRCLY for these cases were all based on

longitudinal strains.



Apart from these select cases where the direction of the critical strain response changed between the

Standard Axle reference damage case and the multiple-axle case, the vast majority of modelled cases

demonstrated a high correlation between the simplified Homsi model and the maximum peak method.

Figure 7.21: Comparison of standard axle loads determined using simplified Homsi and

maximum peak methods (CIRCLY responses)

Figure 7.22 shows the same agreement between standard axle loads determined using the maximum peak

and summed peaks methods as that demonstrated using 3D-FEM modelling (Figure 7.18).

Figure 7.22: Comparison of standard axle loads determined using summed peaks and maximum

peak methods (CIRCLY responses)

A comparison between the standard axle loads determined using 3D-FEM and linear-elastic analysis is

shown in Figure 7.23. There is general broad agreement in the results obtained from the two methods, with

those cases where significant differences are observed being limited to thin and low stiffness asphalt cases

with low subgrade support.



Figure 7.23: Comparison of standard axle loads determined using 3D-FEM and CIRCLY modelling

(a) All cases (b) Cases distinguished by asphalt

thickness

(c) Cases distinguished by asphalt stiffness

(d) Cases distinguished by subgrade type

7.12 Conclusions

The work conducted by Homsi (Homsi 2011, Homsi et al. 2012) represents the most detailed assessment

of the flexural fatigue performance of asphalt when subjected to multiple-axle loads. Her laboratory-based

controlled-strain study yielded an equation to predict the fatigue life of a sample as a function of the

maximum strain level applied, the number of peak strains (i.e. axles), and two strain shape factors relating

to load duration and strain direction.

A simplification of Homsi’s model reduced the prediction to being the function of the maximum strain level

and the number of peaks. Response-to-load analyses, using 3D-FEM, were conducted in order to assess

how grouping axles together affected the strain level obtained. Results of the analyses were expressed in

terms of standard loads that, when applied to multiple-axle groups, would lead to the same asphalt fatigue

damage that would occur under a single Standard Axle load. The analyses clearly indicated that the

standard load for an axle group is dependent upon the thickness of the asphalt, the modulus of the asphalt,

and the underlying pavement structure. This is in contrast to the use of constant standard loads across all

pavement configurations in the current Austroads mechanistic design procedure.

Direct application of either the full or simplified Homsi models for pavement design purposes is hampered

by the use of a single asphalt mix in the development of the models. In a pavement design context, the lack

of means of discerning between the fatigues properties of alternative asphalt mixes and binder types is

problematic.



However, analysis of strain responses using both 3D-FEM and linear-elastic response-to-load models

demonstrated that results almost identical to those obtained from the Homsi simplified model could be

achieved using a summed peaks method to calculate damage. In this method, the damage resulting from

the peak strain response of each axle within a group is summed to determine the overall damage caused

by the group (Equation 36). This method would allow use of the current Austroads asphalt fatigue

performance model, or indeed any future performance model with a strain damage exponent of five,

wherein the constant 𝑘 in the model is dependent upon properties of the asphalt mix. The summed peaks

method is, therefore, seen to be better suited to the pavement design context than Homsi’s models.

𝐷𝑛 = ∑ (

휀𝑖

𝑘)

5𝑛

𝑖=1

36

where

𝐷𝑛 = damage caused by an axle group with 𝑛 axles

𝑛 = number of axles in the axle group

휀𝑖 = tensile strain under axle 𝑖 within the group

𝑘 = constant

It is, therefore, suggested that using the summed peaks method would provide a more rigorous

representation of the asphalt fatigue damage caused by multiple-axle groups than the current Austroads

approach. Such a design process would require determining the damage (using Equation 36) resulting from

each axle load and each axle group within a traffic load distribution, as detailed in Section 9.2.1.

Section 9 of this report, by way of a series of design examples, examines whether this more rigorous

approach yields significantly different design outcomes.



8. Fatigue of Cemented Materials

8.1 General

The laboratory study reported here had the following broad characteristics:

use of established laboratory, controlled load, test process for assessing the flexural modulus and

fatigue characteristics of cemented materials

simulation of multiple-axle loads in the laboratory fatigue testing using a range of load shapes

designed not to precisely simulate truck axle groups, but rather to allow examination of the underlying

characteristics of the load shapes linkable to material performance

development of the relationship between fatigue performance and load level for each simulated load

shape, and subsequent comparison of those relationships

use of materials samples extracted from an existing, untrafficked pavement.

An alternative to the use of samples extracted from a pavement would have been the manufacture of

samples in the laboratory. This approach was not adopted for the following reasons:

Sample manufacture in the laboratory is a labour-intensive exercise, and the manufacture of a large

number of samples would be both costly and take several months to undertake.

After manufacture of samples, a minimum period of six months would be needed to cure and age the

samples to a condition approximating field conditions.

Concerns regarding the difference between compaction levels achieved in the laboratory not matching

field conditions would be negated if field samples were used.

Access to an existing two-year-old, well-documented, weather-protected, untrafficked cemented pavement

was available, and a large number of samples could be readily removed.

8.2 Laboratory Flexural Test Methods

In recent years, a suite of test methods have been developed by Yeo (Austroads 2008a) for assessing the

flexural behaviour of cemented materials. These methods were used as the basis for the laboratory study

test procedures. The methods cover determination of the following characteristics of rectangular beam

samples:

flexural resilient modulus

flexural strength

flexural fatigue.

The methods are based on the use of rectangular test beams (i.e. beams with uniform parallel surfaces)

whose cross-sectional dimensions may vary from 80 mm upwards, with a typical dimension of 100 mm.

The methods describe the manufacture of samples in the laboratory, and also the use of beams prepared

from pavement beds constructed in the field as in this study.

The beams are supported by apparatus used in concrete testing (AS 1012.11-2000), as shown in Figure

8.1.



Figure 8.1: Flexural beam roller supports and load rollers

Source: AS 1012.11–2000.

The pulsed load for each of the tests is applied via a pneumatic or hydraulic testing machine, following a

haversine shape. For each loading pulse, the displacement of the test sample is measured at the vertical

mid-span (i.e. between the two upper load rollers) and this displacement is then used, assuming simple

beam theory, to determine the resilient modulus.

The standard flexural fatigue test defines the fatigue life of a sample as the number of cycles to reduce the

flexural modulus of the sample to a value equal to half the initial value. The initial modulus of the sample is

defined as the average of the modulus values determined in the first 50 cycles of the test.

The testing apparatus used to conduct the testing is described in more detail in Section 8.4. The study

made use of the standard methods for determining flexural modulus and fatigue life, but with the following

refinements:

load shapes emulating multiple-axle groups were used (Section 8.4.4)

the definition of the initial condition of the test was altered (Section 8.5.5).

8.3 Sample Preparation

Yeo fully describes the construction of two pavements with cemented bases, both 150 mm thick, intended

for subsequent testing with ALF (Austroads 2008b). The pavements were constructed inside the large ALF

shed located in the Melbourne suburb of Dandenong South. The following is a brief summary of Yeo’s

report, focussing on the pavement area relevant to this study.

At the time of construction, each possible location for subsequent ALF trafficking was given a unique

numerical identifier, and all construction data was referenced to these sections. Samples for this laboratory

study were extracted from an untrafficked section of one of these constructed pavements, experiment

location 3300, where shrinkage cracking had not been observed during the construction and curing phases.

Additionally, the section was relatively uniform in thickness density and in deflection responses measured

with a falling weight deflectometer (Austroads 2008b).



The cemented material was sourced from the Boral Para Hills quarry in South Australia, and met the

Department of Planning, Transport and Infrastructure South Australia’s specification for a 20 mm

PM2/20QG Class 2 quarry produced stabilised material (DPTI 2014). The source rock was a

siltstone/quartzite. The material was bound with 4%, by dry mass, general purpose (GP) cement sourced

from Blue Circle (Victoria), with an additional retarding agent, Daratard, added at the manufacturer’s

recommended rate of 600 ml per 100 kg of cement. Addition of the retarder, whilst uncommon in Victoria

(where the pavement was placed), is common in South Australia. The retarder slowed the cement

hydration process, and provided an increased working time of up to four hours, increasing the likelihood of

achieving a uniform construction.

The sample size for flexural modulus and fatigue samples typically used in the test method is 100 (width) x

100 (depth) x 400 mm (length). Prior work had demonstrated that a skilled operator using a diamond

bladed concrete saw could accurately cut 100 (width) x 400 mm (length) samples from an in situ pavement,

provided that accurate guidelines were painted on the surface to be cut. Material cut in this manner

requires only the removal of surfacing material and trimming to the specified depth to yield test samples of

the required dimensions.

Exactly two years after construction of the cemented base, cutting guidelines were painted on the asphalt

surface of location 3300 (Figure 8.2). The painted pattern would produce a concentrated mass of 270

samples, nine samples across the width of the section, and 30 samples along its length. The lines were cut

on the same day using a diamond bladed concrete saw lubricated with water (Figure 8.3).

The samples were carefully extracted the following day (Figure 8.4), and were placed, packed with damp

sand, into storage bins (Figure 8.5). Despite the action of water and the saw blade, the cut faces of the

samples did not show signs of significant material erosion.

Figure 8.2: Marking saw cut lines for sample extraction



Figure 8.3: Precise cutting of samples using a concrete saw

Note: The samples being cut are not those used in the laboratory study.

Figure 8.4: Extraction of cut samples from road bed



Figure 8.5: Samples being packed in damp sand in storage bins

Before laboratory testing, samples were removed from the storage bins and trimmed to an even 100 mm

depth using a water lubricated saw in the laboratory (Figure 8.6). Again, no significant erosion of the cut

faces was evident. Once cut to final dimensions, the samples were stored indoors on rigid shelves,

wrapped in moist hessian fabric.

In accordance with the test procedure, the samples were transferred to the moist atmosphere of a fog room

at least two days before flexural testing.

Figure 8.6: Cutting samples to the required depth



8.4 Laboratory Test Equipment

8.4.1 General

Two alternative loading frames within the ARRB laboratories were assessed for possible use in the

laboratory study. The frames were controlled by similar closed-loop control hardware and software

produced by IPC Global. The first frame was an MTS Systems Corporation 25 kN hydraulic system, and

the second an IPC Global 14 kN pneumatic system. Surprisingly, it was found that the pneumatic system

was able to provide much smoother load shapes at high loading speeds than the hydraulic system. The

load shape generated on the hydraulic system exhibited a stepped shape rather than following the gradual

transition of the required haversine shape. Additionally, in recent months, the hydraulic system had proved

unreliable for long duration work such as fatigue tests, and timing of the necessary maintenance and

service checks would have compromised the planned testing program.

Accordingly, the IPC Global pneumatic testing system was selected for the laboratory study. A second,

identical unit was also used to help progress the testing program.

8.4.2 IPC Global Universal Testing System

The IPC Global 14 kN Universal Testing Machine (UTS-14P) is a closed-loop testing system that

incorporates a 14 kN pneumatic actuator on a large capacity load frame with integrated load cell. The

system can utilise a range of transducers and loading jigs. Control of the system is achieved through

software. Two calibrated Linear Variable Differential Transformers (LVDTs) were attached to the system to

measure mid-span displacement during testing. These LVDTs were anchored to the sample by a support

frame resting over the support rollers. Three different support frames were used during the study, as

discussed in Section 8.5.2.

Figure 8.7: Loading frame



8.4.3 IPC Global Test Control Software

IPC Global supplied flexible programmable test software UTS019 User Programmable Test was used for

the laboratory study. This test software allowed the following:

a user interface and output data that could be programmed to suit flexural beam testing

programming of equations to calculate stresses, strains and resilient modulus values based on applied

load, beam and test geometry, and measured displacements

a user definable sequence of load shapes

recording of raw sensor data at a user-definable frequency.

The software was programmed to conduct both flexural resilient modulus testing and repeated flexural

fatigue testing under a variety of different load shapes. In line with the standard method, the software was

programmed to run controlled load tests, i.e. the load applied during each pulse cycle was automatically

adjusted to follow the load shape and magnitude selected by the user.

The control software allows adjustment of the proportion-integral-derivative (PID) characteristics of the

controller. By adjusting the PID parameters, the user can ‘tune’ the control system to best follow the load

shape and system response required. A lengthy trial-and-error exercise was undertaken to determine what

load magnitude and cycle frequencies could be achieved in the control system, whilst ensuring both of the

following requirements:

the requested load magnitude entered into the system is achieved and sustained over repeated cycles

the load shape entered into the system is achieved and sustained over repeated cycles.

This exercise was conducted using a range of superfluous cement treated samples from previous research

work, and an aluminium rectangular hollow section with flexural modulus similar to that expected from the

field samples to be tested.

8.4.4 Pulse Shape Generation

The flexural modulus and fatigue test procedures discussed in Section 8.2 are controlled load tests, i.e. the

equipment control system controls the load applied during the test, ensuring that it follows a user-defined

shape. Alternative controls include controlled strain tests, in which the load is adjusted during the test to

ensure that a measured strain response follows a user-defined shape.

This controlled load approach was retained for the multiple-axle laboratory study, with different load shapes

developed to simulate different multiple-axle groups. The standard tests use a haversine load shape to

simulate a single axle, and haversine shapes were used as the basis for the multiple-axle load shapes.

Figure 8.8 shows a load shape representing a tandem axle, and shows some of the underlying

assumptions that were made when generating the load shapes:

the peak-to-peak spacing of the shape (a in Figure 8.8) matches the axle spacing at a given travel

speed

the load rise at the start of the pulse (a/2 in Figure 8.8) added to the load drop at the end of the pulse

(a/2) is the same as the spacing between axles (a).



Figure 8.8: Assumed relationship between load pulse shape and axle spacing

Using these assumptions, a relationship between the vehicle travel speed and the width of loading pulse

used in the simulation was determined. Figure 8.9 shows this relationship using a typical spacing between

axles within a group of 1.25 m. It can be seen that the standard tests’ use of a haversine representation of

a single axle with a pulse width of 250 ms corresponds with a travel speed of approximately 18 km/h. This

same pulse width also corresponds with a quad-axle group travelling at 72 km/h. Trial-and-error determined

that the pneumatic equipment could repeatedly apply a quad-axle shape in this time period, but was unable

to do so at faster test speeds, i.e. shorter pulse widths. Thus, the pulse width of 250 ms was fixed for the

quad-axle group.

Figure 8.9: Assumed relationship between vehicle speed and load pulse width



Given the long-term nature of fatigue testing and a finite number of samples, the testing program was

limited as follows (Figure 8.10):

one travel speed was simulated (72 km/h)

one axle spacing within multiple-axle groups was simulated (1.25 m)

the peak loads of all axles within a load shape were the same (i.e. the load applied by each simulated

axle within a group was equal)

the pulse width was varied between axle groups to ensure a single travel speed was simulated for all

axle groups (250 ms for a quad-axle, down to 250/4 = 62.5 ms for a single axle)

a rest period equal to the difference between the 250 ms and the pulse width was built into the load

shape

an additional rest period of 250 ms was added to all axle group shapes, giving a total 500 ms between

axle group simulations.

Figure 8.10: Load pulse shapes showing rest periods used in fatigue testing

The varying rest period was due to the desire to keep the simulated travel speed constant for all load

shapes, and the practical constraints of the test control software.

In the tandem axle simulation shown in Figure 8.8, the load is seen to drop off between the two axles.

Figure 8.11 demonstrates the two extremes of load behaviour that could occur between axles in a group.

Using the term interaction to describe the degree to which the two haversine shapes interact with each

other, it can be seen that full interaction, i = 1, results in a situation where a single sustained load is

applied, whereas no interaction at all, i = 0, results in two distinct loads.

In order to determine how much the interaction affected the performance of the samples, two different

levels were used for all multiple-axle load simulations. The lowest level of interaction that could be reliably

achieved by the pneumatic equipment was i = 0.4. Lower levels could be achieved with longer pulse widths

(i.e. slower travel speeds); however, it was decided that it was important to maintain a reasonably high

simulated travel speed to ensure that the tests were representative of in-service pavements. The other

level of interaction was set at i = 0.8.



Figure 8.11: Interaction between axle peaks within load pulse shape

Table 8.1 and Figure 8.12 show the load shapes used in the study. Flexural modulus tests were conducted

using all load shapes, including the standard test haversine shape; and flexural fatigue tests were

conducted using all shapes, with the exception of the haversine shape. Given a lack of observed field data

for cemented pavement materials, these shapes were generated mathematically by combining haversine

functions. Nevertheless, the generated load shapes compare well with strain data collected on asphalt

pavements (Section 4.6).

Table 8.1: Description of load pulse shapes

Shape name Axle group simulated Interaction between axles within group

Haversine Standard tests pulse shape –

1_00 Single axle –

2_40 Tandem 40% (i = 0.4)

2_80 Tandem 80% (i = 0.8)

3_40 Triaxle 40% (i = 0.4)

3_80 Triaxle 80% (i = 0.8)

4_40 Quad-axle 40% (i = 0.4)

4_80 Quad-axle 80% (i = 0.8)



Figure 8.12: Load pulse shapes

8.4.5 Control Software

Using the geometry of the sample and supporting rig, the measurement of vertical displacement mid-span

due to an applied load, and assuming linear elastic behaviour, the standard test method for determining

flexural modulus uses simple beam theory to determine the peak tensile stress and strain developed mid-

span at the bottom of the sample (Equations 37 and 38). The flexural modulus of the sample is determined

as the ratio of the stress and strain (Equation 39).



𝜎𝑡 =𝑃𝐿

𝑤ℎ2× 106

37

휀𝑡 =108ℎ𝛿𝑑

23𝐿2× 106

38

𝑆𝑚𝑎𝑥 =𝜎𝑡

휀𝑡× 103

39

where

𝜎𝑡 = peak tensile stress (kPa)

휀𝑡 = peak tensile strain (microstrain)

𝐸𝑚𝑎𝑥 = flexural modulus (MPa)

𝑃 = peak force (kN)

𝐿 = beam span (mm)

𝑤 = sample width (mm)

ℎ = sample height (mm)

𝛿𝑑 = peak mid-span displacement (mm)

Initially, the mid-span displacement was measured using a single LVDT mounted in an existing support

frame and anchored to the sample in line with the lower support rollers. When vibration concerns prompted

changes to the support frame design (Section 8.5.2), an additional LVDT was incorporated. The

displacements measured by the two LVDTs were averaged, unless examination of the data demonstrated

that one of the devices was generating spurious results, in which case, data from a single LVDT was used.

All these calculations were programmed into the control software. This allowed the software to provide real-

time charting of modulus as a function of loading cycles as the tests progressed.

At the end of a test, be it modulus or fatigue, the control software generated an ASCII text file listing the

following data for each load cycle applied:

cycle number

maximum and minimum load applied during the loading cycle (kN)

maximum and minimum displacement of the actuator used to apply the load (mm)

maximum and minimum displacement measured by each LVDT (micron)

maximum resilient displacement measured by each LVDT (i.e. the difference between the minimum

and maximum displacements) (micron)

peak tensile stress (kPa)

peak tensile strain determined from each LVDT (microstrain)

flexural modulus determined from each LVDT (MPa)

mean flexural modulus (i.e. the average of the flexural modulus determined by both LVDTs) (MPa).

8.5 Alterations to Test Procedures and Equipment

8.5.1 General

In addition to the use of multiple-axle load shapes, elements of the testing process established at the start

of the testing program were also refined during the testing. The following sections briefly outline the

changes made.



8.5.2 LVDT Frame Alterations

During the initial machine and software investigation work, and before testing had commenced, the

lightweight aluminium LVDT support frame shown in Figure 8.13(a) was used. This pre-existing frame,

which supported a single LVDT, was found to vibrate during testing, especially when multiple-axle load

shapes were applied. This vibration was evident in the raw data files as excessive noise in the LVDT

response trace during each cycle. This vibration was attributed to the thin elements used in the frame, and

to its width (designed to ensure the frame stood clear of the load rollers). This support frame had support

rollers fixed at 300 mm.

A revised aluminium support frame was designed incorporating considerably stiffer members and a much

narrowed width. The new frame (Figure 8.13(b)) sat much closer to the sample than the initial frame, and

the load rollers were accommodated within the design by scalloping sections out of the side elements. An

additional LVDT was incorporated into the design, allowing simultaneous monitoring with two LVDTs. This

support frame also had support rollers fixed at 300 mm, and all tests conducted at this spacing used this

support rig.

As discussed in Section 8.5.3, once testing had commenced, it was found that the flexural modulus of the

samples was much stiffer than expected and that high strains could not be developed on the underside of

the samples. In order to ensure that high strains could be generated, it was decided that the test geometry

be changed to a load span of 375 mm (with the top load rollers spaced at 125 mm). This change in

geometry necessitated the design and construction of new support frames. Two of these new frames

(Figure 8.13(c)) were used for the majority of testing during the study. The frames were designed to allow

testing at spans of both 300 mm and 375 mm. During the study, these frames were only used for testing

samples at 375 mm spans.

Figure 8.13: Succession of LVDT support frames used

8.5.3 Test Geometry

The initial loading jig used had a span of 300 mm between the support rollers (dimension L in Figure 8.1)

and 100 mm between the upper load rollers (dimension l in Figure 8.1). As the study aimed to use fatigue

testing to develop a relationship between fatigue performance and tensile strain for each load shape,

fatigue testing using a range of strain levels was required. After some modulus and flexural fatigue tests

had been conducted, it became apparent that the loading frame was unable to produce high enough tensile

strains at the bottom of the unexpectedly high stiffness material to generate a significantly wide enough

range of strain levels. Whilst the actuator in the pneumatic rigs was rated as having a capability of applying

a 14 kN peak load, it was found that application of the complex multiple-axle load shapes in a 250 ms cycle

was only reliably and sustainably achievable at about a 5 kN peak load.



As a result, it was decided that a simple change to the test geometry would enable the generation of higher

strains in the samples, without compromising the ability to also conduct tests at lower strain levels. As the

extracted samples were of 400 mm length, a final span of 375 mm was selected for the revised geometry

(i.e. L equal to 375 mm, and l equal to 125 mm in Figure 8.1).

A revised test jig was designed and two units created, one for each of the two pneumatic systems used in

the study. The revised jig allowed a spacing of 375 mm and the original 300 mm. Once these systems were

put into operation, all subsequent testing was conducted at 375 mm spacing. Some initial data was

collected using the 300 mm span jig. Figure 8.14 shows both the initial and final loading jigs used.

Figure 8.14: Load support roller jigs

(a) Initial jig (300 mm span) (b) Final jig (300 and 375 mm span)

As an alternative means of generating higher strain levels, changes in the load shapes, and particularly

changes in the load rates, were considered. However, reductions in pulse width time would have led to a

directly proportionate increase in the duration of each fatigue test. Additionally, such changes would result

in tests that could not be compared to the tests completed to date (conducted over several months), so

these changes were not made. It was considered that simple changes to the geometry of the test would

achieve the same outcome (higher strain levels), whilst still allowing test results that could be compared to

those conducted to date. As the test procedure simply uses the displacement response to an applied load

to determine strain and modulus, results conducted using different test geometries should be comparable

with each other.

8.5.4 Sample Size

The increased span of the loading jig allowed the generation of higher strain levels, but not high enough to

produce flexural fatigue of stiff materials in 10 000 to 50 000 load cycles. Having increased the span length

of the sample to the practical limit and rejected changes in pulse width, the only other recourse was to

reduce the cross-sectional area of the samples. Given the maximum aggregate size in the material was

20 mm, it was determined that 80 mm width by 80 mm depth was the smallest cross-sectional area that

could be achieved without compromising the homogeneity of the material within the sample.

8.5.5 Definition of Initial Modulus and Strain for Fatigue Testing

The standard test method to determine the flexural fatigue life of a sample defines the initial modulus of the

sample as the average modulus of the first 50 cycles of loading. The definition of the initial modulus was

changed to the modulus value at cycle 50, rather than the average of the first 50 cycles. Subsequent

versions of the test methods have also adopted this definition of the initial modulus as the value at cycle 50.

These revised test methods can be found in Austroads (2014b).



8.6 Data

8.6.1 Test Sequence

For each sample, the following testing sequence was followed:

the sample was prepared for testing

the flexural modulus was determined using all of the eight load shapes

flexural fatigue testing was conducted using a single load shape at a selected load level.

Sample preparation

The saw cut samples were removed from their storage in moist hessian and plastic wrapping and were

placed in the ARRB laboratory fog room for a minimum of two days of preconditioning prior to testing. A

sample ready for testing was then removed from the fog room and left standing whilst its dimensions were

measured and recorded on both paper log sheets and in the control software. The mass of the beam,

termed the wet mass, was measured to enable subsequent determination of the moisture content of the

sample.

The sample was then wrapped in thin plastic cling wrap to minimise any moisture loss during testing. The

wrapped sample was placed in the loading rig, and the LVDT support frame placed and held onto the

sample by use of rubber bands anchored to the lower support rollers. Flexural modulus testing was then

conducted.

Flexural modulus test

The modulus testing applied sequences of 100 cycles of each of the load shapes, shown in Figure 8.12,

with each pulse shape having a width of 250 ms and followed by a 750 ms rest period. The 100 cycles of

each load shape were separated by a five-second rest period prior to application of the 100 cycles of the

next shape. Each load shape sequence used the same maximum load level, which was set by the user at a

low enough value to ensure that the beam was not damaged by successive cycles, but high enough to

ensure that displacement transducer output was high enough to overcome any signal noise. This

displacement was typically 5 micron (i.e. 0.005 mm). Fatigue testings of the sample was commenced

immediately after the modulus tests were conducted.

Flexural fatigue test

Fatigue tests were conducted as load-controlled tests using a single load shape and load level. The pulse

width of the applied load shape was the same 250 ms used in the modulus test, but the rest period that

followed the load application was decreased to 250 ms in line with the standard method for fatigue

assessment.

Rather than conduct tests for a single load shape before progressing to the next load shape, tests for all

load shapes were interleaved so that the fatigue relationship for each shape could be developed

progressively. This allowed for progressive monitoring of results for all shapes, and also acted to neutralise

the effects of any unrecognised progressive systematic errors that may have occurred over the course of

the testing.

During fatigue testing of some samples, it was apparent that the load being applied was below the fatigue

threshold as the modulus was not reducing over time. In some very long-term tests, and in spite of the cling

film wrapping, the modulus of the sample was seen to gradually increase with slow drying of the sample

(i.e. the sample was slowly stiffening and the applied load level was no longer damaging). In both of these

cases, the testing was halted, the load level increased, and testing restarted. These cases were flagged for

subsequent examination, and in the majority of cases, they were excluded from subsequent analysis. The

only restarted tests that have been retained were those for which examination of the raw data showed a

reasonably smooth continuous transition between phases of the test. These cases were limited to those

where the increase in load after restarting the test was very minor, but enough for the sample to start to

exhibit deteriorating modulus with cycles. Excluded data is not represented in this document.



Following flexural fatigue testing, the sample was weighed and then oven dried to determine the moisture

content and dry density of the sample. This was done using the dry mass and the volume of the beam, a

method which would yield spurious results if the sample’s surface had been eroded during saw cutting.

Determination of the sample volume by immersion in water would have overcome this issue, but was not

considered warranted given the limited number of samples affected by erosion.

8.6.2 Flexural Modulus Data

The data collected during each modulus test was carefully examined for the following cases:

A degradation of the sample was observed during the modulus test (i.e. displacement was seen to

increase with successive applications of the same load level). These cases were noted and the sample

discarded.

The two LVDTs provided significantly different results, with one sensor obviously anomalous. One

case was found in which it was clear that one LVDT had become stuck, and the other was recording

appropriate results.

The two LVDTs provided significantly different results, with no way of determining which sensor was at

fault. In all cases where this occurred, there was evidence that the sample had either been dropped or

mishandled, and a note was subsequently made and the sample discarded.

A sudden increase in displacement, as measured by both LVDTs, leading to a drop in calculated

modulus occurred during the testing. This phenomenon was attributed to the expansion of pre-existing

micro-cracks within the sample. In such cases a note was made and the sample discarded.

The range of modulus values measured under the standard haversine loading across the samples is shown

in Figure 8.15. It can be seen that the modulus varied over a very wide range, 4000 to over 30 000 MPa,

with the majority of samples exhibiting a modulus between 15 000 and 22 000 MPa. This wide range of

modulus values was unexpected given the uniform nature of the field-collected density and FWD deflection

data, as was the magnitude of the modulus. As discussed in Section 8.5, the high modulus of the material

resulted in changes to the test geometry and sample size. A variety of strain levels were used in conducting

the modulus tests and no attempt has been made to standardise the test results to a single strain level.

Figure 8.15: Distribution of modulus of samples (haversine pulse)



After fatigue testing of each sample, the density of the sample was determined. Figure 8.16 shows that the

spread of modulus data is not readily explained by sample density. The modulus tests were conducted at

similar, but not identical, load levels, and so the variation cannot be directly attributed to a modulus

dependency on load level (a dependency was observed but the dependency was not significant enough to

explain this range of data).

Given the lack of alternative explanations, this range of modulus values observed was attributed to natural

variation in material and cement binder composition and distribution, and on the likely presence of varying

amounts of micro-cracking within the samples caused by shrinkage-related stresses.

Figure 8.16: Relationship between flexural modulus and relative density of samples (haversine

pulse)

8.6.3 Flexural Fatigue Data

Over 1400 hours of flexural fatigue testing time was used to generate the data set for analysis. In addition

to this testing, many hundreds of hours of compromised data were collected. This compromised data

included the following cases:

tests that did not fatigue the sample

tests that were prematurely halted by electrical power failure

tests that were prematurely halted by computer or operator error (unfortunately, these tests were often

long-term tests, with the error occurring after more than 500 000 cycles had been applied)

tests on 80 mm x 80 mm beams that had previously been subjected to repeated fatigue test cycles

when sized 100 mm x 100 mm

tests that were halted and restarted at higher load levels

fatigue tests that ran for less than 500 cycles

fatigue tests for which the modulus determined at cycle 50 was less than 10 000 MPa (as the majority

of samples exhibited much higher moduli, it was considered that modulus values lower than

10 000 MPa indicated a substantially different material – probably as the result of more extensive

micro-cracking within the sample).



The definition of fatigue life or performance of a sample used in this study was the number of cycles of load

applied before the resilient modulus fell to a level equal to half the initial value. This definition is obviously

dependent upon determination of the initial modulus.

In any closed-loop laboratory test where a pulsed loading is applied, there will be a short period

immediately after the commencement of the test before the pulse shape stabilises. The length of time

required before this occurs obviously varies according to the testing equipment (pneumatic, hydraulic, etc.),

the testing conditions (pulse shape, cycle time, etc.) and the material being tested (sample dimensions,

stiffness, etc.). It was found in this study that the pulse shape did not stabilise until three or four cycles had

been applied. As a result, the data related to the application of the first four pulses was discarded and, for

reporting and analysis, the fifth load pulse application was considered to be the ‘first’ pulse of the test

proper.

Three different fatigue lives, each based on a different definition of the initial modulus, were determined:

the initial modulus is that calculated from the displacement response to the first cycle (i.e. the first

pulse after the excluded pulses discussed above)

the initial modulus is that calculated from the displacement response to the 50th cycle – this is the

definition that was used for subsequent analysis

the initial modulus is the average of the moduli calculated from the displacement responses to the first

50 pulses (this is the definition used in the standard method).

The fatigue test results are presented in Appendix I.

8.7 Flexural Fatigue for Each Load Type

Figure 8.17 to Figure 8.20 presents the number of cycles to reach fatigue failure, 𝑁, as a function of the

initial strain level applied. Also shown are the 95% confidence limits of the slope of the linear regression

lines plotted through the data. The regression equations are listed in Table 8.2. Underlying relationships

between fatigue life and material modulus, sample dimensions, and material density were explored but

were unable to provide improved fits to the data.

Figure 8.17: Flexural fatigue results for single axle load shape



Figure 8.18: Flexural fatigue results for tandem axle group load shapes with interactions between

axles of 40% and 80%

(a) 40% interaction (b) 80% interaction

Figure 8.19: Flexural fatigue results for triaxle axle group load shapes with interactions between





Figure 8.20: Flexural fatigue results for quad-axle group load shapes with interactions between



Table 8.2: Fatigue regression equations for each load shape

Pulse shape Regression equation Number of beams r2

1_00 log10(𝑁) = 29.942 − 12.91 log10(𝜇𝜖) 16 0.55

2_40 log10(𝑁) = 59.149 − 27.95 log10(𝜇𝜖) 9 0.56

2_80 log10(𝑁) = 23.586 − 9.82 log10(𝜇𝜖) 9 0.60

3_40 log10(𝑁) = 36.989 − 16.44 log10(𝜇𝜖) 8 0.63

3_80 log10(𝑁) = 20.032 − 8.04 log10(𝜇𝜖) 12 0.80

4_40 log10(𝑁) = 41.007 − 18.64 log10(𝜇𝜖) 6 0.81

4_80 log10(𝑁) = 16.302 − 6.13 log10(𝜇𝜖) 8 0.84

Figure 8.21 (a) represents the resulting regression equations. In this figure, the parameter 𝑁 corresponds

to the loading cycle, or axle group being simulated; and so both a pulse of the single axle simulation and a

pulse of, say, the triaxle simulation would correspond to 𝑁 = 1.

Figure 8.21 (b) presents the same results but using the number of peaks, 𝑛, corresponding to the number

of axles. One pulse of the single axle would have 𝑛 = 1, and one pulse of the triaxle group would have 𝑛 =

3.



Figure 8.21: Flexural fatigue relationships expressed in terms of cycles (axle groups) of loading

and peaks (axles) of loading

(a) Cycles to half modulus (b) Peaks to half modulus

A disappointingly very wide range of scatter was observed in the flexural fatigue results. The test method,

apparatus, equipment, control and analysis software used for this study have produced more uniform data

when testing laboratory prepared and cured samples as part of subsequent research work (Austroads

2014a), and so the scatter observed here has been attributed to the use, and possibly the handling, of field

extracted samples. Despite uniform construction and the absence of trafficking, the test pavement would

have been subjected to shrinkage-related stresses during its initial curing period, leading to the possible

generation of micro-cracks within the material.

As a result of the scattered test results, there is a large amount of uncertainly in the performance models

determined for each load shape. This is particularly evident by the wide bands of the 95% confidence

interval for the slopes shown in Figure 8.17 to Figure 8.20. Given this uncertainly; it is difficult to draw

definitive conclusions from the grouped models shown in Figure 8.21. Attempts to provide meaningful

interpretation of the test results were largely unsuccessful, until the concept of developing a separate strain

damage model for each load type was abandoned. As discussed in Section 8.8, an analysis concept

developed after the conclusion of the testing program was utilised to greater success.

8.8 Analysis Using Estimated Strain Reach 100 000 Cycles of

Loading

8.8.1 Background

Jameson (Austroads 2014a) provides a summary of an extremely comprehensive research program

examining the flexural fatigue characteristics of cemented materials. A common issue to the undertaken

work was the difficulty in predicting laboratory and in-service modulus and fatigue life due to the very high

variability of mix composition, material density and, significantly, shrinkage cracking. The high variability

seen in the above multiple-axle laboratory testing can, therefore, be seen to be reasonably expected.



When the multiple-axle testing program was conducted, progress in the completed research program (later

summarised by Jameson), had concluded that a flexural strain based fatigue relationship could be

determined from a moderate number of beam samples subjected to repeated flexural loading (Austroads

2008a). As noted by Jameson’s summary, in order to further validate this encouraging conclusion, an

exhaustive program of fatigue testing was conducted on a wide range of cemented materials. Alderson and

Jameson (Austroads 2014b) summarised this work, and in conjunction with additional parallel analysis

work undertaken by Jameson (Austroads 2014a), drafted revisions of the Austroads processes for

designing flexible pavements containing cemented materials and laboratory test methods.

The findings of this research work, and the proposed new design procedures, were utilised to re-analyse

the multiple-axle fatigue data.

8.8.2 Tolerable Strain

As a result of the high variability of fatigue results between samples of essentially the same composition,

the proposed new procedures recommend that fatigue testing be limited to determining the initial strain

level which will lead to a laboratory fatigue life of 105 repetitions. In doing so, the procedure recommends

that a strain damage exponent of 12 be presumed, and that a fatigue testing program should focus effort on

obtaining replicate test determinations of this strain value, rather than undertaking tests across a wide

range of strain levels in order to determine the strain-damage exponent. Alderson and Jameson (Austroads

2014b) had concluded that the exponent of 12 could reasonably be presumed.

For the purposes of the following discussion, the initial strain level that will lead to sample fatigue failure in

105 controlled-load cycles is called the tolerable strain.

For each of the fatigue tests conducted in the multiple-axle study, the tolerable strain was estimated using

Equation 43. These values are listed in Appendix J.

𝑁𝑖 = (𝑘

휀𝑖)

12

40

solving Equation 40 for 𝑘:

𝑘 = 휀𝑖(𝑁𝑖)1

12 41

expressing Equation 40 in terms of tolerable strain:

105 = (𝑘

휀5𝑖

)

12

42

substituting Equation 41 in Equation 42 and solving for 휀5:

휀5𝑖= 휀𝑖 (

𝑁𝑖

105)

112

43

where

𝑁𝑖 = number of load cycles to fatigue failure in test 𝑖

𝑘 = constant

휀𝑖 = initial strain during fatigue test 𝑖 (μm/m)

휀5𝑖 = tolerable strain for sample 𝑖 (μm/m)



8.8.3 Correcting Tolerable Strains for Varying Density Condition

Estimates of the tolerable strain for different load pulse shapes could be compared and conclusions drawn

as to the significance of applying grouped axle pulses on the fatigue life of the test beams. However, as

demonstrated in Figure 8.16, the tested beams had a wide range of moduli and densities. The results of the

testing summarised by Jameson enabled him to determine that the tolerable strain of a sample was, in part,

significantly dependent upon the sample’s stiffness and density (Austroads 2014a). Therefore, before an

examination of the different load shapes was made, the estimates of tolerable strain were normalised to

values representative of single modulus and density values. This was done by combining a series of

correction relationships, developed by Alderson and Jameson (Austroads 2014b) and Jameson (2014a), as

follows.

Firstly, an examination of the densities of each of the samples determined that a representative density of

98% of maximum dry density was mid-way within the spread of sample densities. Seven samples tested

had a relative density that differed from this representative value by more than 2% (i.e. they had a relative

density less than 96% or greater than 100%). The test results for these samples were dropped from further

analysis, as it was considered that the density was excessively different to the representative value of 98%.

Jameson did not develop a direct factor to correct measured tolerable strain values at a given sample

density and/or modulus to an estimated tolerable strain for different density/modulus conditions. He did,

however, develop a relationship to predict the tolerable strain that would result from a sample of given

modulus and flexural strength (Equation 44).

휀5 = 62.7𝐹𝑆 +

722700

𝐸− 74.6

44

where

휀5 = tolerable strain for a fatigue life of 105 cycles (μm/m)

𝐹𝑆 = flexural strength (MPa)

𝐸 = flexural modulus (MPa)

In order to correct the multiple-axle test results, a correction factor, 𝑓, was developed by determining the

tolerable strain estimates using Equation 44, using flexural strength and modulus values of individual

samples and flexural strength and modulus value at average conditions (Equation 45).

𝑓𝑖 =(휀5𝑒98%

)

(휀5𝑒𝑖)

=[ 62.7𝐹𝑆98% +

722700𝐸98%

− 74.6]

[ 62.7𝐹𝑆𝑖 +722700

𝐸𝑖− 74.6]

45

where

𝑓𝑖 = factor to be applied to tolerable strain values determined from each fatigue test result to

correct it to standard sample density conditions

휀5𝑒𝑖 =

estimate of tolerable strain for sample 𝑖, estimated from the sample’s flexural strength

of 𝐹𝑆𝑖 and modulus of 𝐸𝑖 using Equation 44

휀5𝑒98% =

estimate of tolerable strain for a sample with a relative density of 98%, estimated using

Equation 44

Regarding the terms in Equation 45, parameter 𝐹𝑆98% was not directly measured during the laboratory

testing. However, Jameson and Alderson (Austroads 2014b) reported the results of four flexural strength

tests conducted on the same material (sampled from the quarry) and mixed with the same binder content

and moist cured for nine months prior to testing. The samples had a mean density ratio of 96.5% and mean

flexural strength of 1.55 MPa. Having reviewed individual test results from a large number of samples and

materials, Alderson and Jameson concluded that a 1% increase in relative density results in a 5% increase

in flexural strength. Using this relationship, the flexural strength of the material at 98% relative density was

estimated to be 1.67 MPa.



Alderson and Jameson also concluded that 1% increase in relative density results in a 5% increase in

modulus. Using the initial modulus of each fatigue test (i.e. the modulus at cycle 50) as input, this

relationship was used to estimate what each sample modulus would have been at relative density of 98%, i.e. 𝐸98%.

The flexural strengths for each density condition of the tested samples were also not known. Using the

presumptive estimate of flexural strength of 1.67 MPa at 98% relative density, the flexural strength was

estimated for each sample’s density condition by Jameson and Alderson’s relationship between density

change and flexural strength change, yielding 𝐹𝑆𝑖.

Values for the modulus of each sample, 𝐸𝑖, were directly measured during the flexural fatigue tests, and the

initial condition value (i.e. the value at cycle 50) was used.

With a separate correction factor, 𝑓𝑖, having been determined for each sample tested, the factors were

used to correct each tolerable strain determined using Equation 43 to an estimated tolerable strain that

would have been determined if the sample had had a relative density equal to the representative value of

98%. The resulting corrected tolerable strains, as well as the correction factors and relevant components of

those factors, are listed in Appendix J.

8.8.4 Effect of Load Shape on Tolerable Strain

The tolerable strains to reach 105 cycles of loading for each applied shape are summarised in Table 8.3.

With the exception of the 2_40 shape, there is a trend of decreasing mean tolerable strain with increasing

number of axles for both of the interaction levels. However, the differences in means can be seen to be

small, especially in comparison to the standard deviation of the tolerable strains for each load shape.

A comparison of mean strains between the two interaction levels shows higher tolerable strains for the 40%

interaction shapes when compared to their counterparts with 80% interaction.

Table 8.3: Summary of tolerable strains for different load shapes

Pulse shape Cases Corrected tolerable strain (μm/m)

Mean Standard deviation

1_00 13 86.8 8.7

2_40 7 81.1 13.7

3_40 6 86.6 11.8

4_40 5 80.3 10.0

2_80 9 80. 8 8.8

3_80 12 79.6 6.3

4_80 7 77. 7 4.5

In order to see whether the differences in strains between the load shapes are statistically significant, even

with the relatively high variations for each shape’s data set, a series of single-sided, Student’s t-tests were

conducted to determine whether the means were the same (null hypothesis) or whether the shapes with

higher axle simulations had lower mean tolerable strains (alternate hypothesis). Use of a single-sided test

was considered appropriate as there was no sound engineering reason to consider that the load shapes

with more axles would have higher tolerable strains (i.e. be less damaging). The results of the statistical

tests are shown in Table 8.4



Table 8.4: Comparison of mean corrected tolerable strains

Pulse shapes t-statistic Degrees of freedom p-value

1_00 and 2_40 1.1329 18 0.14

1_00 and 3_40 0.0412 17 0.48

1_00 and 4_40 1.3514 16 0.10

2_40 and 3_40 –0.7612 11 0.77

2_40 and 4_40 0.1065 10 0.46

3_40 and 4_40 0.9336 9 0.19

1_00 and 2_80 1.5777 20 0.07

1_00 and 3_80 2.324 23 0.01

1_00 and 4_80 2.704 18 0.01

2_80 and 3_80 0.3473 19 0.37

2_80 and 4_80 0.9839 14 0.17

3_80 and 4_80 0.9014 17 0.19

The p-values indicate that the chance that any observed difference in the mean tolerable strains may be

the result of random sampling, rather than resulting from a true difference in strain, ranges from 1% to 77%.

Despite the use of the tolerable strain approach, and the correction of those strains to reflect differences in

sample density, some of the load shape data sets still exhibit a wide range of scatter. However, the

statistical tests do indicate some clear differences in mean tolerable strains between some load shapes.

Raising the ratio of the mean tolerable strains of a pair of load shape data sets to the power of 12 enables

the difference in tolerable strains to be reflected as a relative damage. Table 8.5 contains the calculated

relative damages for all of the load shape pairs for which the t-tests indicated that there was more than an

80% chance that the observed difference in mean tolerable strains was the result of a true difference in

value, and not the result of random differences (i.e. p-value less than 0.20).

Table 8.5: Relative damages between different load shapes

Pulse shapes Axle ratio Relative damage

2_40 cf. 1_00 2.0 2.2

4_40 cf. 1_00 4.0 2.5

4_40 cf. 3_40 1.33 2.5

2_80 cf. 1_00 2.0 2.4

3_80 cf. 1_00 3.0 2.8

4_80 cf. 1_00 4.0 4.1

4_80 cf. 2_80 2.0 1.7

4_80 cf. 3_80 1.33 1.5

Also included in Table 8.5 is the ratio of the number of axles within the paired load shapes. In many cases,

especially for the shapes with an interaction of 80%, there is quite a good match between the relative

damages and the axle ratios. A perfect match would indicate that relative damage was solely the result of

the difference in the number of axles within the shapes. Figure 8.22 presents relative damage as a function

of axle ratio, and also includes a line of equality.

For the 80% interaction shapes, there is a clear relationship between the relative damage of a load pair and

the ratio of the number of axles within that pair. Further, the correspondence appears to be one-to-one: a

difference in number of axles of 𝑛 resulted in a relative damage of 𝑛. The results are considerably less

clear for the 40% load shapes.



Figure 8.22: Relative damages between different load shapes as a function of axle ratio

8.9 Summary

A laboratory study was undertaken in an attempt to relate the shape of simulated multiple-axle loads to the

flexural fatigue of cemented materials. At the time the approach was formulated and undertaken, the

outcome of then-available Austroads research indicated that a flexural strain-based relationship could be

determined from a moderate number of beam samples subjected to repeated flexural loading. Subsequent

extensive testing of a wider range of materials and samples has indicated, however, that there is a very

large amount of scatter to be expected in fatigue results. This high variability was certainly observed in the

results of the multiple-axle study, and as a result, the initial analysis of the data did not allow the

formulation of conclusive findings.

However, subsequent analysis presuming a strain damage exponent of 12, and based around determining

the initial strain that would lead to failure at 105 load cycles (the tolerable strain), led to more consistent

findings.

Whilst there was still a large amount of variation in the estimated tolerable strains, even after an attempted

normalisation of those strains to represent a single density condition, comparison of the mean tolerable

strain values for each load shape generally showed that the relative damage caused by different numbers

of axles within a load shape was relatable to the difference in the number of axles within the group.

This relationship between relative damage and axle count is the same as that determined for asphalt in

Section 7. Accordingly, it is suggested that the same method to relate damage caused by a loaded

multiple-axle group proposed for asphalt also be used for cemented material. This would entail determining

the damage (using Equation 46) resulting from each axle load and each axle group within a traffic load

distribution.

𝐷𝑛 = ∑ (

휀𝑖

𝑘)

12𝑛

𝑖=1

46

where

𝐷𝑛 = damage caused by axle group with 𝑛 axles


휀𝑖 = peak tensile strain under each axle 𝑖 of the axle group

𝑘 = constant



In order to determine whether this more rigorous approach to modelling the axle load/group traffic

distribution yields significantly different design outcomes to the current Austroads process, a series of

design examples are examined in Section 9 of this report.



9. Framework to Incorporate Multiple-axle

Responses in Flexible Pavement Design

9.1 Empirical Design of Unbound Granular Pavements with Thin

Bituminous Surfacing

The current Austroads pavement design procedure for unbound granular pavements with thin bituminous

surfacings is a chart-based empirical procedure which characterises the design traffic in terms of

Equivalent Standard Axles (ESA).

Whilst the results of the ALF experiments detailed in Section 6 were scattered, it was concluded that the

results did not indicate any reason to alter current standard loads used to determine design ESAs. Hence,

no change is proposed to the design method using the empirical design chart.

9.2 Mechanistic Design of Bound Materials

9.2.1 Modelling Each Axle Group/Load Combination

Section 7 concluded that grouped pulses of equal strain, simulating grouped axles, did not cause any

significantly different asphalt fatigue damage to that caused by the same number of ungrouped pulses.

That is, there is no damaging or ameliorating effect of grouping strain pulses. Section 8 reached the same

conclusion regarding the fatigue damage resulting from grouped pulses of equal load level.

Section 7 also concluded that the grouping of axles has an effect on the magnitude of the peak tensile

asphalt strains developed, and that the magnitude of this effect is dependent upon the pavement structure

being considered. A similar exercise conducted for cemented material found the same dependence. This is

unsurprising, as the only significant difference between asphalt and cemented materials when response-to-

load modelling is conducted in the Austroads design context is the Poisson’s ratio used for the material

(0.4 for asphalt, 0.2 for cemented materials).

Therefore, the multiple-axle standard loads used to equate tensile strain associated damage to bound

materials are dependent upon the pavement structure.

The current Austroads processes for mechanistic design of flexible pavements with bound layers uses a

single standard load, for each axle group, to transform an axle group/load distribution into a design count of

Standard Axle Repetitions (SAR5 for asphalt, and SAR12 for cemented materials). The composition of the

pavement structure does not have an impact upon the transformation.

The Austroads rigid pavement design process incorporates the calculation of damage associated with each

axle group and each load level on those axle groups within a design traffic load distribution. This approach

can also be used for flexible pavements, and doing so would align the rigid and flexible design traffic

calculations. Design of both pavement types would characterise the design traffic as a distribution of axle

groups and loads and a total expected number of Heavy Vehicle Axle Groups (HVAGs). Such an approach

would not make use of the standard load concept, but rather would consider the damage caused by the

strains developed by each combination of axle group and load level.

The steps would be:

1. Select a traffic load distribution, including the proportion of axle group types and the range of loads on

those groups.

2. Determine the design number of heavy vehicle axle groups (HVAGs).

3. Using steps one and two, determine the number of expected repetitions of each axle group and load

level combination expected in the design period.



4. Select a candidate pavement structure.

5. Calculate the response-to-load of the candidate structure for each axle group and load combination.

Determine the peak tensile strain response for each bound material layer under each axle within the

modelled group. These peaks should be determined under the tyre of single-tyre axles, and both under

the innermost tyre and between the tyres of dual-tyred axles.

6. For these strain responses, determine the allowable loading for each axle group and load using

Equation 47. The allowable loading for the combination shall be the minimum of the results obtained

under the tyre of single-tyre axles, and both under the innermost tyre and between the tyres of dual-

tyred axles. Note, an upper limit of strain to account for maximum material breaking strain should be

considered.

𝑁 =

1

∑ (휀𝑖

𝑘)

𝑆𝐷𝐸𝑛𝑖=1

47

where

𝑁 = allowable loading repetitions for an axle group and load level combination


휀𝑖 = tensile strain under axle 𝑖

𝑘 = constant (values would remain unchanged from current Austroads practice)

𝑆𝐷𝐸 = strain damage exponent (5 for asphalt, 12 for cemented materials)

7. For each axle group and load combination, determine the percentage damage that will occur in the

design period by dividing the expected loading repetitions of that combination (step three) by the

allowable loading repetitions for the combination (step six).

8. Sum the percentages of damage for all axle group types and load levels.

9. If the sum determined in step 8 is less than or equal to 100% for each bound material layer, the

candidate pavement structure is acceptable. If step 8 is greater than 100%, a new candidate structure

must be selected and the process repeated from step 4.

9.2.2 Scaling Response-to-load Calculations for Different Load Levels

Step five of the process outlined above would require running the linear-elastic response-to-load model for

each combination of axle group and load in the group/load distribution. Unless the radius of the loaded area

changes, the responses calculated by linear-elastic models are linearly proportional to the load applied. In

such cases, only a single calculation is needed for each axle group type, at an arbitrary load level, from

which the results for all load levels can be linearly determined. However, if the load contact area also

changes, then scaling of results will not provide exactly the same results as direct calculation.

Section 10.5.4 demonstrates that the difference in direct calculation and scaled calculations is not

significant.

9.2.3 Excluding Superposition of Responses – Considering Isolated Axles

The method described in Section 9.2.1 differs from the current SARs approach in two significant ways:

Unlike the SARs method, the above approach considers the peak strain response developed by each

axle within a multiple-axle group for each group/load combination within the design traffic distribution.

This means that the damage associated with a group comprised of 𝑛 axles with a load of 𝐿 is the same

as 𝑛 times the damage caused by a single axle loaded with 𝐿/𝑛.

Additionally, the grouping of axles can, by means of superposition of strain responses, affect the peak

strain obtained under each axle within the group.



A simplification of the method outlined in Section 9.2.1 can be made by only considering the first of these

points. In effect, this would be to consider that the damage caused by each axle within an axle group was

independent of the presence of other axles within the group. When conducting response-to-load modelling

for this simplified method, only responses under single axles need to be determined.

This simplified process would be the same as listed in Section 9.2.1, with the following replacements for

steps five and six:

Step 5 (a): Divide each multiple-axle group, for each load level, into a series of single axles with a load

equal to the group load divided by the number of axles in the group. Calculate the response-to-load for

the candidate structure for all of the resulting single axles at their assigned load levels.

Step 5 (b): Determine the peak tensile strain response, for each bound material layer, under each axle.

These peaks should be determined under the tyre of single-tyre axles and both under the innermost

tyre and between the tyres of dual-tyred axles.

Step 6: For these strain responses, determine the allowable loading for each axle load using

Equation 48. The allowable loading for the combination shall be the minimum of the results obtained

under the tyre of single-tyre axles and both under the innermost tyre and between the tyres of dual-

tyred axles.

𝑁 =

1

𝑛× (

𝑘

휀𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑)

𝑆𝐷𝐸

48

where

𝑁 = allowable loading for axle group caused by axle group and load level

combination


휀𝑖𝑠𝑜𝑙𝑎𝑡𝑒𝑑 = tensile strain under single axle with load equal to the group load divided by 𝑛

𝑘 = constant (values would remain unchanged from current Austroads practice)

𝑆𝐷𝐸 = strain damage exponent (5 for asphalt, 12 for cemented materials)



10. Determination of Characteristic Values of

Parameters for multiple-axle group Modelling

and Example Design Outcomes

10.1 Introduction

Section 9.2 describes two alternative frameworks for incorporating multiple-axle group modelling into the

mechanistic design process for flexible pavements:

modelling constituent axles of groups as isolated axles

modelling of combined multiple-axle groups.

This section of the report demonstrates the difference in design thicknesses that could arise from using

these frameworks when compared to the current SARs method, and example calculations were

undertaken. Additionally, when considering the modelling of combined multiple-axle groups, the effect of

changing the spacing of axles within groups, and of dynamic loading effects, are also examined. Using the

findings of these analyses, characteristic values for axle spacing and dynamic load parameters are

proposed.

10.2 Design Traffic Distributions

In conducting the design analyses, four design traffic distributions, representing urban highway/motorway traffic for which asphalt and cemented material pavement structures would be common candidates, were used. The distributions had previously been used in the preparation of Appendix D of the Austroads Guide to Pavement Technology: Part 2 – Pavement Structural Design (Austroads 2012a), and Table 10.1 shows how the short names used to identify these distributions within this report relates to the full details of the distribution as listed in the Guide. The four distributions are listed in Appendix K.

Table 10.1: Axle group/load distributions used in example calculations

Short name Full details as listed in Austroads (2012a) ESA/HVAG

Pacific Motorway Pacific Highway (Pacific Motorway) Hotham Creek S (10036) 1.93

Pacific Highway 2010 Pacific Hwy (HW2) HVCS: 12 Mile Creek, Southbound (251) 0.95

Monash Freeway Monash Freeway (Greater Dandenong) East (see) 0.76

Kwinana Freeway Kwinana Freeway (Mandurah) South (50164) 1.05

10.3 Design Pavement Structures

Separate assessments were made on the effect of modelling axle group/load distributions for asphalt and

cemented materials. For each material assessment, the remaining material layers within the candidate’s

structures were kept constant, and the thickness of bound material that would be required to withstand

fatigue was determined for a range of design HVAG levels. The thickness required was also determined

using the current Austroads processes by determining the design SAR5 and SAR12 values represented by

the traffic load distributions and HVAG levels.

To assess the effect of modelling approaches on the determination of asphalt thickness, the pavement

composition shown in Table 10.2 was used. Candidate asphalt thickness was varied in 1 mm amounts, and

asphalt thicknesses below 40 mm were not considered. Separate analyses were conducted for two

different asphalt stiffness, 3000 and 5000 MPa.



Table 10.2: Parameters used in asphalt pavement design cases

Parameter Value

Asphalt thickness Minimum thickness determined

Asphalt modulus (isotropic) 3000 MPa and 5000 MPa

Asphalt Poisson’s Ratio 0.4

Volume of bitumen in asphalt 11%

Granular thickness 300 mm – modelled in five sublayers with modulus varying as per Austroads (2012a) design rules

Granular modulus (cross-anisotropic: 𝐸𝑣 = 2𝐸ℎ)

500 MPa maximum vertical modulus – actual modulus dependent upon thickness of asphalt and subgrade stiffness as per Austroads (2012a) design rules

Granular Poisson’s Ratio 0.35

Subgrade vertical modulus (cross-anisotropic: 𝐸𝑣 = 2𝐸ℎ)

70 MPa

Subgrade Poisson’s Ratio 0.45

The pavement composition shown in Table 10.3 was used to assess the effect of axle group/load

combination modelling approaches on the determination of cemented material thickness. An asphalt

thickness of 175 mm was used in all cases; this being the minimum thickness of cover over cemented

materials to inhibit reflection cracking (Austroads 2012a). Candidate thickness was varied in 1 mm

increments, with a minimum thickness of 100 mm selected. An analysis was conducted for a typical

cemented material with a design modulus of 4000 MPa. Additionally, analysis was conducted using

presumptive properties for a lean mix concrete subbase and the untested assumption that the summed

peaks model determined for cemented materials was applicable.

Table 10.3: Parameters used in cemented material pavement design cases

Parameter Value

Asphalt thickness 175 mm

Asphalt modulus (isotropic) 3000 MPa

Asphalt Poisson’s Ratio 0.4

Cemented material (isotropic) 4000 MPa cemented material (𝑘 = 308)(1) and lean mix concrete (𝐸 = 10 000 MPA, 𝑘 = 260)

Cemented material thickness Minimum thickness determined (100 mm minimum thickness)

Cemented material Poisson’s Ratio 0.2

Subgrade vertical modulus (cross-anisotropic: 𝐸𝑣 = 2𝐸ℎ)

70 MPa

Subgrade Poisson’s Ratio 0.45

1 Proposed as presumptive design values for cemented material in Austroads (2014b).

Thicknesses were determined for discrete levels of HVAGs, selected to represent the range of traffic levels

and spaced so as to be evenly distributed on a logarithmic scale. The HVAG levels in the resultant tables

and figures have also been transformed into Equivalent Standard Axle (ESA) counts, using the ESA/HVAG

factors listed in Table 10.1, in order to assist those readers more familiar with expressing flexible pavement

design traffic in these units.

10.4 Modelling Constituent Axles of Groups as Isolated Axles

Table 10.4 and Table 10.5 present the minimum asphalt and cemented material thicknesses determined

using the current Austroads design approach and the isolated axles approach (Section 9.2.3). A single

design traffic distribution was used in conducting these analyses – the effect of design traffic distribution

selection is examined in Section 10.5.6. The tables also include the results of modelling grouped axles

(Section 9.2.1) – these results are discussed later in Section 10.5.



In determining the strain responses resulting from a specific group/load combination, the strains generated

by an arbitrary load were linearly scaled as described in Section 9.2.2. Section 10.5.4 discusses the

insignificant differences between the results using this simplification and the results obtained by specifically

modelling each axle load individually.


damage models (Pacific Motorway traffic distribution)

HVAGs ESAs Minimum asphalt thickness (mm)

Austroads Isolated axles

Sec. 10.4

Grouped at 1.0 m

spacing

Sec. 10.5.2

Grouped at 1.3 m

spacing

Sec. 10.5.2

Grouped at 1.5 m

spacing

Sec. 10.5.2

Grouped at 1.3 m

spacing (calc.)

Sec. 10.5.3

3000 MPa asphalt

1 x 105 2 x 105 75 76 78 79 79 72

3 x 105 6 x 105 108 106 105 107 107 104

1 x 106 2 x 106 151 144 139 141 142 139

3 x 106 6 x 106 191 181 174 176 177 176

1 x 107 2 x 107 234 219 207 209 211 210

3 x 107 6 x 107 278 259 243 245 247 246

1 x 108 2 x 108 332 308 289 290 292 291

3 x 108 6 x 108 387 359 333 338 338 339

5000 MPa asphalt

1 x 105 2 x 105 73 72 73 74 74 70

3 x 105 6 x 105 101 97 96 97 98 95

1 x 106 2 x 106 140 113 128 130 131 128

3 x 106 6 x 106 169 162 155 157 158 157

1 x 107 2 x 107 207 194 184 186 187 186

3 x 107 6 x 107 246 229 216 217 218 217

1 x 108 2 x 108 294 273 255 257 258 258

3 x 108 6 x 108 343 318 295 299 300 299



Table 10.5: Minimum thicknesses of cemented material determined using current Austroads and

multiple-axle damage models (Pacific Motorway traffic distribution)

HVAGs ESAs Minimum cemented material thickness (mm)

Austroads Isolated axles

Sec. 10.4

Grouped at 1.0 m

spacing

Sec. 10.5.2

Grouped at 1.3 m

spacing

Sec. 10.5.2

Grouped at 1.5 m

spacing

Sec. 10.5.2

Grouped at 1.3 m

spacing (calc.)

Sec. 10.5.3

4000 MPa cemented material

1 x 105 2 x 105 161 135 121 122 123 123

3 x 105 6 x 105 181 154 139 140 140 141

1 x 106 2 x 106 204 175 159 161 161 162

3 x 106 6 x 106 226 195 179 179 180 180

1 x 107 2 x 107 251 219 202 201 203 202

3 x 107 6 x 107 276 241 225 222 223 222

1 x 108 2 x 108 304 268 252 247 247 249

3 x 108 6 x 108 331 293 279 271 271 274

10 000 MPa lean mix concrete

1 x 105 2 x 105 100 100 100 100 100 100

3 x 105 6 x 105 114 100 100 100 100 100

1 x 106 2 x 106 132 110 100 100 100 100

3 x 106 6 x 106 150 126 114 115 115 116

1 x 107 2 x 107 170 144 131 132 132 133

3 x 107 6 x 107 189 162 149 148 149 149

1 x 108 2 x 108 210 182 169 167 168 168

3 x 108 6 x 108 231 202 189 186 186 187

In comparison to the asphalt and cemented material thicknesses determined using the current Austroads

approach, Table 10.4 and Table 10.5 demonstrate that lower thicknesses result from calculating the strain

generated by each axle within groups, assuming no interaction between axles, and directly determining the

damage associated with each axle.

The reduction in asphalt thickness (Table 10.4) changes from relatively little to no reduction at low traffic

levels, and rises up to 20–30 mm at high traffic levels (a 7–8% reduction). The significant reductions in

cemented material thickness of 25–40 mm represent proportional reductions of between 11 and 16%.

Thus, by directly considering the damage caused by each axle of a multiple-axle group, in complete

isolation to its partner axles within the group, significant reductions in asphalt and cemented material

thickness can be obtained in comparison to those determined using the current Austroads design method.

10.5 Modelling of Combined Multiple-axle Groups

10.5.1 General

The design approach proposed in Section 9.2.1 entails separate modelling of each axle group type, at each

load level within the design traffic distribution, and determining the resultant peak strains under each axle

within the group. This section of the report examines the significance of both the assumed axle spacing

within the modelled groups and dynamic loading considerations on the outcomes of the design process.



10.5.2 Axle Spacing

The spacing of axles within a multiple-axle group will affect the combined strain response associated with

the combined group. In the modelling described in Section 7, a spacing of 1.25 m was used for tandem,

triaxle and quad-axle groups. That value was selected at the time that the modelling was conducted as it

represented the typical spacing for triaxle groups. This section of the report examines whether differences

in modelled axle spacings result in significantly different design outcomes, therefore a range of spacings

were considered.

Weigh-in-motion (WIM) data was used to ascertain the axle spacings that most commonly occur in vehicles

in use at present. Data from a range of Melbourne WIM sites, collected over a six-month period, were

obtained and the 50–90 percentile values of the axle spacing were determined (Table 10.6). The mean

spacing for the combined data was 1.30 metres.

Table 10.6: Axle spacings determined from WIM data

Axle group Observations Percentiles of axle spacing (m)

50 90 95 97.5 99

Tandem 7 934 798 1.31 1.40 1.45 1.55 1.93

Triaxle 4 571 459 1.25 1.41 1.50 1.54 1.56

In order to examine the effect that axle spacing has on the calculated design thicknesses, calculations were

conducted assuming different spacings:

1.5 m – representing the 95th percentile of axle spacings for triaxle groups within the WIM data

summarised in Table 10.6 (the 95th percentile of the spacing of tandem groups was slightly lower, at

1.45 m)

1.3 m – representing the median of tandem groups and the mean of tandem and triaxle groups within

the WIM data summarised in Table 10.6

1.0 m – representing an extreme lower bound.

The results of these calculations are listed above in Table 10.4 and Table 10.5. The difference in asphalt

and cemented material thicknesses that result from using the extremes of this range of axle spacings can

be seen to be 3 mm or less. The computed design thicknesses using the mean spacing of 1.3 mm and the

95th percentile spacing of 1.5 m are generally identical, with only the occasional 1 to 2 mm difference.

It is concluded that the choice of axle spacing does not need to play a critical role in the design process

proposed in Section 9.2.1. It is suggested that a value of 1.3 m be used as the spacing between adjacent

axles on all tandem, triaxle and quad-axle groups in that process, as this was the average spacing

determined from the WIM data. This is the value that has been used in the following sections of this report.

10.5.3 Effect of Superimposing Responses from Grouped Axles

Having determined that an axle spacing of 1.3 m is suitable for modelling tandem, triaxle and quad-axle

groups, a comparison of the minimum asphalt and cemented material thicknesses that result from using the

design approach proposed in Section 9.2.1 was made.

Generally lower asphalt thicknesses were determined when using this grouped method in comparison to

the isolated axles method (Table 10.4). This difference is solely the result of the potential reduction in peak

values resulting from super-positioning strains from adjacent axles within an axle group. The difference

between the isolated axles method and the grouped axles method is generally smaller than the difference

between the isolated axles method and the current Austroads method.

The difference in asphalt thickness determined using the proposed grouped axles approach and the current

Austroads approach varies from little-to-no reduction at low traffic levels, and increases with traffic level

rises up to a 40–50 mm (13%) reduction at the highest levels considered.



As shown in Table 10.5, the results of the cemented materials design analyses followed the same trends

as the asphalt designs. Total reductions in the 4000 MPa cemented material thickness of 55–60 mm

occurred at the highest traffic level considered. Maximum reductions for the lean mix concrete were 40–

45 mm. These represent potential cemented material thickness reductions of up to 18–20%.

Super-positioning will only result in lower peak strain values for strain responses that include a significant

compressive component, such as strains in the longitudinal direction. Strains in this direction were found to

be the most critical strains, i.e. they had the highest magnitudes in all cases examined.

10.5.4 Comparison of Scaled and Calculated Responses

As raised in Section 9.2.2, with a fixed radius of load, the responses calculated by linear-elastic models are

linearly proportional to the load applied. In such cases, only a single calculation is needed for each axle

group type, at an arbitrary load level, from which the results for all load levels can be linearly determined.

The results described in Section 10.4, 10.5.2 and Section 10.5.3 were obtained from response-to-load

calculations that were scaled in this manner, from response-to-load calculations conducted at a single load

level for each axle group type.

As change in both contact area radius and tyre pressure can be assumed to occur with change in axle load

(Section 7.2.2), it can be seen that the above linear scaling of responses is a simplification.

In order to determine whether this simplified scaling of responses is unreasonable, individual modelling of

each individual axle group type and load combination was also undertaken. The minimum asphalt and

cemented material thicknesses determined using these calculations is presented as the last column in

Table 10.4 and Table 10.5, respectively. For all but the lowest design traffic levels, the difference in asphalt

thickness determined using the simplified scaled approach and the rigorous individually modelled

approach, can be seen to be no more than 2 mm. At low traffic levels, with corresponding low asphalt

thicknesses, the difference between the two methods is larger – up to 7 mm. Differences in cemented

material thickness were found to be no more than 2 mm.

Given these results, it is considered that conducting a separate response-to-load model for each axle group

type and load combination does not result in significantly different design results to those obtained by

scaling the responses, for each group type, obtained at a single load level.

10.5.5 Dynamic Load Considerations

All of the analyses described above have considered that the total load applied to a multiple-axle group is

equally distributed amongst the constituent axles of the group. Whilst this assumption may be reasonable

for static loads, it has been demonstrated (e.g. Sweatman 1983) that this equal distribution of load may not

occur under travelling conditions. This section of the report considers the effect on design outcomes if

unequal distribution of load between axles within a group is considered.

It is recognised (e.g. OECD 1998) that, dependent upon chassis and suspension characteristics and

pavement surface profile, the magnitude of total load on an axle group may exceed the static load on the

group. This report does not directly examine this dynamic effect for the following reasons:

The current Austroads flexible pavement design process does not explicitly consider such effects.

Design traffic distributions are determined from WIM data that does include the instantaneous

measurement of total dynamic loads at a single point along the pavement at which the data collection

system is located. Whilst it is typically ensured that the road surface profile at weigh-in-motion sites is

smooth so as to reduce contribution to dynamic effects, these smooth profiles also reflect typical road

profiles of newly constructed pavements.



The Austroads pavement design procedure utilises the response-to-load modelling of newly

constructed pavement structures – comprised of pavement materials in an undamaged condition – and

does not consider variations in pavement material condition along the length of pavement, or over the

passage of time. Such newly constructed pavements have good ride quality, similar to weigh-in-motion

sites. Direct consideration of dynamic load effects with length of pavement, or elapsed time, is,

therefore, incompatible with the structure of the current design approach, and would require the

utilisation of an incremental-recursive response-to-load modelling approach. Within the framework of

the current Austroads design approach, indirect consideration of increased vertical loads resulting from

dynamic loading is considered to be a component of the reliability factors used to link material

performance relationships to observed field performance.

Therefore, the following discussion is limited to consideration of the unequal sharing of dynamic total group

loads, measured at WIM sites, by the component axles of the group.

The parameter that is most commonly used to examine load sharing between axles of a multiple-axle group

is the Load Sharing Coefficient (𝐿𝑆𝐶). First proposed by Sweatman (1983), the 𝐿𝑆𝐶 for an axle within a

group is typically expressed in modern times as Equation 49.

𝐿𝑆𝐶𝑖 =

𝑛 × 𝐹𝑖

𝐹𝑔𝑟𝑜𝑢𝑝

49

where

𝐿𝑆𝐶𝑖 = load sharing coefficient for axle 𝑖

𝐹𝑖 = load on axle 𝑖 (kN)

𝐹𝑔𝑟𝑜𝑢𝑝 = total load on axle group (kN)

𝑛 = number of axles within group

Six months’ worth of data from numerous WIM sites around metropolitan Melbourne were obtained from

VicRoads. The WIM equipment at these sites contained multiple sensors, allowing the determination of

individual axle masses with axle groups. Using Equation 49, the maximum 𝐿𝑆𝐶 for each observed axle

group was determined, and is summarised in Figure 10.1 and Table 10.7. Mean maximum 𝐿𝑆𝐶s for both

tandem and triaxle groups were found to be 1.05.

Figure 10.1: Distribution of maximum LSC in WIM data

(a) tandems (b) triaxles



Table 10.7: Maximum axle load sharing coefficients determined from WIM data

Axle group Observations Percentiles of maximum 𝑳𝑺𝑪

50 90 95 97.5 99

Tandem 7 934 798 1.03 1.11 1.16 1.24 1.36

Triaxle 4 571 459 1.02 1.12 1.17 1.24 1.34

The design examples were re-analysed assuming that all tandem and triaxle groups in the design traffic

distribution had uneven load sharing between axles, and that the maximum 𝐿𝑆𝐶 was 1.1 (approximately the

90th percentile of the observed maximum 𝐿𝑆𝐶s). In running these examples, it was assumed that the

minimum 𝐿𝑆𝐶 of the tandem and axle groups was equal to 0.1, and that the middle axle of a triaxle group

had an 𝐿𝑆𝐶 of 1.0. The minimum asphalt and cemented material thicknesses are shown in Table 10.8 and

Table 10.9, respectively.


damage models (Pacific Motorway traffic distribution)


Austroads Isolated axles Grouped 𝑳𝑺𝑪 = 1.0 Grouped 𝑳𝑺𝑪 = 1.1

3000 MPa asphalt

1 x 105 2 x 105 75 76 79 80

3 x 105 6 x 105 108 106 107 107

1 x 106 2 x 106 151 144 141 143

3 x 106 6 x 106 191 181 176 177

1 x 107 2 x 107 234 219 209 211

3 x 107 6 x 107 278 259 245 248

1 x 108 2 x 108 332 308 290 294

3 x 108 6 x 108 387 359 338 342

5000 MPa asphalt

1 x 105 2 x 105 73 72 74 74

3 x 105 6 x 105 101 97 97 98

1 x 106 2 x 106 140 131 130 131

3 x 106 6 x 106 169 162 157 158

1 x 107 2 x 107 207 194 186 187

3 x 107 6 x 107 246 229 217 219

1 x 108 2 x 108 294 273 257 260

3 x 108 6 x 108 343 318 299 303




multiple-axle damage models (Pacific Motorway traffic distribution)




1 x 105 2 x 105 161 135 122 128

3 x 105 6 x 105 181 154 140 146

1 x 106 2 x 106 204 175 161 167

3 x 106 6 x 106 226 195 179 187

1 x 107 2 x 107 251 219 201 210

3 x 107 6 x 107 276 241 222 233

1 x 108 2 x 108 304 268 247 260

3 x 108 6 x 108 331 293 271 287


1 x 105 2 x 105 100 100 100 100

3 x 105 6 x 105 114 100 100 100

1 x 106 2 x 106 132 110 100 104

3 x 106 6 x 106 150 126 115 120

1 x 107 2 x 107 170 144 132 138

3 x 107 6 x 107 189 162 148 155

1 x 108 2 x 108 210 182 167 176

3 x 108 6 x 108 231 202 186 196

It can be seen that assuming a maximum 𝐿𝑆𝐶 for each multiple-axle group had only a very minor effect on

the calculated minimum asphalt thickness for the design cases (Table 10.8). Thicknesses determined using

the uneven load distribution were higher than the case assuming perfect load sharing, as would be

expected, but the maximum thickness increase was only 4 mm.

With a load damage exponent of 12 in the cemented material performance model, cf. a value of 5 for

asphalt, it would be expected that the uneven load sharing within groups would lead to higher design

thicknesses. Table 10.9 does show a more significant effect of uneven load sharing on the determined

cemented material thicknesses than that observed for asphalt thicknesses. In comparison to the design

cases which assumed perfect load sharing between axles, additional cemented material thickness of up to

16 mm was found.

The modelling of uneven load sharing between axles clearly has an effect, especially on cemented material

design thicknesses. However, the challenge is to determine what level of assumed uneven load sharing is

reasonable to consider in the design process. The selection of a maximum 𝐿𝑆𝐶 value of 1.1 used for the

analyses presented in Table 10.8 and Table 10.9 was made solely on the basis that this value represented

the 90th percentile of the maximum 𝐿𝑆𝐶s observed in the extensive VicRoads WIM data.

In order to determine whether this value was reasonable, additional design analyses were conducted in

which the maximum 𝐿𝑆𝐶s for each axle group were selected from a range of 𝐿𝑆𝐶s observed in the WIM

data. That is, instead of assuming a single maximum 𝐿𝑆𝐶 for all groups within the design HVAG count, the

maximum 𝐿𝑆𝐶 was varied in the same proportions as the observed WIM data.

For the asphalt design examples, it was found that modelling the full spectrum of maximum 𝐿𝑆𝐶s produced

the same asphalt thicknesses as analyses with a maximum 𝐿𝑆𝐶 of 1.05 applied to all axle groups. For the

cemented material design examples, it was found that a single maximum 𝐿𝑆𝐶 of 1.07 produced the same

design outcomes as modelling the complete spectrum of maximum 𝐿𝑆𝐶 values.



As the use of a single maximum 𝐿𝑆𝐶 value of 1.1 produced only slightly more conservative design

outcomes than the complex and time-consuming analyses required to model a full spectrum of maximum

𝐿𝑆𝐶 values, it is proposed that a single value of 1.1 be used in implementing uneven load sharing within the

pavement design procedure.

10.5.6 Significance of Design Traffic Distribution

The detailed modelling and conclusions discussed above were all based upon a single traffic distribution.

That distribution was selected as it represented an extreme case with a high proportion of heavily loaded

axle groups, and it was assumed that the determination of a suitable maximum 𝐿𝑆𝐶 based upon that

distribution could be conservatively applied to other distributions.

Having determined that an 𝐿𝑆𝐶 value of 1.1 was appropriate, Table 10.10 to Table 10.15 list the minimum

asphalt and cemented materials thicknesses determined using the three other traffic spectrums listed in

Table 10.1. Figure 10.2 to Figure 10.5 graphically presents these minimum thicknesses. In these tables

and figures, the following terms are used to describe the manner in which the axle loads were modelled:

Austroads – damage calculated using current Austroads design approach (i.e. converting the traffic

distribution and HVAG level to a number of SAR5 for asphalt, and SAR12 for cemented materials, and

by modelling the candidate structure under a Standard Axle load).

Isolated axles – damage calculated using the simplified approach described in Section 9.2.3, which

undertakes a response-to-load determination for each axle group/load combination by modelling the

response under a single axle and assuming the same response occurs under each other axle within a

multi-axle group (only the scaled method was used).

Grouped axles – damage calculated using the approach described in Section 9.2.1, which undertakes

a response-to-load determination for each axle group/load combination by modelling the full axle group

for each case. Uneven load sharing was modelled with an 𝐿𝑆𝐶 of 1.1. Response to load analyses for

varying load levels on an axle group were linearly scaled from a single linear elastic analysis

conducted for the axle group.

Modelling with the isolated axles method resulted in generally lower asphalt thicknesses than the current

Austroads approach. The reduction in thickness changes from relatively little to no reduction at low traffic

levels, and rises up to 17–31 mm at high traffic levels (a 6–8% reduction). Thus, by considering each axle

of a multiple-axle group in complete isolation to its partner axles within the group, a significant reduction in

asphalt thickness can be achieved for moderate-to-highly trafficked pavements.

Generally, lower asphalt thicknesses were determined when modelling the grouped axles (with an 𝐿𝑆𝐶 of

1.1) in comparison to modelling the isolated axles. This difference is solely the result of a potential

reduction in peak values resulting from super-positioning strains from adjacent axles within an axle group.

The difference between the isolated and grouped methods is generally smaller than the difference between

the isolated and current Austroads methods. The difference between grouped and Austroads methods

varies from little to no reduction at low traffic levels, and increases as traffic levels rise up to a 31–46 mm

reduction at the highest levels considered. This represents an 11–13% reduction in asphalt thickness.

Super-positioning will only result in lower peak strain values for strain responses that include a significant

compressive component, such as strains in the longitudinal direction. Strains in this direction were found to

be the most critical strains, i.e. they had the highest magnitudes in all cases examined.

The results of the cemented materials design analyses followed the same trends as the asphalt designs. A

substantial decrease in cemented material thickness occurred for both materials and for all traffic

distributions at moderate-to-high traffic loadings when the single method was used instead of the current

Austroads SAR12 method. A potential second decrease in design cemented material thickness results from

consideration of the strain reducing effect of superimposing responses from adjacent axles within a group.

Total reductions in the 4000 MPa cemented material thickness of 44–56 mm (13–20%) occurred at the

highest traffic level considered. Maximum reductions for the lean mix concrete were

31–43 mm (18–22%).



Table 10.10: Minimum thicknesses of asphalt determined using current Austroads and multiple-

axle damage models (Pacific Highway traffic distribution)



3000 MPa asphalt

1 x 105 1 x 105 40 40 40 40

3 x 105 3 x 105 80 80 83 84

1 x 106 1 x 106 115 112 112 113

3 x 106 3 x 106 156 149 145 147

1 x 107 1 x 107 200 188 181 183

3 x 107 3 x 107 240 223 212 214

1 x 108 1 x 108 289 268 252 255

3 x 108 3 x 108 339 313 293 297

5000 MPa asphalt

1 x 105 1 x 105 40 40 50 51

3 x 105 3 x 105 76 75 77 78

1 x 106 1 x 106 109 104 104 105

3 x 106 3 x 106 145 140 133 134

1 x 107 1 x 107 176 170 162 163

3 x 107 3 x 107 212 200 188 190

1 x 108 1 x 108 255 240 223 225

3 x 108 3 x 108 300 280 260 263


multiple-axle damage models (Pacific Highway traffic distribution)




1 x 105 1 x 105 110 100 100 100

3 x 105 3 x 105 128 100 100 100

1 x 106 1 x 106 148 118 106 111

3 x 106 3 x 106 167 136 123 128

1 x 107 1 x 107 189 156 142 148

3 x 107 3 x 107 210 175 160 166

1 x 108 1 x 108 235 198 180 188

3 x 108 3 x 108 258 219 200 210


1 x 105 1 x 105 100 100 100 100

3 x 105 3 x 105 100 100 100 100

1 x 106 1 x 106 100 100 100 100

3 x 106 3 x 106 103 100 100 100

1 x 107 1 x 107 121 100 100 100

3 x 107 3 x 107 137 111 100 104

1 x 108 1 x 108 157 128 117 122

3 x 108 3 x 108 175 145 132 138




axle damage models (Monash Freeway traffic distribution)



3000 MPa asphalt

1 x 105 8 x 104 40 40 40 40

3 x 105 2 x 105 67 72 77 77

1 x 106 8 x 105 108 107 107 108

3 x 106 2 x 106 147 141 138 139

1 x 107 8 x 106 192 182 176 177

3 x 107 2 x 107 231 216 206 208

1 x 108 8 x 107 279 259 245 247

3 x 108 2 x 108 328 304 286 288

5000 MPa asphalt

1 x 105 8 x 104 40 40 40 40

3 x 105 2 x 105 70 70 72 72

1 x 106 8 x 105 101 98 98 99

3 x 106 2 x 106 137 130 127 128

1 x 107 8 x 106 170 162 157 158

3 x 107 2 x 107 204 191 183 184

1 x 108 8 x 107 247 229 217 219

3 x 108 2 x 108 291 269 253 255


multiple-axle damage models (Monash Freeway traffic distribution)



4 000 MPa cemented material

1 x 105 8 x 104 107 100 100 100

3 x 105 2 x 105 125 102 100 100

1 x 106 8 x 105 145 121 111 114

3 x 106 2 x 106 164 139 128 132

1 x 107 8 x 106 186 159 148 152

3 x 107 2 x 107 207 179 166 171

1 x 108 8 x 107 231 201 187 193

3 x 108 2 x 108 254 223 208 215


1 x 105 8 x 104 100 100 100 100

3 x 105 2 x 105 100 100 100 100

1 x 106 8 x 105 100 100 100 100

3 x 106 2 x 106 100 100 100 100

1 x 107 8 x 106 118 100 100 100

3 x 107 2 x 107 134 113 104 107

1 x 108 8 x 107 154 131 121 125

3 x 108 2 x 108 172 148 137 141




axle damage models (Kwinana Freeway traffic distribution)


Austroads Isolated axles Grouped

𝑳𝑺𝑪 = 1.0 Grouped 𝑳𝑺𝑪 = 1.1

3000 MPa asphalt

1 x 105 8 x 104 40 40 49 51

3 x 105 2 x 105 87 86 89 89

1 x 106 8 x 105 122 118 117 118

3 x 106 2 x 106 165 156 151 153

1 x 107 8 x 106 207 195 186 188

3 x 107 2 x 107 248 230 218 220

1 x 108 8 x 107 299 276 258 261

3 x 108 2 x 108 350 322 300 304

5000 MPa asphalt

1 x 105 8 x 104 50 52 57 57

3 x 105 2 x 105 82 80 82 82

1 x 106 8 x 105 116 111 110 111

3 x 106 2 x 106 151 142 138 140

1 x 107 8 x 106 183 172 166 167

3 x 107 2 x 107 219 204 193 195

1 x 108 8 x 107 264 244 228 231

3 x 108 2 x 108 310 285 266 269


multiple-axle damage models (Kwinana Freeway traffic distribution)


Austroads Isolated axles Grouped

𝑳𝑺𝑪 = 1.0 Grouped 𝑳𝑺𝑪 = 1.1


1 x 105 1 x 105 130 100 100 100

3 x 105 3 x 105 149 116 105 108

1 x 106 1 x 106 170 135 123 127

3 x 106 3 x 106 190 153 140 144

1 x 107 1 x 107 213 174 160 165

3 x 107 3 x 107 236 195 179 185

1 x 108 1 x 108 262 218 200 208

3 x 108 3 x 108 286 241 222 230


1 x 105 1 x 105 100 100 100 100

3 x 105 3 x 105 100 100 100 100

1 x 106 1 x 106 105 100 100 100

3 x 106 3 x 106 121 100 100 100

1 x 107 1 x 107 140 110 100 103

3 x 107 3 x 107 157 126 115 119

1 x 108 1 x 108 177 144 132 137

3 x 108 3 x 108 197 162 148 154



Figure 10.2: Minimum thickness of 3000 MPa asphalt for different design traffic levels

(a) Pacific Motorway (b) Monash Freeway

(c) Pacific Highway (d) Kwinana Freeway



Figure 10.3: Minimum thickness of 5000 MPa asphalt for different design traffic levels





Figure 10.4: Minimum thickness of 4000 MPa cemented material for different design traffic levels





Figure 10.5: Minimum thickness of lean mix concrete for different design traffic levels



10.6 Summary

The linear-elastic and FEM analyses in Section 7 demonstrated that for pavements with asphalt

thicknesses of 100 mm or more, the current standard loads used in the Austroads SAR approach results in

less damage than that caused by the Standard Axle. The analyses showed that, for each axle group type,

the standard load that would cause the same damage as the Standard Axle was dependent upon the

pavement structure.

In order to take this variation into account in the pavement design process, the design process outlined in

Section 9.2 considers the damaging effects of each axle group type/load combination on the bound

materials within a candidate pavement structure. As a result, it is considerably more numerically intensive

than the current Austroads SAR approach.



The design example analyses described within this section of the report have demonstrated that at low

traffic levels, the additional complexity in calculation does not generally result in a significantly different

design outcome. However, for moderate traffic levels and above, the material thicknesses resulting from

the multiple-axle group method can be significantly lower than those determined from using the current

SAR approach.

It was found that the assumed spacing of axles with multiple-axle groups had little effect on design

outcomes. In the proposed alternative procedures, an axle spacing value of 1.3 m should be presumed to

apply to all tandem, triaxle and quad-axle groups.

Dynamic loading effects on design outcomes were also examined, and it was found that the determination

of cemented material design thicknesses was sensitive to the level of load sharing that was assumed to

occur within multiple-axle groups. When modelling grouped loads, it is suggested that uneven load sharing

be modelled and that an 𝐿𝑆𝐶 of 1.1 be used.



11. Conclusions

11.1 General

Different international pavement systems consider relative damage factors for multiple-axle groups in

various ways. The AASHTO (1993), French (LCPC & SETRA 1997) and AASHTO (2008) MEPDG design

methods all consider that the pavement structure affects relative damage factors, whereas the current

Austroads (2012a) approach considers the damage factors to be constant.

The AASHTO 1993 and French methods’ relative damage factors are lower than those currently used by

Austroads, resulting in higher equivalent loads on multiple-axle groups than those used in the Austroads

approach. The South African (SANRAL 2013) and MEPDG (AASHTO 2008) methods both determine

strains resulting from different axle groups. In doing so, these methods do not use relative damage factors,

but rather use the calculated strains from multiple-axle groups loaded directly in the pavement material

damage models. In general, these methods will result in higher multiple-axle group loads than the

Austroads loads to cause the same pavement damage.

A review of other methods highlighted a number of theoretical frameworks for considering the relative

damage caused by multiple-axle groups. However, only a very limited number of studies were identified

that examined the actual performance of pavement materials or structures when loaded with varying types

of multiple-axle groups. The focus of the project was on utilising the performance data that had been

collected, and collecting new performance data related to the pavement design performance criteria

considered in the current Austroads pavement design processes:

deformation of unbound granular pavements with thin bituminous surfacings – for use with the current

empirical, chart-based pavement design procedure

flexural fatigue of asphalt – for use with the mechanistic design procedure for flexible pavements

flexural fatigue of cemented materials – for use with the mechanistic design procedure for flexible

pavements.

The conclusions drawn from the work conducted for each of these design criteria is summarised below.

11.2 Empirical Design of Unbound Granular Pavements with Thin

Bituminous Surfacings

The Accelerated Loading Facility was used to assess the deformation of a typical granular pavement and

subgrade. A wide range of variation occurred between the deformation observed under the same loading

conditions but at different locations and times during the loading. This variation was attributed to wide

variations in the pavements’ moisture contents. Only a direct comparison of the deformation obtained under

an 80 kN single axle and a 180 kN triaxle group was possible. From this analysis, load equivalency factors

(𝐿𝐸𝐹) were found to range from 0.8 to 1.0 for most of the experiment test points – i.e. the 180 kN triaxle

group was found to have caused 0.8 to 1.0 times the damage caused by the 80 kN single axle. Lower 𝐿𝐸𝐹s

occurred for stiffer pavement structures (i.e. when the pavement materials were in a dryer moisture state)

than for weaker structures (when the moisture contents were presumed to be higher).

However, there was a significant degree of spread in the observed data and it is considered that the

experimental results cannot be reasonably considered to provide enough evidence that the currently used

standard load for triaxles of 181 kN (full axle) is inappropriate. The small difference in 𝐿𝐸𝐹 to current

practice (0.8 cf. 1.0) is insignificant in comparison to the variation in experimental results and the variety of

assumptions made in the analysis.



Accepting that the 𝐿𝐷𝐸 was four, and that the standard load for the (full) triaxle group was 181 kN (current

practice), it can be concluded that the interaction between axles does not affect the deformation damage,

and that the axles can be considered to each contribute to the overall damage in isolation to each other.

This assumption would allow the numerical calculation (Section 6.10) of standard loads for multiple-axle

groups for use with the empirical design procedure. This calculation results in the same (within 1 kN)

standard loads currently used in the Austroads procedure, with the exception of the quad-axle group, for

which the calculated standard load would be 226 kN rather than the current 221 kN.

It is proposed that the current standard reference load for a triaxle group of 181 kN be retained. It is also

proposed that the standard loads listed within the Austroads guide be those calculated using the formula

discussed in Section 6.10 and that the current analysis design processes be retained.

11.3 Mechanistic Design of Bound Materials

A laboratory-based study conducted in France (Homsi 2011) provided the basis for an examination of the

effect of multiple-axle group loads on the fatigue of asphalt for pavement design purposes. A similar study

was undertaken for cemented materials as part of this Austroads project. Both of these studies used pulses

simulating multiple-axle groups within existing flexural fatigue testing protocols. Analysis of the French

asphalt work indicated that grouped pulses of equal strain magnitude, simulating grouped axles, did not

cause any significantly different asphalt fatigue damage to that caused by the same number of ungrouped

pulses of the same magnitude. That is, there is no damaging or ameliorating effect of grouping strain

pulses. Analysis of the cemented material study data reached the same conclusion regarding the fatigue

damage resulting from grouped pulses of equal load level.

However, for both materials, it was demonstrated that the grouping of axles has an effect on the magnitude

of the peak strains developed, and that the magnitude of this effect is dependent upon the pavement

structure being considered. Therefore, the standard load used to equate tensile strain-associated damage

to bound materials is dependent upon the pavement structure.

The current Austroads process for mechanistic design of flexible pavements with bound layers uses a

single standard load, for each axle group, to transform an axle group/load distribution into a design count of

Standard Axle Repetitions (SAR5 for asphalt, and SAR12 for cemented materials). The composition of the

pavement structure does not have an impact upon the transformation.

The Austroads rigid pavement design process incorporates calculation of damage associated with each

axle group and each load level on those axle groups within a design traffic load distribution.

It is proposed that this approach also be used for flexible pavements. This approach would not make use of

the standard load concept, but rather would consider the damage caused by the strains developed by each

combination of axle group and load level. It would also align the rigid and flexible (mechanistic) design

traffic calculations into a common method – characterising the design traffic as a distribution of axle groups

and loads and a total expected number of HVAGs. The calculation and use of SAR5 and SAR7 would no

longer be required.

This proposal does not alter the assumed relationship relating strain level to allowable repetitions, and so

use of current performance relationships for asphalt and cemented materials could continue. Significantly,

the approach addresses the effect of multiple-axle grouping in isolation to other factors, and so future

refinements to the performance relationships for bound materials can be accommodated with no change to

the traffic characterisation method.

Using a range of axle group/load distributions demonstrated that using this approach would result in little to

no reduction in design asphalt thickness when compared to the method for lightly trafficked pavements.

However, for moderate-to-heavily trafficked pavements, the proposed approach resulted in progressively

lower asphalt thicknesses than the current method. Reductions in thickness were found to be typically 31–

46 mm (11–13%) for reduction, high traffic levels of 108 HVAG and above.

Similar changes in design thickness were found for a typical cemented material subbase and for a lean mix

concrete subbase used in heavily trafficked flexible pavements. Reductions of up to

18–22% were found.



The potentially lower design thickness for bound materials determined using the proposed traffic

characterisation process in the mechanistic design procedure are significant, and represent considerable

savings in material and construction costs.

11.4 Design Reliability

The reliability factors used by the current Austroads flexible pavement design procedure consider the

uncertainty relating to the future performance of pavement structures designed using the procedure. Any

change to the pavement design procedure, such as that proposed by this report, requires a determination

of the overall reliability level of pavements that are constructed in accordance with the changed procedure.

The analyses contained in Section 10 did not examine design reliability, and associated reliability factors.

Revision of the reliability factors is outside the scope of this report, but it will be required in order for the

revised procedure to be implemented. Such revision would consider how uncertainties in future increases

in axle loads could be incorporated, such as load factors.



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Appendix A Mean Deformation after Bedding-in: Tabulated

The following tables list the mean deformation for each chainage against the number of cycles applied after

bedding-in. Prior to calculating these values, the raw data presented in Austroads (2013) were examined to

ensure that inconsistent readings were identified. For each chainage, the progression of deformation with

increasing loading cycles was plotted, and visual examination was used to identify readings which were

inconsistent with readings taken at adjacent cycle counts. The excluded data points are denoted N/A in the

following tables. Additionally, only chainages that were considered to have been evenly loaded

(Section 6.6.2) are presented.

Table A 1: Mean deformation (mm) after bedding-in – Experiment 3500

Cycles Chainage (m)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

5 000 0.1 0.2 N/A 0.0 0.1 0.0 0.2 0.3 0.3 N/A 0.2 0.2 0.1 0.1 0.2

12 500 0.2 0.6 0.1 0.2 0.4 0.4 0.5 1.1 0.8 0.4 0.9 0.5 0.2 0.9 0.5

20 000 0.3 0.8 0.4 0.4 0.5 0.7 1.3 1.2 1.0 0.9 1.4 0.8 0.3 1.3 1.1

50 610 1.4 1.7 0.9 1.0 1.8 1.9 2.6 2.0 2.2 1.5 2.2 1.7 1.1 1.9 2.0

64 611 2.0 2.3 1.5 1.2 1.9 2.0 3.0 2.5 2.6 2.1 2.9 2.0 1.5 2.2 2.0

71 250 2.0 2.4 1.7 1.4 2.1 N/A 3.0 2.5 2.5 2.2 3.0 2.3 1.5 2.3 2.2

79 000 2.2 2.5 1.8 1.6 2.4 N/A 3.2 2.6 2.7 2.5 3.1 2.4 1.6 2.5 2.4

90 000 2.5 2.6 1.7 1.6 2.4 N/A 3.3 2.7 2.9 2.8 3.1 N/A 1.8 2.5 2.7

112 000 N/A 3.0 2.1 2.3 N/A 2.9 3.7 3.2 3.3 3.0 3.3 3.1 N/A 3.1 N/A

165 000 3.0 3.8 2.8 2.7 4.0 3.8 4.7 3.5 4.0 3.7 3.7 3.8 3.1 3.8 3.9

190 000 3.2 4.0 2.9 2.9 4.3 4.0 5.0 N/A 4.2 4.0 3.9 4.0 3.2 4.1 4.1

215 000 3.2 N/A 3.0 3.0 4.5 4.3 5.2 4.2 N/A 4.1 4.1 4.4 3.4 4.1 4.3

285 000 3.7 4.5 N/A 3.5 5.2 4.6 5.6 N/A 4.8 4.8 4.5 4.8 3.6 4.6 N/A

315 000 3.7 4.6 3.6 3.7 N/A 4.7 5.7 4.8 4.9 4.8 4.5 N/A 3.7 4.6 4.8

337 450 3.7 4.6 N/A 3.8 5.6 4.9 5.8 5.0 5.1 5.0 4.6 5.1 3.8 4.7 4.9


Cycles Chainage (m)

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5

2 500 1.6 0.9 0.9 0.6 0.8 0.6 0.4 0.5 0.3 0.2 0.2

5 000 2.5 1.6 1.5 1.5 1.3 1.0 0.6 0.5 0.5 0.4 0.4

15 500 5.8 4.1 3.3 2.9 2.5 2.1 1.7 1.1 1.0 1.1 0.8

30 000 8.3 6.1 5.0 4.8 3.8 3.4 2.5 2.1 1.6 1.6 1.2

66 000 10.7 8.8 7.3 6.5 5.5 4.8 3.7 3.0 2.6 2.2 2.0

90 000 11.8 9.7 8.4 7.5 6.3 5.5 4.3 3.5 3.3 2.6 2.2

120 000 12.4 10.4 9.1 8.0 7.0 6.2 4.8 4.0 3.6 2.9 2.5

139 000 12.9 11.0 9.3 8.3 N/A 6.6 5.1 N/A N/A 3.0 2.6

161 303 13.2 11.3 9.4 8.9 7.3 6.7 5.3 4.5 3.8 3.2 2.7

190 000 N/A N/A N/A N/A N/A 6.9 5.5 N/A 4.0 N/A N/A

239 000 13.7 12.0 10.0 9.3 7.9 7.3 5.8 4.9 4.3 3.5 3.1

290 000 14.0 12.4 10.4 9.9 8.3 7.6 6.2 5.2 4.5 3.6 3.1

315 000 14.2 N/A 10.4 N/A N/A 7.6 6.1 5.2 4.5 3.7 3.2

338 000 14.3 12.6 10.6 10.1 8.4 7.7 6.3 5.4 4.6 3.8 3.3

380 000 14.8 12.9 10.9 10.1 8.6 7.9 6.5 5.5 4.8 N/A 3.4




Cycles Chainage (m)

4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

5 500 0.7 0.2 0.0 0.2 N/A 0.2 0.1 0.2 0.2 0.1 0.4 0.3 0.1

8 500 0.7 0.3 0.3 0.3 0.2 0.5 0.4 N/A 0.4 0.3 0.4 0.3 0.4

15 000 0.8 0.5 0.2 0.6 0.3 0.5 0.6 0.4 0.5 0.8 0.5 0.3 0.5

23 000 1.0 0.5 0.5 0.5 0.4 0.6 0.7 0.5 0.7 0.8 0.7 0.5 0.6

30 000 1.0 0.8 0.6 0.5 0.5 0.7 0.8 0.4 0.8 1.0 0.8 0.5 0.7

38 000 1.0 0.8 0.4 0.7 0.6 0.8 0.9 0.6 1.0 1.1 0.9 0.6 0.7

50 000 1.2 1.0 0.6 0.8 0.7 1.0 1.0 0.7 0.8 1.0 0.8 0.6 0.8

65 000 1.4 1.3 0.9 1.1 1.1 1.2 1.2 1.0 1.1 1.1 1.0 0.7 0.9

102 000 1.7 1.6 1.2 1.2 1.2 1.1 1.5 1.2 1.3 1.4 1.3 1.2 1.2

115 000 1.6 1.6 1.2 1.2 1.3 1.2 1.5 1.2 1.3 1.4 1.4 1.1 1.2

130 000 1.9 1.7 1.3 1.3 1.3 1.2 1.8 1.2 1.5 1.5 1.5 1.2 1.4

161 850 1.8 1.7 1.4 1.5 1.3 1.4 1.7 1.4 1.6 1.5 1.6 1.1 1.3

220 000 1.9 1.8 1.5 1.4 1.4 1.5 1.7 1.6 1.8 1.8 1.8 1.2 1.4

253 101 2.1 2.1 1.7 1.8 1.7 1.7 2.2 1.7 2.0 1.8 1.9 1.5 1.6

265 350 2.1 2.0 1.7 1.8 1.5 1.7 2.2 1.7 2.0 1.8 2.0 1.5 1.8

279 111 2.2 2.1 1.7 1.8 1.5 1.7 2.1 1.8 2.0 1.7 1.9 1.4 1.8


Cycles Chainage (m)

4.0 4.5 5.0 5.5 7.0 7.5 8.0 8.5 9.0 9.5

1 000 0.1 N/A N/A 0.1 0.3 N/A 0.5 N/A N/A 0.1

6 000 0.5 N/A 0.1 0.5 0.2 0.0 0.4 0.2 N/A 0.1

11 750 0.8 0.4 0.5 0.7 0.3 0.2 0.8 0.0 0.0 0.5

25 750 1.4 1.1 0.9 1.3 0.8 0.6 1.2 0.7 0.5 0.8

35 001 1.9 1.7 1.3 1.9 1.2 0.8 1.4 1.0 0.7 0.8

41 000 2.1 1.9 1.6 2.0 1.3 0.8 1.4 0.9 0.8 0.8

55 088 2.4 2.3 2.1 2.0 1.7 0.9 1.5 0.9 0.8 0.9

77 000 3.1 2.8 2.4 2.5 2.0 1.1 1.7 1.2 1.2 1.1

90 000 3.4 3.1 2.7 2.6 1.9 1.5 1.6 1.2 1.3 1.4

103 615 3.5 3.3 2.8 2.8 2.0 1.2 1.8 1.4 1.4 1.4

125 000 3.7 3.6 2.9 3.0 2.1 1.2 1.8 1.4 1.5 1.4

155 000 4.1 3.9 3.2 3.3 2.3 1.5 2.0 1.8 1.8 1.5

181 148 4.3 4.2 3.3 3.6 2.6 1.6 2.1 2.0 2.2 1.8

194 600 4.4 4.3 3.4 3.7 2.8 1.6 2.2 2.0 2.3 2.0

212 419 4.5 4.4 3.6 4.0 3.0 2.1 2.4 2.1 2.3 2.2

245 190 5.0 5.3 N/A N/A 3.4 2.5 2.7 2.5 2.7 2.2

272 200 5.5 5.6 4.4 4.7 3.4 2.6 2.9 2.7 2.9 2.2

279 400 5.4 5.6 4.4 4.5 3.3 2.5 2.9 2.7 3.1 2.4

294 820 5.4 5.8 4.7 5.0 3.5 2.7 3.0 2.9 3.0 2.7




Cycles Chainage (m)

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0

5 000 1.4 1.2 1.3 1.1 1.3 1.7 1.3 1.4 1.8 1.5 1.4 1.4 2.2 1.5 1.3 0.6 0.8

10 800 1.8 1.9 1.8 1.9 2.0 2.1 1.9 2.4 2.9 2.7 2.5 2.7 3.3 2.6 1.9 1.3 1.6

13 000 2.1 2.0 2.6 2.2 2.9 2.3 3.0 2.9 3.3 3.0 2.9 3.4 3.5 3.0 2.3 1.6 0.9

20 000 2.2 2.7 2.7 2.5 3.3 2.7 3.2 3.3 3.9 3.4 3.6 4.0 4.0 3.4 2.3 1.7 0.9

25 900 2.6 3.1 2.9 3.0 3.4 3.1 3.5 3.9 3.9 3.9 4.3 4.5 4.7 4.0 2.8 2.1 1.3

33 030 3.2 3.4 3.0 3.7 3.9 3.6 3.7 4.9 4.5 4.5 4.6 4.8 5.3 4.8 3.3 2.3 1.7

44 000 3.9 3.8 3.4 3.8 4.2 4.3 4.3 5.5 5.1 4.9 5.1 5.6 6.1 5.3 3.8 2.8 2.2

52 572 4.2 4.4 3.9 3.9 4.8 4.8 4.1 5.2 5.3 5.0 5.6 5.7 6.8 6.1 4.4 3.3 2.8

66 700 4.6 4.7 4.4 4.6 5.3 5.4 4.7 5.8 5.5 5.9 6.3 6.3 7.4 6.8 5.1 3.6 3.2

79 900 4.6 4.8 4.2 4.9 5.2 5.4 4.9 6.0 6.1 5.9 6.6 6.6 7.8 7.3 5.1 3.7 3.4

113 000 5.0 5.4 4.8 5.4 6.1 5.8 5.8 6.7 6.9 7.3 7.2 N/A

8.3 8.0 5.6 4.6 3.3

123 200 5.1 5.4 5.0 5.7 6.1 6.1 5.8 6.9 7.1 7.8 7.3 N/A

8.4 8.4 5.8 4.9 3.3

140 000 5.4 5.6 5.3 5.9 6.1 6.1 6.1 7.1 7.4 7.7 7.4 7.4 8.6 8.8 6.2 5.0 3.6

158 000 5.5 6.0 5.7 N/A

6.4 6.2 6.3 7.6 7.5 7.6 7.9 7.6 9.0 8.4 6.9 5.0 4.1

180 267 5.8 6.3 5.7 6.2 N/A

6.7 6.6 7.8 N/A

8.4 8.0 N/A

9.3 9.2 7.4 5.9 4.4

194 000 5.9 6.5 5.8 6.4 6.6 6.8 6.5 7.7 7.8 8.2 8.3 8.2 9.5 9.0 7.1 5.7 4.5

222 656 6.1 6.5 6.1 6.7 6.8 6.7 7.1 7.8 8.1 8.9 8.7 8.6 9.7 9.5 7.4 6.1 4.6

238 900 6.2 N/A

6.2 6.8 6.8 7.1 7.1 7.9 N/A

8.7 8.7 8.8 9.7 9.7 7.8 6.5 5.1

260 000 6.4 6.9 6.3 7.1 7.1 7.1 NA 8.2 8.5 8.8 N/A

8.9 9.8 10.2

8.0 6.7 5.6


Cycles Chainage (m)

3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

3 000 0.1 N/A N/A 0.2 0.2 0.3 N/A 0.2 0.1 0.1 0.1 0.0 N/A 0.2 0.1 N/A

8 280 0.8 0.7 0.5 0.6 0.8 0.8 0.5 0.7 0.5 0.8 0.5 0.4 0.4 0.6 0.5 0.2

14 000 1.0 0.9 0.7 0.9 1.1 1.1 0.7 1.1 0.8 1.0 0.6 0.5 0.6 0.8 0.6 0.5

23 000 1.3 1.4 1.1 1.4 1.6 1.8 1.2 1.4 1.3 1.4 1.1 1.0 1.1 1.2 0.9 0.9

44 000 2.0 2.3 1.8 1.8 2.2 2.1 1.7 2.1 1.8 2.0 1.5 1.3 1.5 1.4 1.2 1.1

68 200 2.3 2.8 2.4 2.3 2.7 2.8 2.1 2.5 2.3 2.3 1.8 1.7 1.7 1.8 1.5 1.5

89 000 2.7 3.1 2.5 2.6 2.9 2.9 2.3 2.8 2.5 2.6 2.1 1.9 1.9 1.9 1.6 1.5

120 000 3.2 3.7 2.9 2.9 3.4 3.3 2.8 3.3 2.7 3.2 2.5 2.2 2.0 2.1 1.9 2.0

150 000 3.3 3.9 3.2 3.1 3.8 3.7 3.0 3.6 3.1 3.1 2.5 2.6 2.5 2.5 2.2 2.4

193 100 3.6 4.1 3.5 3.5 4.1 4.1 3.4 4.0 3.3 3.4 2.9 2.8 2.8 2.6 2.3 2.4

233 000 4.0 4.5 3.7 3.8 4.3 4.4 3.5 4.4 3.6 3.8 3.1 3.2 3.1 3.0 2.6 2.6

254 600 4.1 4.3 3.8 4.0 4.5 4.6 3.8 4.5 3.8 3.8 3.2 3.0 3.1 3.1 2.6 2.7

287 500 4.3 4.7 4.3 4.1 4.6 4.6 3.9 4.7 3.9 4.0 3.4 3.3 3.4 3.1 2.7 2.8

312 223 4.3 5.0 4.4 4.4 4.8 4.7 4.2 4.8 4.1 4.0 3.5 3.4 3.4 3.3 2.8 3.1

360 000 4.6 5.0 4.4 4.6 4.9 4.7 4.3 5.1 4.2 4.3 3.5 3.4 3.6 3.4 2.9 2.9




Cycles Chainage (m)

3.5 4.0 5.0 6.0 6.5 7.0 8.0 8.5 9.0 9.5 10.0 10.5 11.0

4 675 0.4 0.5 0.3 0.2 0.2 0.3 0.3 0.3 0.1 0.0 0.2 0.2 0.2

7 650 1.3 0.7 0.8 0.2 0.5 0.4 0.7 0.6 0.3 0.4 0.4 0.7 0.3

13 300 1.1 1.1 1.0 0.4 0.7 0.5 0.7 0.7 0.3 0.4 0.7 0.7 0.5

21 150 1.7 1.4 1.2 0.7 0.8 0.9 1.0 1.0 0.8 1.1 1.1 1.2 1.0

30 000 2.2 2.0 2.0 1.4 1.2 0.9 1.4 1.4 1.4 1.4 N/A 1.2 1.6

40 001 2.6 2.5 2.2 1.3 1.5 1.0 1.7 1.5 1.4 1.6 1.8 1.4 1.5

45 296 2.9 2.7 2.2 1.5 1.5 0.9 1.7 1.5 1.5 1.6 1.9 1.5 1.5

54 000 3.3 2.9 2.7 1.9 1.9 1.3 2.0 1.7 2.0 1.6 2.3 1.5 1.6

63 401 3.4 3.0 2.7 1.9 1.9 1.5 2.4 1.9 2.3 1.7 2.5 1.8 1.6

70 000 3.3 3.1 2.8 2.0 2.0 1.6 2.6 1.9 2.4 1.6 2.4 2.0 1.5

77 549 3.6 3.2 2.9 1.9 2.1 1.7 2.7 2.0 2.6 2.0 2.6 2.1 1.7

88 201 3.9 3.5 2.9 2.2 2.1 2.1 2.7 2.2 2.9 2.1 2.7 2.3 1.8

101 350 4.0 3.6 3.0 2.2 2.4 1.8 2.9 2.3 2.9 2.2 2.8 2.5 1.7

108 000 4.0 3.6 3.0 2.6 2.5 2.0 3.0 2.3 2.9 2.3 3.0 2.4 1.9

116 000 4.2 3.9 3.2 2.6 2.6 2.2 2.9 2.3 3.2 2.4 3.0 2.4 2.4

124 000 4.3 3.9 3.3 2.7 2.5 2.2 3.0 2.5 3.2 2.5 3.2 2.2 2.1

139 200 4.4 4.3 3.4 2.7 2.6 2.2 3.0 2.7 3.5 2.5 3.3 2.3 2.1

155 000 4.5 4.3 3.4 2.7 2.7 2.2 3.1 2.5 3.3 2.7 3.4 2.5 2.3

170 000 4.8 4.3 3.6 2.9 2.8 2.5 3.3 2.6 3.4 2.9 3.6 2.6 2.2

186 500 4.7 4.6 3.5 3.1 3.0 2.5 3.4 2.7 3.5 2.7 3.5 2.8 2.5

206 500 5.3 4.4 3.9 3.1 3.2 2.6 3.4 3.1 3.5 2.8 3.5 N/A 2.5

216 000 5.1 4.5 3.7 3.1 3.0 2.6 3.6 3.0 3.5 3.0 3.7 N/A 2.7

230 765 5.0 4.6 4.1 3.3 3.1 2.7 3.5 3.1 3.8 3.0 3.7 3.0 2.7

240 600 5.3 4.8 4.0 3.4 3.3 2.9 3.6 3.2 3.7 3.0 3.7 2.8 2.8

265 000 5.3 5.0 4.1 3.7 3.3 3.0 3.6 3.3 3.9 3.2 3.8 2.9 2.7

280 000 5.6 5.1 4.3 3.5 3.3 3.0 3.7 3.3 3.9 3.2 3.9 3.0 2.9

304 003 5.8 5.0 4.2 3.4 3.5 3.1 N/A 3.4 3.9 3.3 3.9 3.1 2.9

312 000 5.7 5.2 4.3 3.5 3.5 3.0 N/A 3.6 4.1 3.3 4.0 3.0 2.9

325 700 5.8 5.1 4.5 3.5 3.5 3.2 N/A 3.4 4.1 3.3 4.0 3.0 2.8


Cycles Chainage (m)

4.0 4.5 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5

8 200 1.0 2.0 1.1 1.6 1.3 1.4 1.2 1.1 0.8 0.5 1.7

15 325 0.3 1.9 1.6 1.7 1.5 2.0 1.8 0.9 1.4 1.1 1.8

36 000 1.4 1.7 1.7 1.7 2.4 2.4 2.6 1.1 2.2 1.7 2.9

66 366 1.7 2.2 2.5 2.4 2.9 3.1 3.1 1.8 3.1 2.3 3.3

73 000 2.1 2.3 2.3 2.5 2.9 3.6 3.2 2.5 3.2 2.1 3.4

174 939 3.0 3.3 3.1 3.9 3.5 4.8 N/A 3.6 4.4 3.4 3.9

180 640 3.1 3.2 3.4 4.3 3.7 N/A 4.2 3.4 4.3 3.4 4.0

192 532 3.4 3.3 3.3 4.3 3.9 5.0 4.1 3.8 N/A 3.6 4.2

211 273 3.1 3.3 3.8 N/A 3.8 4.9 4.1 4.1 4.9 3.6 4.3

230 402 3.2 N/A 3.9 4.4 4.1 5.2 4.3 4.0 N/A N/A 4.4

268 232 3.9 3.5 3.7 N/A 4.3 N/A 4.7 4.0 5.1 3.9 4.7




Cycles Chainage (m)

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5

4 525 0.9 0.9 1.1 0.8 0.8 0.8 1.0 1.3 0.8 1.2 1.0 1.4 1.3 1.1 1.0 1.2 0.9

12 900 2.6 2.1 2.9 1.7 2.5 2.5 2.5 2.9 1.7 2.5 1.5 3.2 4.2 2.7 2.8 2.3 2.6

18 418 3.0 2.3 3.4 2.1 2.7 2.8 3.1 3.3 2.1 3.0 2.0 3.9 5.2 3.2 3.3 2.6 3.2

28 000 4.0 3.2 4.4 3.4 4.0 3.9 4.2 4.5 3.2 4.0 2.9 5.7 6.5 4.9 4.9 4.6 4.8

42 100 5.3 4.3 5.6 4.4 4.7 4.8 5.2 5.5 4.1 4.9 4.1 6.7 7.8 5.8 5.8 5.3 5.9

51 000 6.1 5.2 6.2 5.1 5.3 5.4 5.7 6.0 4.7 5.7 4.4 7.2 8.4 6.6 6.3 6.1 6.6

72 300 7.2 6.2 7.1 6.0 6.2 6.3 6.7 6.7 5.6 6.2 5.3 8.3 9.6 7.8 7.2 7.2 7.5

81 701 7.8 6.3 7.6 6.4 6.8 6.7 6.9 7.2 6.0 6.6 5.6 8.8 10.0 8.1 7.5 7.3 8.2

94 657 7.8 6.4 7.6 6.7 6.7 6.7 7.2 7.6 5.9 6.8 6.1 9.1 10.2 8.6 8.2 8.1 8.4

102 257 8.2 6.9 8.3 7.1 7.1 7.3 7.2 7.5 6.0 7.0 6.1 9.2 10.3 8.3 8.2 8.3 8.7

178 000 9.8 8.9 8.5 8.6 7.9 7.7 8.3 8.6 8.2 8.9 8.2 10.0 10.9 10.6 9.6 10.5 10.4

183 764 9.7 8.8 8.3 8.5 8.0 7.9 8.4 8.6 8.3 9.0 8.3 10.0 10.9 10.6 9.5 10.6 10.3

190 426 9.9 8.9 8.8 9.0 8.0 8.2 8.6 8.8 8.2 8.8 8.0 10.2 11.5 10.9 10.2 10.6 10.4

197 000 10.0 9.0 8.9 8.9 8.3 8.3 8.6 8.8 8.3 9.0 8.2 10.3 11.5 10.9 10.0 10.8 10.7

204 400 10.2 9.2 8.8 8.8 8.4 8.3 8.8 8.9 8.2 9.0 8.1 10.3 11.4 10.9 10.0 10.7 10.6

212 700 10.1 9.1 8.8 8.9 8.2 8.4 8.8 9.0 8.4 9.1 8.2 10.4 11.6 10.9 10.1 10.7 10.7

226 400 10.4 9.2 9.1 8.9 8.5 8.5 8.8 9.1 8.4 9.0 8.3 10.6 11.8 11.0 10.3 11.0 10.6

239 100 10.4 9.4 9.0 9.0 8.5 8.6 9.0 9.3 8.4 9.1 8.4 10.7 11.9 11.2 10.5 11.0 10.9

247 320 10.3 9.6 9.2 9.2 8.6 8.6 9.2 9.3 8.7 9.4 8.5 10.9 12.2 11.4 10.6 11.1 10.9

254 958 10.5 9.5 9.1 9.1 8.4 8.6 9.3 9.3 8.7 9.3 8.5 NA 12.1 11.3 10.5 11.1 10.9

260 900 10.7 9.4 9.4 9.1 8.6 8.9 9.2 9.5 8.7 9.5 8.7 11.0 12.1 11.5 10.6 11.3 11.1

281 878 10.8 9.6 9.6 9.4 8.8 8.9 9.4 9.6 8.8 9.5 8.6 11.2 12.3 11.6 10.7 11.6 11.1


Cycles Chainage (m)

3. 5 4.0 4. 5 5.0 5. 5 7.0 7. 5 8.0 8. 5 9.0

7 500 0.7 0.9 0.8 0.0 0.6 0.5 0.7 0.7 0.5 0.1

15 000 1.1 1.1 1.1 1.0 0.7 1.2 1.1 0.9 0.4 0.4

20 000 1.2 1.3 1.6 1.1 1.1 1.7 1.5 1.3 0.9 0.9

28 900 1.9 1.8 1.6 1.8 1.7 2.3 1.9 1.7 1.4 1.4

40 000 2.4 2.8 1.9 2.4 2.1 3.0 0.8 2.8 1.6 1.6

50 000 2.3 2.9 2.2 2.0 2.0 3.1 1.6 2.4 1.6 1.6

65 000 2.3 2.4 2.1 2.4 2.5 2.1 2.0 1.8 1.1 1.5

80 000 2.5 2.3 N/A 2.3 2.5 2.3 N/A 2.1 N/A 1.6

115 000 2.5 N/A 2.8 2.4 N/A 2.6 3.0 2.4 1.7 2.0

140 000 2.6 2.8 3.1 2.5 3.1 2.8 3.1 2.6 2.0 2.0

161 695 2.8 3.1 3.3 2.6 3.1 2.8 3.5 2.7 1.9 2.1

190 000 2.7 3.2 3.5 2.7 3.3 3.0 3.5 2.8 2.4 2.2

224 500 N/A 3.5 3.7 2.8 N/A 3.2 4.0 3.2 2.4 2.3



Appendix B Mean Deformation after Bedding-in: Plotted

Figure B 1: Experiment 3500

(a) Chainage 1.0 m (b) Chainage 1.5 m

(c) Chainage 2.0 m (d) Chainage 2.5 m

(e) Chainage 3.0 m (f) Chainage 3.5 m



Figure B 2: Experiment 3500 (continued)

(g) Chainage 4.0 m (h) Chainage 4.5 m

(i) Chainage 5.0 m (j) Chainage 5.5 m

(k) Chainage 6.0 m (l) Chainage 6.5 m




(m) Chainage 7.0 m (n) Chainage 7.5 m

(o) Chainage 8.0 m












(k) Chainage 8.5 m
















(m) Chainage 10.5 m


























(o) Chainage 10.0 m (p) Chainage 10.5 m

(q) Chainage 11.0 m

































(m) Chainage 11.0 m












Figure B 22: Experiment 3508 (continued

(k) Chainage 9.5 m



















(q) Chainage 10.5 m








(g) Chainage 7.5 m (h) Chainage 8 m

(i) Chainage 8.5 m (j) Chainage 9 m



Appendix C Pavement Deflection and Back-Calculated Moduli

Table C 1: Pavement thickness, deflection and back-calculated moduli after bedding-in – Experiment 3500

Chainage (m)

Thickness (mm)

Deflection (500 kPa load) (µm) Back-calculated moduli (MPa) Offset from load (mm)

Base Clay 0 200 300 450 600 750 900 1200 1500 𝑬1 𝑬2 𝑬3 𝑬4 𝑬5 𝑬6 𝑬7 𝑬8

2.0 300 403 814 586 409 255 159 109 85 61 50 1000 341 52 35 83 120 178 137

2.5 292 404 929 605 431 253 153 108 83 61 51 757 232 75 26 120 85 241 135

3.0 284 405 994 701 494 287 171 116 90 62 52 1000 195 53 26 71 84 158 132

3.5 285 408 1108 802 557 318 185 124 94 65 51 999 139 50 24 79 55 128 130

4.0 286 410 1012 726 494 297 174 119 90 63 49 1000 167 53 28 94 59 126 137

4.5 288 406 1002 704 497 291 164 112 87 58 48 936 201 50 26 86 72 153 141

5.0 289 401 972 670 464 266 153 101 79 56 46 1000 175 59 25 71 119 180 147

5.5 288 401 936 647 425 241 136 94 75 56 46 750 217 50 33 76 120 239 149

6.0 287 401 902 635 427 240 139 94 75 54 46 1000 198 50 30 101 120 212 151

6.5 290 403 967 649 425 233 134 93 76 57 49 865 163 50 31 107 120 276 144

7.0 292 404 876 621 420 239 138 99 80 60 49 948 225 50 33 107 112 252 140

7.5 296 402 892 611 429 249 151 104 83 58 50 1000 196 76 28 72 118 228 139

8.0 299 399 931 624 446 259 157 108 84 63 53 995 226 50 27 120 119 232 131





Chainage (m)

Thickness (mm)



5.0 283 419 836 550 370 220 141 98 77 54 51 956 253 54 50 66 109 262 144

6.0 286 405 818 547 386 208 130 89 71 50 43 1000 225 50 47 98 120 176 166

7.0 286 406 772 512 346 194 120 80 66 52 46 1000 230 50 52 120 120 300 161

8.0 285 422 850 572 371 209 129 87 72 54 46 1000 188 50 48 87 119 274 153

9.0 279 422 855 604 421 268 176 120 92 58 47 1000 272 75 45 63 68 97 148

10.0 269 411 945 656 457 293 189 129 100 63 49 995 216 60 48 65 59 74 142

Chainage (m)

Thickness (mm)



3.5 300 378 1925 1286 846 430 220 122 95 77 66 255 74 50 10 37 119 300 107

4.0 294 380 1808 1250 813 402 211 121 96 75 63 549 50 50 13 29 120 300 108

4.5 287 382 1836 1262 813 386 186 104 91 73 61 419 50 50 12 46 120 300 115

5.0 284 384 1648 1135 721 341 169 101 88 73 58 586 50 50 13 82 120 300 118

5.5 281 385 1546 1034 603 308 157 102 86 69 58 465 66 50 16 72 96 298 122

6.0 279 393 1492 1034 645 319 174 104 83 69 56 540 73 50 17 40 119 262 123

6.5 277 401 1354 938 587 312 168 108 88 66 55 752 84 50 19 64 93 178 125

7.0 279 408 1251 846 548 304 169 106 87 64 53 790 100 50 22 55 103 172 129

7.5 280 415 1165 786 519 289 159 102 82 62 53 788 132 50 21 68 99 280 131

8.0 283 421 1119 731 473 255 151 98 79 59 50 865 109 50 33 54 115 201 139

8.5 285 427 958 708 472 263 154 101 82 61 55 1000 170 50 27 68 120 300 130




Chainage (m)

Thickness (mm)



4.5 300 347 933 617 399 204 119 83 72 53 42 1000 105 53 46 120 120 191 164

5.5 275 368 909 592 354 189 108 75 66 51 42 1000 109 50 47 120 120 295 167

6.5 279 360 725 421 255 144 92 67 59 46 39 914 127 91 112 120 120 300 192

7.5 293 349 636 434 271 146 94 71 61 47 39 1000 201 69 120 120 120 300 187

8.5 297 340 664 435 263 150 94 67 58 44 36 1000 203 63 115 120 120 300 198

9.5 294 355 673 456 274 152 92 68 58 43 34 1000 200 57 113 120 120 300 200


Chainage (m)

Thickness (mm)



3.0 301 383 1390 860 675 371 209 134 100 85 69 206 387 50 12 120 120 300 102

4.0 282 398 1384 983 702 381 207 129 97 84 70 809 93 50 13 55 120 300 101

5.0 292 399 1420 981 685 371 209 135 100 87 73 874 73 50 15 45 120 287 100

6.0 291 402 1543 1017 788 439 232 135 99 88 74 295 173 50 13 28 120 300 100

7.0 292 387 1647 1017 779 385 211 121 91 81 69 154 260 50 10 117 120 300 106

8.0 293 384 1781 1092 806 400 200 121 90 81 68 542 58 50 10 99 120 300 106

9.0 286 390 1671 1019 778 383 193 112 83 77 63 162 211 50 10 101 120 300 115

10.0 296 377 1467 925 674 332 174 108 81 74 59 297 139 50 14 64 120 299 120




Chainage (m)

Thickness (mm)



3.0 270 376 1033 779 498 250 125 77 64 53 48 1000 87 50 23 100 120 300 157

4.0 295 367 947 728 473 246 133 89 70 55 46 999 133 50 28 74 120 300 151

5.0 296 363 1000 673 463 247 140 93 71 56 48 1000 142 50 25 95 120 300 147

6.0 290 362 1119 742 481 259 143 88 70 53 51 690 120 50 33 67 106 132 159

7.0 295 366 1048 740 478 250 138 85 67 51 42 1000 103 50 28 67 120 210 164

8.0 291 372 1007 765 481 255 132 79 61 49 41 1000 105 50 29 47 120 300 169

9.0 288 373 912 678 441 212 113 71 56 45 38 1000 118 50 35 73 120 300 186

10.0 284 375 776 537 339 190 113 75 59 43 37 997 208 50 56 107 120 185 196

Table C 7: Pavement thickness, deflection and back-calculated stiffnesses after bedding-in – Experiment 3507

Chainage (m)

Thickness (mm)



2.5 289 331 1254 919 588 285 131 78 65 55 48 989 50 50 18 118 120 300 154

3.5 289 336 1313 875 555 277 140 82 68 58 47 829 61 50 26 40 120 300 150

4.5 293 334 1094 811 513 257 134 86 71 56 47 1000 76 50 24 78 120 300 149

5.5 293 336 993 613 401 199 107 72 64 52 43 996 80 50 43 120 120 300 168

6.5 285 354 850 566 332 181 104 71 61 52 42 1000 117 50 59 120 120 300 173

7.5 288 353 762 545 343 183 105 70 61 51 41 1000 175 50 55 120 120 300 177

8.5 296 351 801 526 334 171 101 68 60 51 38 1000 136 50 71 120 120 300 183

9.5 287 357 776 511 319 170 100 69 58 45 38 1000 168 50 64 120 120 300 190

10.5 289 355 770 483 306 167 99 68 58 44 37 864 202 50 72 120 120 294 194



Table C 8: Pavement thickness, deflection and back-calculated stiffnesses after bedding-in – Experiment 3508

Chainage (m)

Thickness (mm)



3.0 280 360 1385 1060 653 335 162 94 83 72 58 881 50 50 15 87 120 300 122

4.0 280 365 1438 1004 638 302 150 96 87 71 58 538 72 50 17 67 120 300 122

5.0 281 351 1329 999 586 301 161 100 85 70 56 992 50 50 18 84 120 276 123

6.0 284 351 1286 928 568 272 134 89 80 69 56 856 50 50 21 120 120 300 130

7.0 285 356 1379 1003 617 286 136 83 77 71 57 705 50 50 18 120 120 300 132

8.0 281 361 1469 1018 621 282 124 84 79 73 57 549 50 50 18 120 120 300 131

9.0 289 365 1530 962 598 262 124 81 78 69 53 486 50 50 19 120 120 300 137


Chainage (m)

Thickness (mm)



3.0 272 386 1581 1095 660 319 138 68 57 62 59 526 50 50 13 97 120 300 154

4.0 277 397 1490 1076 674 328 144 76 67 65 58 631 50 50 15 80 120 300 140

5.0 272 413 1761 1224 769 366 170 91 75 69 63 486 50 50 12 54 120 300 123

6.0 284 418 1674 1173 737 387 198 117 94 75 67 376 80 50 14 29 120 300 107

7.0 281 430 1577 1015 661 328 173 106 92 76 67 692 50 50 16 81 120 300 109

8.0 280 424 1699 1218 770 399 209 127 100 80 68 360 83 50 15 28 70 300 103

9.0 290 416 1748 1102 736 369 203 128 107 76 70 602 50 50 16 36 120 200 102

10.0 292 404 1601 989 636 334 178 111 89 74 66 390 82 50 16 56 120 300 112




Chainage (m)

Thickness (mm)



3.5 294 368 1633 1032 615 300 131 75 67 66 51 442 50 50 15 120 120 300 146

4.5 293 368 1726 958 572 243 86 51 60 64 54 225 50 50 20 119 120 300 184

5.5 290 358 1499 948 573 252 99 57 59 64 55 417 50 50 20 120 120 300 171

6.5 291 350 1543 894 530 218 74 53 60 63 53 298 50 50 26 120 120 300 189

7.5 288 350 1494 1021 607 283 119 67 64 64 55 409 53 50 19 103 117 300 154

8.5 294 348 1379 865 543 242 106 71 66 65 54 571 50 50 25 120 120 300 152



Appendix D Comparison of Deflection Data: Observed and Back-calculated

Figure D 1: Experiment 3500






Figure D 2: Experiment 3500 (continued)







(m) Chainage 8.0 m













(k) Chainage 8.5 m
























(a) Chainage 3.0 m (b) Chainage 4 m

















(i) Chainage 10.5 m








(g) Chainage 9.0 m




















Appendix E Method of Equivalent Thickness

Odemark (Ullidtz 1998) developed an approximate method for transforming multi-layer structures into an

equivalent single layer structure with equivalent thicknesses and a modulus. The concept assumes that the

stresses and strains below a layer depend only upon the stiffness of that layer. Odemark defines that

stiffness layer as proportional to:

ℎ3𝐸

1 − 𝜈2

A1

where

ℎ = thickness of the layer

𝐸 = elastic modulus of the layer

𝜈 = poisson’s ratio of the layer

It holds that if the two layers shown in Figure E 1 have the same stiffness, then the following equality applies:

ℎ13 𝐸1

1 − 𝜈12 =

ℎ23 𝐸2

1 − 𝜈22

A2

Figure E 1: Different layers

If the Poisson’s ratio of the two materials is the same, this equality can be transformed to yield:

ℎ2 = ℎ1 √

𝐸1

𝐸2

3

A3

Attempting to match stresses and strains calculated using Odemark’s method with those obtained from

elastic theory has prompted some researchers to incorporate a correction factor, 𝑓, whose range has been

found to vary from 0.8 to 0.9 (Subagio et al. 2005) and 0.5 to 0.9 (Nataatmadja et al. 2012).

ℎ2 = 𝑓 ℎ1 √

𝐸1

𝐸2

3

A4

This equation can be used to determine the stiffness of a single layer equivalent to two or more separate

layers.



Figure E 2: Transformation of two layers into single equivalent layer

Layer 1: ℎ𝑒 1 = 𝑓 ℎ1 √𝐸1

𝐸𝑒

3

Layer 2: ℎ𝑒 2 = 𝑓 ℎ2 √𝐸2

𝐸𝑒

3

Summing: ℎ𝑒 = ℎ𝑒 1 + ℎ𝑒 2 = (𝑓 ℎ1 √𝐸1

𝐸𝑒

3

) + (𝑓 ℎ2 √𝐸2

𝐸𝑒

3

)

→ ℎ𝑒 =

𝑓

√𝐸𝑒3

(ℎ1 √𝐸13 + ℎ2 √𝐸2

3 )

→ 𝐸𝑒 = [𝑓

ℎ𝑒

(ℎ1 √𝐸13 + ℎ2 √𝐸2

3 )]3

→ 𝐸𝑒 = 𝑓′ [(ℎ1𝐸1

1 3⁄+ ℎ2𝐸2

1 3⁄)

ℎ𝑒

]

3

If, ℎ𝑒 = ℎ1 + ℎ2

then: 𝐸𝑒 = 𝑓′ [(ℎ1𝐸1

1 3⁄+ ℎ2𝐸2

1 3⁄)

ℎ1 + ℎ2

]

3

A5

Equation A5 allows the combination of two layers into a single layer with an equivalent modulus and

thickness equal to the sum of the two layers. The general form of the equation, allowing the determination of

the equivalency of 𝑛 layers is shown in Equation A6.

𝐸𝑒 = 𝑓′ [∑ (ℎ𝑖𝐸1

1 3⁄)𝑛

𝑖=1

∑ ℎ𝑖𝑛𝑖=1

]

3

A6



Appendix F Data Used in Load Pairing Analyses

The following tables include the estimated number of loading cycles needed to reach the various deformation

levels used in the load pairing analyses in Section 6.9, as well as the aggregate stiffness parameters used in

those analyses. Definitions of the aggregate parameters can be found in Section 6.7.4.

The tables are presented in the following order:

40 kN single axle – cycles to 4 mm deformation

60 kN tandem group – cycles to 3 mm deformation



90 kN triaxle group – cycles to 3 mm deformation

90 kN triaxle group – cycles to 4 mm deformation.



Table F 1: Cycles to 4 mm deformation level and aggregate stiffness parameters for 40 kN single axle locations

Experiment Chainage (m)

Group Load (kN)

Cycles to 4 mm

deformation

D0

(µm) E4

(MPa) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure

(MPa) Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3500 3.0 single 40 165 778 994 26 416 60 145 137 98 297 115 58

3500 4.0 single 40 110 931 1012 28 407 60 132 123 85 281 104 56

3500 5.0 single 40 175 369 972 25 411 72 164 149 112 287 110 67

3500 6.0 single 40 198 339 902 30 416 84 182 167 132 292 113 78

3500 8.0 single 40 200 571 931 27 424 89 182 175 141 287 117 81

3507 3.5 single 40 96 251 1313 26 313 62 225 157 145 190 56 48

3511 10.0 single 40 22 033 1601 16 174 64 206 140 142 137 65 57

3511 3.0 single 40 20 028 1581 13 209 77 227 150 151 149 50 63

3511 4.0 single 40 26 425 1490 15 244 72 220 151 148 162 50 62

3511 5.0 single 40 23 075 1761 12 195 62 212 139 138 142 50 54

3511 7.0 single 40 24 265 1577 16 264 72 205 153 148 168 50 67

3511 8.0 single 40 14 745 1699 15 164 38 202 122 118 137 67 36

3511 9.0 single 40 19 068 1748 16 234 57 151 117 106 151 50 51

Table F 2: Cycles to 3 mm deformation level and aggregate stiffness parameters for 60 kN tandem group locations


Group Load (kN)

Cycles to 3 mm

deformation

D0

(µm) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure

(MPa) Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3508 4.0 tandem 60 153 880 1438 220 68 211 151 147 161 62 56

3508 6.0 tandem 60 69 090 1286 319 87 215 170 164 188 50 72

3508 7.0 tandem 60 42 326 1379 268 86 216 163 161 168 50 70

3508 8.0 tandem 60 105 092 1469 216 86 216 157 161 148 50 71

3508 9.0 tandem 60 120 479 1530 195 86 219 154 161 135 50 72

3514 4.5 tandem 60 123 103 1726 108 86 242 139 162 91 50 73

3514 5.5 tandem 60 132 681 1499 172 87 236 151 162 124 50 72





Group Load (kN)

Cycles to 3 mm

deformation

D0

(µm) E4

(MPa) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure

(MPa) Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3505 3 tandem 80 25 340 1390 12 214 84 201 161 155 177 164 67

3505 4 tandem 80 25 111 1384 13 317 63 201 157 140 214 71 53

3505 5 tandem 80 17 361 1420 15 332 60 194 151 134 202 61 52

3505 6 tandem 80 18 621 1543 13 173 54 200 136 130 154 102 44

3505 7 tandem 80 12 286 1647 10 155 82 203 148 152 139 132 65

3505 8 tandem 80 13 405 1781 10 217 76 203 148 148 147 54 61

3505 9 tandem 80 9780 1671 10 141 77 208 144 149 132 118 62

3505 10 tandem 80 22 778 1467 14 162 66 210 143 143 141 88 54

3506 3 tandem 80 93 896 1033 23 379 81 229 180 159 250 70 71

3506 4 tandem 80 110 665 947 28 394 74 226 180 156 251 86 66

3506 5 tandem 80 71 568 1000 25 397 80 224 184 160 254 89 70

3506 6 tandem 80 127 141 1119 33 287 69 146 119 94 204 82 63

3506 7 tandem 80 120 974 1048 28 384 72 187 150 123 234 74 63

3506 8 tandem 80 216 738 1007 29 385 65 235 170 148 239 75 58

3506 9 tandem 80 231 735 912 35 389 76 243 181 159 250 81 70





Group Load (kN)

Cycles to 4 mm

deformation

D0

(µm) E4

(MPa) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure

(MPa) Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3505 10.0 tandem 80 38 461 1467 14 162 66 210 143 143 141 88 54

3505 3.0 tandem 80 51 405 1390 12 214 84 201 161 155 177 164 67

3505 4.0 tandem 80 52 555 1384 13 317 63 201 157 140 214 71 53

3505 5.0 tandem 80 33 547 1420 15 332 60 194 151 134 202 61 52

3505 6.0 tandem 80 35 696 1543 13 173 54 200 136 130 154 102 44

3505 7.0 tandem 80 21 844 1647 10 155 82 203 148 152 139 132 65

3505 8.0 tandem 80 22 323 1781 10 217 76 203 148 148 147 54 61

3505 9.0 tandem 80 15 627 1671 10 141 77 208 144 149 132 118 62

3506 3.0 tandem 80 255 188 1033 23 379 81 229 180 159 250 70 71

3506 4.0 tandem 80 291 016 947 28 394 74 226 180 156 251 86 66

3506 5.0 tandem 80 180 451 1000 25 397 80 224 184 160 254 89 70

3506 6.0 tandem 80 346 622 1119 33 287 69 146 119 94 204 82 63

3506 7.0 tandem 80 349 890 1048 28 384 72 187 150 123 234 74 63

Table F 5: Cycles to 3 mm deformation level and aggregate stiffness parameters for 90 kN triaxle group locations


Group Load (kN)

Cycles to 3 mm

deformation

D0

(µm) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure (MPa)

Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3501 5.5 triaxle 90 13 712 1546 194 61 210 142 141 145 58 54

3501 6 triaxle 90 17 954 1492 221 59 193 135 126 163 62 50

3501 6.5 triaxle 90 30 464 1354 295 59 152 125 102 204 68 54

3501 7 triaxle 90 47 737 1251 313 60 151 127 101 218 75 57

3501 7.5 triaxle 90 71 700 1165 323 63 206 159 137 235 89 59

3501 8 triaxle 90 138 534 1119 341 67 170 143 118 231 78 66

3501 8.5 triaxle 90 242 093 958 407 72 215 180 151 281 103 70

3504 4.5 triaxle 90 63 777 933 386 95 178 160 135 234 76 88

3504 5.5 triaxle 90 88 701 909 386 96 231 195 174 259 80 90



Table F 6: Cycles to 4 mm deformation level and aggregate stiffness parameters for 90 kN triaxle group locations

Experiment Chainage (mm)

Group Load Cycles to 4 mm

D0

(µm) Ebase

(MPa) Eclay

(MPa) Esg

(MPa) Estructure

(MPa)

Esupport

(MPa) Erock

(MPa) Ebase_low

(MPa) Eimp_sg

(MPa)

3501 4 triaxle 90 11 181 1808 216 54 204 134 130 142 50 42

3501 4.5 triaxle 90 14 941 1836 173 59 208 133 136 126 50 48

3501 5 triaxle 90 17 635 1648 229 72 209 148 147 152 50 59

3501 5.5 triaxle 90 24 691 1546 194 61 210 142 141 145 58 54

3501 6 triaxle 90 33 227 1492 221 59 193 135 126 163 62 50

3501 6.5 triaxle 90 64 374 1354 295 59 152 125 102 204 68 54

3501 7 triaxle 90 113 701 1251 313 60 151 127 101 218 75 57

3501 7.5 triaxle 90 192 493 1165 323 63 206 159 137 235 89 59

3504 4.5 triaxle 90 133 404 933 386 95 178 160 135 234 76 88

3504 5.5 triaxle 90 235 555 909 386 96 231 195 174 259 80 90



Appendix G Axle Loads in Multiple-axle Groups that Cause the Same Damage as a Standard Axle Determined from 3D-FEM Analyses and using Homsi’s Damage Model

The following figures show the calculated axle loads with tandem, triaxle and quad-axle groups that will

cause the same damage as that caused by the Standard single axle with a load of 80 kN. Damage was

calculated as the inverse of the number of cycles to reach fatigue failure according to Homsi’s full multi-linear

model, using strain results from 3D-FEM modelling using Cast3M.

Figure G 1: Axle loads in multiple-axle groups that cause the same damage as a Standard Axle using

Homsi’s damage model – asphalt model: 1000 mpa / granular model: high quality crushed rock

(a) Granular thickness = 200 mm / subgrade = highly

plastic clay (b) Granular thickness = 200 mm / subgrade = sand

(c) Granular thickness = 400 mm / subgrade = highly

plastic clay (d) Granular thickness = 400 mm / subgrade = sand



(e) Granular thickness = 600 mm / subgrade = highly

plastic clay (f) Granular thickness = 600 mm / subgrade = sand


Homsi’s damage model – asphalt model: 1000 MPa / granular model: lower subbase










Homsi’s damage model – asphalt model: 3000 MPa / granular model: high quality crushed rock




















Homsi’s damage model – asphalt model: 5000 MPa / granular model: high quality crushed rock





















Appendix H Cemented Material Flexural modulus test results

Table H 1: Summary of flexural modulus tests under different load pulse shapes

Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C001 97.0 100.8 300 97.4 Sample deteriorated during test. Sample discarded.

C002 97.8 100.8 300 97.9 Large differences between LVDTs during tests. Logs indicated poor sample handling. Sample discarded.

C003 82.3 80.8 375 97.8 14 105 7 738 7 812 7 813 7 834 7 823 7 879 7 916 7 881

C004 80.5 82.5 375 97.1 12 207 17 874 17 778 17 740 17 660 18 134 18 079 18 214 18 093

C005 81.8 82.5 375 97.3 12 202 16 798 16 777 16 783 16 661 16 783 16 701 16 748 16 635

C006 81.5 81.5 375 99.0 15 139 9 213 9 374 9 234 9 251 9 434 9 511 9 484 9 485

C007 81.5 82.0 375 97.7 13 205 16 245 16 550 16 447 16 499 16 482 16 384 16 438 16 399

C008 96.0 100.8 300 96.4 28 431 16 059 15 955 15 765 15 480 15 561 15 464 15 331 15 222

C009 96.5 101.5 300 97.0 22 483 22 115 22 854 22 727 22 506 22 605 22 471 22 408 22 166

C010 95.0 102.5 300 97.8 27 451 16 441 16 791 16 842 16 674 16 962 16 837 16 834 16 585

C011 95.0 100.8 300 – Sample deteriorated during test. Sample discarded.

C012 104.3 101.3 300 98.3 23 449 19 882 19 742 19 545 19 470 19 560 19 435 19 610 19 461

C013 96.5 102.5 300 96.5 19 473 25 354 25 581 25 539 25 476 25 232 25 140 25 309 25 095

C014 102.0 102.0 300 100.0 24 452 19 255 19 296 19 145 18 828 19 075 18 859 19 093 18 848

C015 95.0 103.3 300 97.0 30 444 15 331 15 373 15 197 15 110 14 971 15 000 14 936 14 936

C016(1) 95.0 102.8 300 96.6 21 479 23 201 23 517 23 507 23 262 23 253 22 925 23 104 22 734

C017 96.5 95.8 300 98.3(2) 22 543 25 667 25 610 25 181 24 913 25 169 24 608 25 053 24 567

C017B 80.0 80.3 375 98.3 13 255 19 913 20 201 20 110 19 941 20 162 20 003 20 201 19 956

C018 96.0 100.3 300 99.5 24 498 21 449 21 590 21 164 20 932 21 380 20 840 21 341 21 155

C019 80.5 81.5 375 96.7 14 235 17 273 17 551 17 468 17 325 17 344 17 139 17 385 17 148

C020 80.8 81.0 375 95.3 14 191 14 336 14 396 14 355 14 309 14 383 14 285 14 401 14 316

C021 95.5 102.3 300 96.0 25 451 18 323 18 165 17 959 17 546 18 109 17 924 18 006 17 810

C022 79.8 79.3 375 101.0 13 262 19 775 19 965 19 882 19 772 19 903 19 729 19 862 19 760

C023 97.8 101.8 300 96.8(2) 23 474 21 143 21 225 20 742 20 515 20 707 20 433 20 876 20 543

C023B 82.0 81.0 375 96.8 13 265 20 549 20 722 20 626 20 549 20 542 20 269 20 133 19 875



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C024 96.3 101.3 300 99.3(2) 23 486 21 847 22 265 21 853 21 463 21 662 21 473 21 662 21 455

C024B 81.3 80.8 375 99.3 12 262 22 055 22 429 22 398 22 219 22 311 22 192 22 296 22 160

C025 95.3 99.3 300 96.9 24 400 16 603 17 144 16 960 16 932 16 709 16 475 16 584 16 419

C026(1) 103.3 99.3 300 97.6(2) 21 472 23 494 23 628 23 474 22 675 23 238 22 654 23 068 22 636

C026B 80.8 82.8 375 97.6 13 271 22 184 21 985 21 879 22 057 21 970 22 015 21 826 21 849

C027 96.0 100.8 300 96.9 28 369 13 315 13 651 13 459 13 282 13 184 13 024 12 971 12 824

C028 103.5 99.0 300 97.9(2) 22 473 21 133 21 788 21 374 21 304 21 439 21 271 21 342 21 462

C028B 79.3 81.0 375 97.9 12 274 22 081 22 428 22 306 22 381 22 374 22 428 22 494 22 592

C029 104.5 101.5 300 97.8(2) 20 446 23 222 22 920 22 445 22 120 22 415 22 208 22 353 22 176

C029B 80.5 80.3 375 97.8 13 289 22 656 22 980 22 842 22 636 22 834 22 636 22 812 22 601

C030 103.0 101.8 300 96.4 24 450 19 438 19 369 19 166 19 203 18 875 18 607 18 980 18 495

C031 78.8 80.3 375 98.9 13 170 13 358 13 620 13 536 13 337 13 483 13 269 13 368 13 365

C032 81.0 81.5 375 98.1 13 230 18 380 18 627 18 681 18 303 18 453 18 190 18 488 18 216

C033 80.3 81.3 375 98.0 14 248 18 580 18 216 18 298 18 340 18 381 18 302 18 456 18 370

C034 80.3 80.8 375 96.7 14 251 18 103 18 274 18 287 18 157 18 181 18 013 18 202 18 029

C035 106.0 99.0 300 88.3 22 232 10 607 10 886 10 860 10 749 10 835 10 723 10 814 10 692

C036 80.5 81.0 375 97.2 14 249 18 042 18 235 18 269 18 163 18 261 18 213 18 201 18 140

C037 99.0 100.5 300 95.1 23 450 19 470 20 100 19 616 19 545 19 445 19 591 19 375 19 383

C038 80.5 80.5 375 97.7 13 252 19 613 19 870 19 825 19 636 19 802 19 610 19 799 19 585

C039 80.8 81.0 375 93.5 13 226 17 064 17 365 17 317 17 250 17 528 17 520 17 489 17 405

C040 79.5 80.5 375 98.9 13 217 16 633 16 908 17 051 16 914 16 735 16 703 16 735 16 644

C041 95.3 102.8 300 98.1(2) 22 477 21 971 21 921 21 960 21 652 21 827 21 560 21 686 21 515

C041B 79.8 82.0 375 98.1 13 259 20 502 20 745 20 624 20 466 20 537 20 409 20 522 20 387

C042 79.5 80.0 375 95.4 13 59 4 412 4 574 4 643 4 596 4 651 4 480 4 585 4 628

C043 100.8 100.8 300 99.2(2) 22 469 21 382 21 811 21 512 20 951 21 408 20 777 21 483 20 763

C043B 80.8 81.5 375 99.2 12 262 22 726 23 103 23 109 23 094 22 956 23 018 22 936 22 977

C044 100.8 101.5 300 98.6(2) 22 464 21 523 21 853 21 276 20 667 21 431 20 861 21 536 20 635

C044B 80.5 82.0 375 98.6 12 260 21 630 22 011 21 895 21 851 21 915 21 887 21 833 21 867

C045 79.8 79.8 375 97.1 13 259 19 394 19 848 19 799 19 808 20 023 19 853 19 996 20 056



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C047 82.3 80.5 375 98.2 13 246 19 617 19 852 19 846 19 774 19 881 19 700 19 845 19 781

C048 96.8 101.3 300 98.5(2) 24 484 20 004 20 653 20 338 20 103 20 136 19 945 20 133 19 945

C048B 96.8 101.3 300 98.5 25 484 19 480 19 872 19 427 19 488 19 442 19 099 19 551 19 258

C048C 81.0 80.3 375 98.5 13 266 20 735 21 063 20 913 20 772 20 907 20 704 20 954 20 740

C049 105.0 99.8 300 97.7(2) 23 459 19 828 20 653 20 045 19 581 20 072 19 655 20 005 19 707

C049B 80.8 80.5 375 97.7 14 287 20 458 20 792 20 737 20 563 20 647 20 560 20 605 20 566

C050 80.5 80.3 375 96.2 16 235 15 149 15 362 15 321 15 289 15 177 15 111 15 067 15 013

C051 81.5 80.8 375 97.2 14 175 13 131 13 302 13 192 13 177 12 964 13 012 12 923 12 865

C052 80.8 81.0 375 94.0 13 163 12 267 12 494 12 307 12 297 12 378 12 414 12 436 12 411

C053 99.3 100.3 300 99.9 23 391 16 688 17 173 17 078 16 968 16 955 16 893 16 977 16 911

C054 80.3 80.3 375 99.3 12 181 15 631 15 822 15 719 15 715 15 741 15 682 15 731 15 689

C055(1) 79.0 79.3 375 98.0 13 136 10 938 11 072 11 058 10 909 11 018 10 987 10 842 10 824

C056 100.3 99.8 300 96.2 23 451 19 672 20 205 19 814 19 611 19 829 19 645 19 833 19 538

C057 80.8 80.3 375 98.9 13 245 19 044 19 340 19 386 19 279 19 229 19 189 19 197 19 165

C058 81.8 79.5 375 98.7 12 254 21 053 21 058 20 996 21 004 20 974 20 968 21 044 20 946

C059 100.8 98.0 300 98.1(2) 23 496 21 728 22 393 22 029 21 977 22 087 21 950 22 054 21 979

C059B 80.5 80.3 375 98.1 12 253 21 096 21 212 21 113 21 027 21 046 20 958 21 022 21 035

C060 80.3 80.3 375 96.2 12 254 20 806 21 105 21 042 20 749 21 023 20 764 20 960 20 679

C061 100.3 101.3 300 96.2(2) 21 467 22 356 22 091 21 753 21 363 22 182 22 132 22 436 22 322

C061B 82.5 79.3 375 96.2 13 271 21 358 21 847 21 810 21 751 21 787 21 760 21 748 21 702

C062 79.5 80.8 375 98.3 13 271 21 080 21 423 21 377 21 243 21 260 21 117 21 170 21 033

C063 79.3 79.3 375 97.5 13 188 14 427 14 613 14 529 14 449 14 488 14 417 14 510 14 451

C064 81.0 81.3 375 95.5 13 217 16 810 17 060 16 879 16 797 16 809 16 779 16 783 16 749

C065 78.5 80.0 375 101.8 13 243 19 528 19 858 19 840 19 694 19 799 19 660 19 793 19 614

C066 96.3 100.5 300 94.6(2) 23 494 21 660 22 497 22 210 21 897 22 125 21 798 22 143 21 872

C066B 81.5 81.3 375 94.6 13 244 18 666 19 253 19 074 18 998 19 065 18 858 18 931 18 936

C067 102.5 100.0 300 96.1 24 380 16 174 16 385 16 168 15 729 16 149 15 659 15 868 15 586

C068 101.5 101.3 300 98.2(2) 20 461 22 971 23 350 23 032 22 891 23 111 22 826 23 131 22 992

C068B 80.0 81.0 375 98.2 12 268 21 839 21 787 21 646 21 717 21 668 21 611 21 731 21 662



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C069 80.5 79.0 375 96.7 13 224 18 419 18 557 18 425 18 337 18 459 18 383 18 433 18 339

C070 79.5 80.5 375 100.7 13 291 23 225 23 374 23 400 23 208 23 372 23 080 23 276 23 096

C071 100.3 103.3 300 98.9(2) 20 449 23 040 23 337 23 326 22 946 23 309 23 279 23 104 23 078

C071B 80.3 79.8 375 98.9 13 294 22 561 22 682 22 630 22 508 22 577 22 487 22 511 22 448

C072 79.5 81.5 375 96.7 14 249 18 218 18 248 18 291 18 254 18 283 18 151 18 278 18 151

C073 101.5 101.5 300 96.5 27 459 17 752 17 883 17 583 17 133 17 565 17 333 17 585 17 271

C075 81.5 81.0 375 96.8 14 228 16 902 17 099 16 996 16 858 16 946 16 853 16 903 16 843

C076 102.5 98.0 300 96.8(2) 23 488 21 215 21 738 21 503 21 068 21 440 21 292 21 377 21 246

C076B 81.3 80.3 375 96.8 12 251 20 694 20 974 20 849 20 598 20 800 20 656 20 588 20 485

C077 79.8 80.3 375 97.1 13 219 17 756 17 922 17 786 17 742 17 782 17 749 17 802 17 744

C078 102.5 99.0 300 95.4 26 299 11 770 12 039 11 927 11 855 11 798 11 680 11 628 11 522

C080 79.0 79.0 375 99.4 12 243 19 839 20 057 20 017 19 916 20 125 19 681 20 028 19 896

C081 80.8 82.3 375 96.8 16 481 30 983 31 311 31 215 31 036 31 121 31 176 31 176 31 044

C082 80.0 79.0 375 97.9 12 225 18 816 19 151 19 074 19 019 19 103 18 923 19 175 19 057

C083 99.8 99.0 300 96.3(2) 24 491 20 541 21 325 21 019 20 661 20 881 20 476 20 723 20 225

C083B 81.0 81.8 375 96.3 13 260 20 186 20 282 20 223 20 083 20 305 20 085 20 115 20 180

C084 81.0 80.5 375 98.0 13 243 19 389 19 808 19 760 19 716 19 722 19 569 19 613 19 433

C086 104.3 99.5 300 96.5(2) 23 465 20 427 21 067 20 565 20 153 20 606 20 047 20 632 20 147

C086B 82.5 80.8 375 96.5 13 261 19 991 20 388 20 316 20 262 20 234 20 184 20 172 20 288

C088 81.0 81.0 375 100.0 14 247 18 528 18 316 18 306 18 139 18 283 18 198 18 400 18 181

C089 96.8 100.5 300 98.5(2) 20 491 25 179 26 237 25 925 25 285 25 423 25 002 25 699 24 931

C089B 80.3 80.5 375 98.5 13 288 22 083 22 392 22 330 22 027 22 274 22 004 22 241 22 006

C090 104.3 100.0 300 99.2(2) 21 460 22 870 23 292 22 781 22 505 22 491 22 296 22 270 22 363

C090B 80.8 80.5 375 99.2 13 287 22 722 23 027 23 021 22 812 22 987 22 834 22 933 22 813

C091 104.0 98.8 300 97.7(2) 20 473 23 748 24 655 23 986 23 129 23 907 23 205 23 734 23 408

C091B 81.5 80.3 375 97.7 13 250 20 170 20 023 19 954 19 808 19 886 20 080 19 881 20 011

C092 98.8 101.5 300 96.8(2) 20 472 23 247 23 751 23 430 22 981 23 497 22 983 23 778 23 203

C092B 79.5 81.0 375 96.8 15 288 20 204 19 968 19 895 19 871 20 006 19 881 19 966 19 866

C094 80.0 79.8 375 97.7 12 221 18 014 18 311 18 233 18 114 18 402 18 200 18 380 18 147



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C095 104.5 98.0 300 96.1(2) 20 478 23 901 24 562 24 255 23 333 24 484 23 712 24 371 23 918

C095B 80.5 81.5 375 96.1 13 246 18 997 19 102 19 143 19 061 19 190 19 024 19 084 19 092

C096 100.3 98.3 300 94.6(2) 22 496 23 374 24 278 23 745 22 811 23 266 22 713 23 088 22 750

C096B 81.3 80.8 375 94.6 12 212 17 402 17 720 17 643 17 480 17 628 17 479 17 566 17 410

C097 103.8 97.8 300 98.3(2) 21 484 22 981 24 105 23 719 23 171 23 493 23 176 23 272 23 093

C097B 79.8 79.5 375 98.3 12 260 21 446 21 662 21 605 21 594 21 532 21 536 21 497 21 492

C098 80.8 79.5 375 95.8 14 220 15 320 15 572 15 542 15 434 15 469 15 313 15 388 15 291

C099 82.0 81.5 375 99.4 13 220 17 207 17 514 17 399 17 317 17 722 17 512 17 338 17 171

C100 101.0 100.5 300 97.2(2) 20 470 23 304 24 031 23 667 23 372 23 601 23 124 23 737 23 059

C100B 101.0 100.5 375 97.2 15 294 18 915 19 176 19 124 19 179 19 175 19 235 19 104 19 266

C101 105.0 97.3 300 – 20 483 24 187 25 164 24 402 24 200 24 421 24 123 24 431 24 506

C101B 105.0 97.3 375 – 14 302 20 697 21 235 21 046 21 129 20 923 21 168 20 719 21 166

C102 81.5 82.0 375 97.5 14 205 14 984 15 150 15 123 14 999 15 105 14 986 15 087 14 976

C104 97.0 97.0 300 97.5(2) 23 526 22 716 23 698 23 268 22 900 23 405 23 064 23 154 23 047

C104B 97.0 97.0 375 97.5 16 308 19 008 19 478 19 479 19 390 19 337 19 397 19 398 19 369

C105 99.8 97.0 300 98.1 24 320 13 390 13 362 13 287 13 222 13 318 13 202 13 339 13 193

C106 98.0 97.3 300 99.9 25 485 19 521 19 947 19 627 19 258 19 643 19 321 19 461 19 340

C107 80.3 82.0 375 99.9 15 208 14 261 14 373 14 321 14 194 14 287 14 178 14 257 14 168

C108 99.8 98.0 300 97.7 24 438 18 764 19 182 18 931 18 945 18 839 18 851 18 792 18 894

C109 80.8 84.0 375 – Distinct and sudden drop in modulus during test sequence. Sample discarded.

C110 95.8 96.0 300 – Large differences between LVDTs during tests. Logs indicated poor sample handling. Sample discarded.

C111 96.0 97.5 300 99.5(2) 23 526 23 075 23 574 23 290 22 827 23 484 23 090 23 340 23 085

C111B 96.0 97.5 375 99.5 15 288 19 594 19 979 19 973 19 936 19 980 19 983 19 965 19 882

C112 80.5 80.3 375 97.7 13 181 14 639 14 767 14 583 14 559 14 624 14 573 14 588 14 554

C113 81.8 80.8 375 98.5 13 162 12 109 12 253 12 137 12 166 12 281 12 218 12 260 12 187

C114 95.8 98.0 300 98.2(2) 23 522 22 606 23 237 22 816 22 323 22 948 22 397 23 005 22 395

C114B 95.8 98.0 375 98.2 14 285 19 898 20 067 19 989 20 043 20 105 20 072 20 140 20 120

C115 81.3 81.3 375 98.1 14 210 15 251 15 403 15 438 15 329 15 395 15 280 15 374 15 251

C116 80.8 82.0 375 98.9 15 242 16 899 17 053 17 009 16 924 17 054 16 908 17 039 16 861



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80

C117 80.5 80.8 375 96.2 12 200 16 284 16 560 16 466 16 363 16 400 16 321 16 403 16 296

C118 80.5 81.0 375 98.2 14 178 12 474 12 638 12 548 12 444 12 536 12 446 12 483 12 485

C119 81.8 81.5 375 98.0 14 207 14 969 15 123 15 042 14 893 15 045 14 861 15 020 14 875

C120 80.8 80.8 375 97.3 13 264 19 888 20 317 20 186 20 059 20 193 19 983 20 203 19 933

C121 80.5 81.8 375 97.5 14 209 14 943 15 196 15 049 14 887 15 012 14 864 15 060 14 899

C122 81.5 82.3 375 98.4 13 250 19 528 19 333 19 222 19 141 18 923 18 853 19 044 18 851

C123 79.8 80.8 375 97.4 12 180 15 276 15 260 15 153 15 296 15 194 15 247 15 041 15 189

C124 80.0 80.0 375 99.5 13 278 21 771 22 170 22 140 21 957 22 130 21 948 22 129 21 920

C125 79.3 82.8 375 98.2 14 242 17 568 17 838 17 866 17 767 17 899 17 793 17 893 17 844

C126 80.3 80.0 375 97.3 13 161 12 731 12 841 12 818 12 665 12 723 12 725 12 824 12 679

C127 79.8 81.0 375 98.1 13 215 17 550 17 710 17 519 17 489 17 503 17 502 17 494 17 483

C128 79.0 80.0 375 – 12 148 12 059 12 195 12 240 12 224 12 150 12 140 12 200 12 116

C129 80.0 80.5 375 98.2 12 246 20 728 20 721 20 707 20 643 20 711 20 508 20 639 20 560

C130 81.0 79.5 375 98.1 13 278 21 289 21 812 21 605 21 459 21 560 21 349 21 502 21 353


C132 80.0 81.8 375 97.7 12 105 8 711 8 879 8 916 8 893 8 872 8 841 8 896 8 860

C133 79.8 81.0 375 – 13 287 22 012 22 465 22 389 22 386 22 429 22 298 22 419 22 321

C134 80.5 82.5 375 97.5 Distinct and sudden drop in modulus during test sequence. Sample discarded.

C135 80.0 81.0 375 60.9 13 79 6 265 6 440 6 441 6 421 6 376 6 359 6 371 6 356


C137 80.3 80.5 375 98.2 14 225 16 729 17 090 17 031 17 003 17 259 17 168 17 209 17 150

C138 81.3 81.3 375 97.1 13 175 13 545 13 695 13 612 13 612 13 577 13 608 13 549 13 565

C139 82.5 80.5 375 96.8 14 281 20 373 20 655 20 718 20 720 20 611 20 668 20 574 20 620

C140 80.3 81.3 375 – 13 212 17 074 17 036 17 068 16 952 17 046 17 017 17 075 17 021


C142 82.5 82.5 375 97.0 14 234 17 294 17 549 17 481 17 505 17 464 17 503 17 383 17 326

C144 82.8 82.0 375 98.1 14 168 12 528 12 713 12 641 12 661 12 639 12 564 12 609 12 515

C145 82.0 80.5 375 98.7 13 282 21 123 21 587 21 513 21 472 21 531 21 479 21 536 21 455

C146 81.5 81.8 375 97.3 14 224 16 141 16 138 16 077 16 034 16 057 16 020 16 012 15 983



Sample Width (mm)

Height (mm)

Span (mm)

Relative density

%

Peak strain

()

Peak stress (kPa)

Modulus (MPa)

Pulse: Haversine

Pulse: 1_00

Pulse: 2_40

Pulse: 2_80

Pulse: 3_40

Pulse: 3_80

Pulse: 4_40

Pulse: 4_80


C150 83.8 88.3 375 96.0 15 172 11 511 11 629 11 569 11 490 11 513 11 477 11 541 11 496

C152 79.8 81.5 375 98.0 14 212 15 476 15 569 15 543 15 465 15 529 15 520 15 475 15 472

C154 81.3 81.5 375 97.6 14 208 14 770 15 025 14 998 14 923 15 014 14 935 15 007 14 912


C158 83.0 82.0 375 97.7 13 242 19 365 19 289 19 194 19 075 18 800 18 804 19 015 18 995

C159 80.0 80.0 375 95.4 15 183 12 726 12 902 12 806 12 651 12 198 12 310 12 377 12 134

C160 80.0 81.8 375 97.0 14 168 12 781 12 928 12 831 12 806 12 890 12 822 12 779 12 810

1 A single spike reading during the modulus test was excluded from subsequent analysis. 2 These density values are assumptions based on the density determined from the resized sample subjected to subsequent fatigue testing.



Appendix I Cemented Material Flexural Fatigue Test Results

Table I 1: Summary of flexural fatigue tests under different load pulse shapes

Sample Height (mm)

Width (mm)

Span (mm)

Moisture content

(%)

Relative density

%

Pulse Modulus test

sample

LVDT data used

Peak load (kN)

Peak stress (kPa)

Initial condition: Cycle 1 Initial condition: Cycle 50 Initial condition: Mean cycles 1–50

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

C005 82.5 81.8 375 9.0 97.3 1_00 C005 LVDT 1 and 2

1.604 1 080 86 12 654 95 023 89 12 247 95 057 87 12 382 95 047

C007 82 81.5 375 8.8 97.7 1_00 C007 LVDT 1 and 2

1.395 954 74 12 894 243 485 81 11 935 243 653 79 12 223 243 617

C020 81 80.8 375 10.2 95.3 1_00 C020 LVDT 1 and 2

1.596 1 129 100 11 363 3 481 105 10 798 3 481 103 10 989 3 481

C022B 79.3 79.8 375 7.6 101.0 1_00 C022 LVDT 1 and 2

1.748 1 306 88 14 885 158 588 88 14 889 158 588 88 14 887 158 588

C037 100.5 99 300 8.4 95.1 1_00 C037 LVDT 1 and 2

3.958 1 187 72 16 531 305 255 73 16 395 305 389 72 16 624 305 129

C056 99.8 100.3 300 9.0 96.2 1_00 C056 LVDT 1 and 2

3.766 1 131 81 13 945 2 152 108 10 700 2 634 101 11 411 2 575

C059B 80.3 80.5 375 9.3 98.1 1_00 C059B LVDT 1 and 2

2.300 1 662 90 18 446 14 297 93 17 947 14 300 92 18 076 14 299

C080 79 79 375 8.8 99.4 1_00 C080 LVDT 1 and 2

1.700 1 293 79 16 434 222 123 81 16 082 222 218 80 16 177 222 198

C082 79 80 375 9.5 97.9 1_00 C082 LVDT 1 and 2

1.689 1 269 83 15 381 79 340 87 14 789 79 342 85 14 994 79 342

C099 81.5 82 375 8.9 99.4 1_00 C099 LVDT 1 and 2

1.650 1 136 80 14 156 189 887 85 13 552 189 941 82 13 839 189 921

C100B 100.5 101 375 8.6 97.2 1_00 C100B LVDT 1 and 2

3.489 1 283 74 17 284 618 211 75 17 190 618 277 75 17 170 618 289

C120 80.8 80.8 375 10.1 97.3 1_00 C120 LVDT 1 and 2

2.022 1 437 84 17 156 15 210 88 16 354 15 223 87 16 658 15 219

C122 82.3 81.5 375 9.5 98.4 1_00 C122 LVDT 1 and 2

2.098 1 425 87 16 494 833 115 90 15 919 833 151 89 16 050 833 145

C123 80.8 79.8 375 9.9 97.4 1_00 C123 LVDT 1 and 2

1.199 863 75 11 576 24 235 82 10 760 24 262 78 11 038 24 254

C124 80 80 375 9.7 99.5 1_00 C124 LVDT 1 and 2

2.156 1 579 82 19 387 297 940 84 18 959 297 941 83 19 104 297 941

C158 82 83 375 9.0 97.7 1_00 C158 LVDT 1 and 2

2.044 1 373 85 16 213 374 748 88 15 747 374 804 87 15 910 374 787



Sample Height (mm)

Width (mm)

Span (mm)

Moisture content

(%)

Relative density

%

Pulse Modulus test

sample

LVDT data used

Peak load (kN)

Peak stress (kPa)


Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

C033 81.3 80.3 375 9.1 98.0 2_40 C033 LVDT 1 and 2

1.794 1 268 85 14 909 98 139 88 14 625 98 142 87 14 677 98 142

C036 81 80.5 375 9.3 97.2 2_40 C036 LVDT 1 and 2

1.794 1 273 87 14 794 164 788 91 14 119 164 826 89 14 318 164 816

C039 81 80.8 375 10.7 93.5 2_40 C039 LVDT 1 and 2

1.778 1 258 85 14 929 83 213 88 14 523 83 214 87 14 606 83 214

C045 79.8 79.8 375 9.3 97.1 2_40 C045 LVDT 1 and 2

1.845 1 362 84 16 221 1 664 90 15 114 1 666 87 15 636 1 665

C047 80.5 82.3 375 9.2 98.2 2_40 C047 LVDT 1 and 2

1.985 1 396 86 16 209 3 253 100 14 110 3 258 94 14 963 3 256

C053 100.3 99.3 300 7.5 99.9 2_40 C053 LVDT 1 and 2

3.574 1 073 85 12 685 3 995 91 11 956 4 010 89 12 171 4 006

C068B 81 80 375 9.4 98.2 2_40 C068B LVDT 1 and 2

2.492 1 781 95 18 786 3 394 100 18 161 3 395 97 18 462 3 394

C090B 80.5 80.8 375 8.5 99.2 2_40 C090B LVDT 1 and 2

2.400 1 719 84 20 401 571 245 85 20 381 571 245 84 20 382 571 245

C117 80.8 80.5 375 10.5 96.2 2_40 C117 LVDT 1 and 2

1.552 1 107 81 13 691 345 669 85 13 129 345 739 83 13 316 345 723

C004 82 80.5 375 9.0 97.1 2_80 C004 LVDT 1 and 2

1.694 1 174 90 13 202 12 922 98 12 231 13 419 94 12 553 13 299

C024B 80.8 81.3 375 8.9 99.3 2_80 C024B LVDT 1 and 2

2.138 1 510 80 18 970 634 960 82 18 298 634 967 80 18 545 634 964

C030 101.8 103 300 9.8 96.4 2_80 C030 LVDT 1 and 2

3.986 1 120 70 16 173 26 575 72 15 729 26 675 71 15 861 26 645

C061BCD 79.3 82.5 375 8.6 96.2 2_80 C061B LVDT 1 and 2

2.000 1 446 75 19 281 482 525 77 18 925 482 543 76 19 035 482 538

C089B 80.5 80.3 375 8.9 98.5 2_80 C089B LVDT 1 and 2

2.202 1 587 82 19 277 57 155 84 18 856 57 165 83 19 028 57 161

C091B 80.3 81.5 375 9.7 97.7 2_80 C091B LVDT 1 and 2

2.385 1 702 101 16 919 2 456 104 16 359 2 459 98 18 814 2 432

C114B 98 95.8 375 8.4 98.2 2_80 C114B LVDT 1 and 2

2.788 1 136 62 18 345 548 320 65 17 580 550 593 64 17 778 550 127

C115 81.3 81.3 375 9.1 98.1 2_80 C115 LVDT 1 and 2

1.617 1 128 96 11 788 7 470 103 10 841 7 486 101 11 096 7 483

C127 81 79.8 375 8.8 98.1 2_80 C127 LVDT 1 and 2

1.601 1 147 81 14 148 11 816 88 12 998 11 837 86 13 348 11 832



Sample Height (mm)

Width (mm)

Span (mm)

Moisture content

(%)

Relative density

%

Pulse Modulus test

sample

LVDT data used

Peak load (kN)

Peak stress (kPa)


Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

C021 102.3 95.5 300 9.6 96.0 3_40 C021 LVDT 1 and 2

3.980 1 195 84 14 216 331 827 90 13 360 331 852 88 13 640 331 844

C023B 81 82 375 10.0 96.8 3_40 C023B LVDT 1 and 2

2.398 1 672 100 16 834 8 949 105 16 071 8 950 103 16 333 8 949

C044B 82 80.5 375 9.4 98.6 3_40 C044B LVDT 1 and 2

2.246 1 556 84 18 690 23 093 89 17 666 23 094 87 18 012 23 094

C060 80.3 80.3 375 9.8 96.2 3_40 C060 LVDT 1 and 2

2.237 1 620 87 18 569 44 255 91 17 991 44 257 90 18 200 44 256

C064 81.3 81 375 9.8 95.5 3_40 C064 LVDT 1 and 2

1.751 1 227 82 14 959 66 0798 83 14 752 660 806 83 14 796 660 805

C065B 80 78.5 375 8.6 101.8 3_40 C065 LVDT 1 and 2

1.998 1 492 100 14 954 48 773 101 14 941 48 773 100 14 930 48 773

C075 81 81.5 375 9.3 96.8 3_40 C075 LVDT 1 and 2

1.653 1 159 96 12 133 1 422 107 10 921 1 423 103 11 247 1 423

C106 97.3 98 300 8.9 99.9 3_40 C106 LVDT 1 and 2

3.978 1 286 83 15 575 49 112 86 15 046 49 180 85 15 182 49 166

C013BC 102.5 96.5 300 9.0 96.5 3_80 C013 LVDT 1 and 2

3.992 1 181 66 17 822 340 929 67 17 700 341 089 67 17 768 340 958

C015 103.3 95 300 9.7 97.0 3_80 C015 LVDT 1 and 2

3.397 1 005 86 11 654 15 623 96 10 515 15 719 93 10 833 15 703

C029B 80.3 80.5 375 9.7 97.8 3_80 C029B LVDT 1 and 2

2.747 1 985 99 20 075 1 794 108 18 468 1 796 104 19 074 1 795

C057 80.3 80.8 375 8.9 98.9 3_80 C057 LVDT 1 and 2

1.996 1 437 96 15 081 15 944 104 13 907 15 950 101 14 229 15 949

C072 81.5 79.5 375 9.7 96.7 3_80 C072 LVDT 1 and 2

1.744 1 238 80 15 527 11 620 85 14 735 11 640 83 14 981 11 635

C076B 80.3 81.3 375 10.1 96.8 3_80 C076B LVDT 1 and 2

2.095 1 499 85 17 674 16 455 88 17 014 16 458 87 17 259 16 457

C094 79.8 80 375 9.3 97.7 3_80 C094 LVDT 1 and 2

1.746 1 286 87 14 847 69 498 91 14 099 69 987 90 14 335 69 872

C102 82 81.5 375 9.5 97.5 3_80 C102 LVDT 1 and 2

1.490 1 020 86 11 819 15 157 95 10 904 15 279 92 11 184 15 258

C109 84 80.8 375 8.7 98.4 3_80 – LVDT 1 and 2

1.804 1 186 87 13 627 15 418 95 12 533 15 655 92 12 865 15 600

C111B 97.5 96 375 8.7 99.5 3_80 C111B LVDT 1 and 2

2.595 1 066 58 18 444 432 552 60 17 841 432 653 59 18 041 432 622



Sample Height (mm)

Width (mm)

Span (mm)

Moisture content

(%)

Relative density

%

Pulse Modulus test

sample

LVDT data used

Peak load (kN)

Peak stress (kPa)


Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

C112 80.3 80.5 375 9.6 97.7 3_80 C112 LVDT 1 and 2

1.499 1 083 91 11 920 12 576 94 11 530 12 588 93 11 700 12 583

C129 80.5 80 375 9.7 98.2 3_80 C129 LVDT 1 and 2

1.895 1 371 87 15 837 11 089 94 14 699 11 100 91 15 053 11 097

C010 102.5 95 300 9.0 97.8 4_40 C010 LVDT 2 3.185 957 74 12 858 99 759 83 11 561 103 963 81 11 945 103 385

C043B 81.5 80.8 375 9.9 99.2 4_40 C043B LVDT 1 and 2

2.383 1 665 90 18 615 3 202 96 17 524 3 207 94 17 879 3 206

C049B 80.5 80.8 375 9.6 97.7 4_40 C049B LVDT 1 and 2

2.501 1 791 102 17 682 4 512 109 16 501 4 519 106 16 890 4 517

C066B 81.3 81.5 375 10.6 94.6 4_40 C066B LVDT 1 and 2

1.897 1 320 80 16 476 153 384 84 16 041 153 392 82 16 166 153 390

C071B 79.8 80.3 375 8.2 98.9 4_40 C071B LVDT 1 and 2

2.199 1 612 82 19 612 589 340 83 19 415 589 340 83 19 454 589 340

C116 82 80.8 375 9.0 98.9 4_40 C116 LVDT 1 and 2

1.805 1 246 97 12 921 1 135 105 11 983 1 138 102 12 239 1 137

C011 100.8 95 300 9.1 97.2 4_80 C011 LVDT 1 and 2

3.395 1 055 50 21 328 452 949 53 20 240 474 828 51 20 608 468 139

C012 101.3 104.3 300 8.8 98.3 4_80 C012 LVDT 1 and 2

3.195 896 63 14 227 99 123 70 12 859 109 229 68 13 274 106 948

C017B 80.3 80 375 9.8 98.3 4_80 C017B LVDT 1 and 2

2.298 1 670 100 16 655 8 015 104 16 130 8 016 103 16 262 8 016

C086B 80.8 82.5 375 9.9 96.5 4_80 C086B LVDT 1 and 2

1.947 1 355 77 17 615 24 304 80 17 066 24 304 79 17 291 24 304

C104B 97 97 375 8.7 97.5 4_80 C104B LVDT 1 and 2

3.497 1 437 81 17 809 63 175 83 17 426 63 186 82 17 571 63 182

C108 98 99.8 300 9.1 97.7 4_80 C108 LVDT 1 and 2

3.689 1 155 84 13 803 9 857 91 12 768 9 931 89 13 096 9 912

C146 81.8 81.5 375 9.4 97.2 4_80 C146 LVDT 1 and 2

1.402 964 74 13 100 48 391 78 12 327 48 850 76 12 662 48 679

C148 82 80.5 375 8.2 99.4 4_80 C148 LVDT 1 and 2

1.806 1 251 81 15 622 86 375 83 15 277 86 381 81 15 414 86 381



Appendix J Estimation of Tolerable Strain from Fatigue Test Results

Table J 1: Estimates of tolerable strain for each fatigue test

Sample Relative density

(%)

Pulse Fatigue test results Correction to 98% density ratio

Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus

Tolerable strain (TS)

()

Modulus (MPa)

Flexural strength at 98% (MPa)

Predicted TS at 98%

density

()

Flexural strength at test

density (MPa)

Predicted TS at test density

()

Correction factor

Tolerable strain at

98% density

()

Parameter (section X) 𝜺𝒊 𝑬𝒊 𝑵𝒊 𝜺𝟓𝒊 𝑬𝟗𝟖% 𝑭𝑺𝟗𝟖% 𝜺𝟓𝒆𝟗𝟖% 𝑭𝑺𝒊 𝜺𝟓𝒆𝒊

𝒇𝒊 𝒇𝒊 × 𝜺𝟓𝒊

C005 97.30% 1_00 89 12 247 95 057 88.62 12 676 1.67 86.89 1.61 85.48 1.02 90.08

C007 97.70% 1_00 81 11 935 243 653 87.24 12 114 1.67 89.53 1.64 88.97 1.01 87.79

C020 95.30% 1_00 105 10 798 3 481 79.37 Relative density of sample less than 96%. Case dropped.

C022B 101.00% 1_00 88 14 889 158 588 91.45 Relative density of sample greater than 100%. Case dropped.


C056 96.20% 1_00 108 10 700 2 634 79.76 11 663 1.67 91.84 1.53 88.67 1.04 82.62

C059B 98.10% 1_00 93 17 947 14 300 79.09 17 857 1.67 70.34 1.67 70.63 1.00 78.77

C080 99.40% 1_00 81 16 082 222 218 86.57 14 956 1.67 78.19 1.77 81.62 0.96 82.94

C082 97.90% 1_00 87 14 789 79 342 85.34 14 863 1.67 78.50 1.66 78.26 1.00 85.60

C099 99.40% 1_00 85 13 552 189 941 89.67 12 603 1.67 87.22 1.77 90.00 0.97 86.89

C100B 97.20% 1_00 75 17 190 618 277 87.30 17 878 1.67 70.30 1.60 68.03 1.03 90.21

C120 97.30% 1_00 88 16 354 15 223 75.22 16 926 1.67 72.57 1.61 70.66 1.03 77.25

C122 98.40% 1_00 90 15 919 833 151 107.39 15 601 1.67 76.20 1.70 77.22 0.99 105.98

C123 97.40% 1_00 82 10 760 24 262 72.87 11 083 1.67 95.08 1.62 94.12 1.01 73.61

C124 99.50% 1_00 84 18 959 297 941 92.00 17 537 1.67 71.08 1.78 75.28 0.94 86.87

C158 97.70% 1_00 88 15 747 374 804 98.24 15 983 1.67 75.09 1.64 74.31 1.01 99.27

C033 98.00% 2_40 88 14 625 98 142 87.86 14 625 1.67 79.29 1.67 79.29 1.00 87.86

C036 97.20% 2_40 91 14 119 164 826 94.87 14 684 1.67 79.09 1.60 77.17 1.02 97.23


C045 97.10% 2_40 90 15 114 1 666 63.98 15 794 1.67 75.63 1.60 73.32 1.03 66.00

C047 98.20% 2_40 100 14 110 3 258 75.18 13 969 1.67 81.61 1.68 82.06 0.99 74.76

C053 99.90% 2_40 91 11 956 4 010 69.60 10 820 1.67 96.67 1.81 99.55 0.97 67.59




(%)


Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus


()

Modulus (MPa)


Predicted TS at 98%

density

()


density (MPa)


()

Correction factor

Tolerable strain at

98% density

()

C068B 98.20% 2_40 100 18 161 3 395 75.43 17 979 1.67 70.07 1.68 70.64 0.99 74.83

C090B 99.20% 2_40 85 20 381 571 245 98.29 Modulus exceeds 20 000 MPa. Case dropped.

C117 96.20% 2_40 85 13 129 345 739 94.26 14 311 1.67 80.37 1.53 76.17 1.06 99.46

C004 97.10% 2_80 98 12 231 13 419 82.90 12 781 1.67 86.42 1.60 84.59 1.02 84.69

C024B 99.30% 2_80 82 18 298 634 967 95.66 17 109 1.67 72.12 1.77 75.69 0.95 91.14

C030 96.40% 2_80 72 15 729 26 675 64.49 16 987 1.67 72.42 1.54 68.05 1.06 68.64

C061BCD 96.20% 2_80 77 18 925 482 543 87.79 20 628 1.67 64.91 1.53 59.31 1.09 96.07

C089B 98.50% 2_80 84 18 856 57 165 80.18 18 385 1.67 69.18 1.71 70.63 0.98 78.53

C091B 97.70% 2_80 104 16 359 2 459 76.37 16 604 1.67 73.40 1.64 72.59 1.01 77.22

C114B 98.20% 2_80 65 17 580 550 593 74.93 17 404 1.67 71.40 1.68 71.95 0.99 74.35

C115 98.10% 2_80 103 10 841 7 486 82.99 10 787 1.67 96.87 1.67 97.02 1.00 82.86

C127 98.10% 2_80 88 12 998 11 837 73.66 12 933 1.67 85.75 1.67 85.96 1.00 73.49

C021 96.00% 3_40 90 13 360 331 852 99.46 14 696 1.67 79.05 1.51 74.25 1.06 105.89

C023B 96.80% 3_40 105 16 071 8 950 85.87 17 035 1.67 72.30 1.57 69.01 1.05 89.96

C044B 98.60% 3_40 89 17 666 23 094 78.77 17 136 1.67 72.05 1.71 73.70 0.98 77.00

C060 96.20% 3_40 91 17 991 44 257 85.02 19 610 1.67 66.73 1.53 61.30 1.09 92.56


C065B 101.80% 3_40 101 14 941 48 773 95.13 Relative density of sample greater than 100%. Case dropped.

C075 96.80% 3_40 107 10 921 1 423 75.07 11 576 1.67 92.30 1.57 90.22 1.02 76.81

C106 99.90% 3_40 86 15 046 49 180 81.06 13 617 1.67 82.95 1.81 87.14 0.95 77.16

C013BC 96.50% 3_80 67 17 700 341 089 74.21 19 028 1.67 67.86 1.55 63.42 1.07 79.41

C015 97.00% 3_80 96 10 515 15 719 82.28 11 041 1.67 95.33 1.59 93.75 1.02 83.67

C029B 97.80% 3_80 108 18 468 1 796 77.26 18 653 1.67 68.62 1.65 68.03 1.01 77.92

C057 98.90% 3_80 104 13 907 15 950 89.25 13 281 1.67 84.29 1.74 86.21 0.98 87.26

C072 96.70% 3_80 85 14 735 11 640 71.05 15 693 1.67 75.93 1.57 72.60 1.05 74.31

C076B 96.80% 3_80 88 17 014 16 458 75.71 18 035 1.67 69.95 1.57 66.52 1.05 79.62

C094 97.70% 3_80 91 14 099 69 987 88.33 14 310 1.67 80.38 1.64 79.68 1.01 89.11

C102 97.50% 3_80 95 10 904 15 279 81.23 11 177 1.67 94.54 1.63 93.72 1.01 81.94




(%)


Initial strain

()

Initial modulus

(MPa)

Cycles to half

modulus


()

Modulus (MPa)


Predicted TS at 98%

density

()


density (MPa)


()

Correction factor

Tolerable strain at

98% density

()

C109 98.40% 3_80 95 12 533 15 655 81.40 12 282 1.67 88.71 1.70 89.48 0.99 80.70

C111B 99.50% 3_80 60 17 841 432 653 67.79 16 503 1.67 73.67 1.78 77.67 0.95 64.29

C112 97.70% 3_80 94 11 530 12 588 79.09 11 703 1.67 91.63 1.64 91.10 1.01 79.55

C129 98.20% 3_80 94 14 699 11 100 78.27 14 552 1.67 79.54 1.68 80.01 0.99 77.80

C010 97.80% 4_40 83 11 561 103 963 83.27 11 677 1.67 91.77 1.65 91.41 1.00 83.59

C043B 99.20% 4_40 96 17 524 3 207 72.07 16 473 1.67 73.75 1.76 76.95 0.96 69.08

C049B 97.70% 4_40 109 16 501 4 519 84.21 16 749 1.67 73.02 1.64 72.21 1.01 85.15

C066B 94.60% 4_40 84 16 041 153 392 87.05 Relative density of sample less than 96%. Case dropped.

C071B 98.90% 4_40 83 19 415 589 340 96.22 18 541 1.67 68.85 1.74 71.47 0.96 92.70

C116 98.90% 4_40 105 11 983 1 138 72.31 11 444 1.67 93.03 1.74 94.56 0.98 71.14

C011 97.20% 4_80 53 20 240 474 828 60.35 Modulus exceeds 20,000 MPa. Case dropped.

C012 98.30% 4_80 70 12 859 109 229 70.52 12 666 1.67 86.93 1.69 87.53 0.99 70.03

C017B 98.30% 4_80 104 16 130 8 016 84.27 15 888 1.67 75.36 1.69 76.14 0.99 83.42

C086B 96.50% 4_80 80 17 066 24 304 71.10 18 346 1.67 69.27 1.55 64.93 1.07 75.85

C104B 97.50% 4_80 83 17 426 63 186 79.88 17 862 1.67 70.33 1.63 68.92 1.02 81.53

C108 97.70% 4_80 91 12 768 9 931 75.07 12 960 1.67 85.64 1.64 85.02 1.01 75.62

C146 97.20% 4_80 78 12 327 48 850 73.48 12 820 1.67 86.25 1.60 84.61 1.02 74.90

C148 99.40% 4_80 83 15 277 86 381 81.99 14 208 1.67 80.74 1.77 83.98 0.96 78.83



Appendix K Axle Group/load Distributions

Table K 1: Traffic load distribution: Pacific Motorway

Axle group load (kN)

Axle group type

SAST % SADT % TAST % TADT % TRDT % QADT %

10 0.0101 1.0001 0.0000 0.0900 0.0000 0.0000

20 1.2666 1.5502 0.0000 0.2100 0.0200 0.0000

30 12.5342 13.5614 0.0000 0.4600 0.0300 0.0000

40 13.9123 14.6415 0.0414 1.7100 0.1100 0.0000

50 13.8717 14.8615 0.1448 2.5000 0.6000 0.0000

60 18.4011 13.5814 1.5517 4.1100 2.0900 0.5539

70 20.6708 10.5511 5.6481 5.7500 3.6800 0.5539

80 14.8445 9.1009 9.0824 7.0100 5.2800 0.3728

90 4.4888 7.1007 8.7825 6.8800 5.6500 2.2262

100 5.3405 10.6031 6.2500 5.2800 5.9438

110 3.7704 13.1271 5.6300 4.8400 9.8530

120 2.3202 13.5306 4.7000 4.3200 18.4065

130 1.4901 14.1202 4.7600 4.3300 12.6438

140 0.7801 10.9341 4.7000 3.8800 5.3899

150 0.3500 6.6205 4.9700 3.8900 2.7908

160 0.0000 3.7550 5.5600 4.1600 2.5991

170 0.0000 2.0585 5.4800 3.9000 2.0452

180 0.0000 5.7200 4.3000 0.7456

190 5.1800 4.3000 1.6723

200 4.8500 4.6000 1.2995

210 4.4200 5.2400 0.5539

220 3.2700 5.1800 1.1184

230 2.3500 5.5300 1.2995

240 1.4300 4.9500 1.4913

250 0.8800 4.2700 1.8641

260 0.5900 3.5600 1.4913

270 0.3000 2.3500 1.4913

280 0.1700 1.5100 0.9267

290 0.0600 0.8700 1.2995

300 0.0100 0.4700 0.9267

310 0.0000 0.3000 0.7456

320 0.0000 0.1800 1.1184

330 0.0000 0.1100 1.6723

340 0.0700 1.6723

350 0.0500 1.4913

360 0.0400 1.2995

370 0.0200 0.9267

380 0.0200 0.9267

390 0.0100 1.8641

400 0.0100 1.1184

410 0.6711

420 1.1184

430 1.5658




Axle group type


440 0.8948

450 0.8948

460 0.4474

470 0.8948

480 1.1184

Proportion of group (%)

35.77 14.96 1.21 30.50 17.52 0.04

Table K 2: Traffic load distribution: Pacific Highway


Axle group type


10 0.0003 0.6399 0.0000 0.0589 0.0003 0.0000

20 0.0343 0.8419 0.0000 0.1951 0.0549 0.0000

30 5.2513 11.3236 0.0000 0.6612 0.0988 0.0000

40 7.3739 18.7895 0.0000 2.3701 0.1836 0.0000

50 26.6742 17.9312 0.1912 2.8199 1.9650 0.0000

60 55.0585 14.6000 4.4393 5.4972 5.0161 0.0000

70 5.5357 10.7853 12.4681 8.4829 7.8058 0.9524

80 0.0618 10.4537 22.7910 8.1220 7.6824 0.0000

90 0.0090 11.6400 17.9269 6.4052 6.0080 3.8095

100 0.0010 2.5302 22.2175 5.3395 4.5971 1.9048

110 0.3690 15.8029 5.2308 3.7932 8.5714

120 0.0642 3.4834 5.7328 3.6554 11.4286

130 0.0280 0.2549 6.7512 3.6457 12.3809

140 0.0035 0.2549 8.2191 3.7700 3.8095

150 0.1487 11.3515 4.1846 4.7619

160 0.0212 12.7967 5.0045 2.8571

170 7.5614 6.5240 2.8571

180 2.0526 8.7055 5.7143

190 0.2610 10.2682 5.7143

200 0.0496 9.0760 2.8571

210 0.0196 5.3317 4.7619

220 0.0123 1.9664 1.9048

230 0.0068 0.5099 3.8095

240 0.0026 0.1021 1.9048

250 0.0279 2.8571

260 0.0088 3.8095

270 0.0050 2.8571

280 0.0050 1.9048

290 0.0033 1.9048

300 0.0008 0.9524

310 0.0000

320 0.9524

330 1.9048

340 0.9524

350 0.9524




Axle group type


360 0.9524

370

380

390

400

410

420

430

440

450

460

470

480

Proportion of group (%)

31.16 6.68 0.37 33.52 28.26 0.01

Table K 3: Traffic load distribution: Monash Freeway


Axle group type


9.8 0.5838 4.6646 0.1030 0.0874 0.0014 0.0000

19.6 3.3239 4.0160 0.1030 0.2637 0.0537 0.0000

29.4 9.2880 8.1740 0.5151 1.0795 0.1439 0.0000

39.2 13.3060 12.5626 1.4423 3.2185 0.1990 0.0000

49.0 37.2624 23.5526 3.6745 5.1012 0.5763 1.0823

58.8 30.8125 17.2424 8.6710 9.6968 2.1386 1.0823

68.6 4.9647 12.7747 9.8558 12.0036 5.8807 2.8139

78.4 0.3914 8.0898 14.6806 10.7106 10.5234 5.6277

88.2 0.0672 5.0981 17.3935 8.0117 12.3969 8.6580

98.0 2.4546 14.7837 5.8960 10.2260 16.2338

107.8 0.9360 12.7747 4.8825 6.7648 12.3377

117.6 0.3380 9.1690 4.9832 4.8796 13.8528

127.4 0.0741 4.4643 5.2834 3.4289 10.8225

137.2 0.0173 1.6827 5.8200 2.7631 3.8961

147.0 0.0051 0.5323 6.5911 2.4415 3.0303

156.8 0.0000 0.1545 7.0403 2.3651 2.3810

166.6 0.0000 5.1661 2.3548 0.6494

176.4 0.0000 2.7243 2.5820 1.2987

186.2 1.0337 3.1101 0.8658

196.0 0.2873 4.1938 1.9481

205.8 0.0760 5.3072 1.5152

215.6 0.0243 5.6624 1.7316

225.4 0.0089 5.2562 1.7316

235.2 0.0066 3.5934 1.0823

245.0 0.0033 1.8466 0.4329

254.8 0.0000 0.8531 0.6494

264.6 0.0000 0.2864 0.8658




Axle group type


274.4 0.0000 0.0978 0.4329

284.2 0.0000 0.0441 0.8658

294.0 0.0000 0.0138 0.0000

303.8 0.0000 0.0076 0.6494

313.6 0.0000 0.0028 0.2165

323.4 0.0000 0.0028 0.2165

333.2 0.0000 0.2165

343.0 0.0007 0.0000

352.8 0.0014 0.0000

362.6 0.0007 0.0000

372.4 0.0000 0.0000

382.2 0.0000 0.2165

392.0 0.0000 0.0000

401.8 0.0000 0.2165

411.6 0.0000 0.4329

421.4 0.0000 0.4329

431.2 0.0000 0.8658

441.0 0.0000 0.4329

450.8 0.2165

460.6 0.0000

470.4 0.0000

Proportion of group (%) 34.07 12.46 0.74 34.30 18.37 0.06

Table K 4: Traffic load distribution: Kwinana Freeway


Axle group type


10 5.8921 16.4096 0.4600 0.7542 0.0032 0.0000

20 25.6345 32.0016 0.1045 1.9000 0.0601 0.0000

30 10.5723 11.3824 0.2300 1.4020 0.2119 0.0000

40 7.1698 9.5948 0.7527 1.2715 0.4238 0.0000

50 9.7216 8.2274 0.4600 3.3480 1.1703 0.0000

60 20.4841 6.9558 0.4391 6.6162 5.8673 0.0000

70 17.1335 5.3176 2.0071 8.6613 10.1594 0.0000

80 3.1570 3.7105 4.3696 8.0255 7.2874 0.0000

90 0.2351 3.1917 11.2273 6.8821 4.4028 0.0000

100 0.0000 1.9708 14.6770 5.5429 3.8209 8.0000

110 0.0000 0.8797 24.9425 4.9531 3.3338 4.0000

120 0.0000 0.2763 26.4269 5.0063 2.9605 8.0000

130 0.0000 0.0648 10.4955 5.6058 2.7454 16.0000

140 0.0000 0.0113 2.7598 5.9128 2.6474 16.0000

150 0.0000 0.0056 0.5436 6.8024 2.5304 0.0000

160 0.0000 0.0000 0.0836 7.6436 2.3785 0.0000

170 0.0000 0.0000 0.0209 7.9288 2.3216 0.0000

180 0.0000 0.0000 0.0000 6.0288 2.6379 0.0000

190 0.0000 0.0000 0.0000 3.5341 2.6189 0.0000




Axle group type


200 0.0000 0.0000 0.0000 1.4601 3.2136 8.0000

210 0.0000 0.0000 0.0000 0.5028 4.5673 0.0000

220 0.0000 0.0000 0.0000 0.1475 5.9653 0.0000

230 0.0000 0.0000 0.0000 0.0459 7.0059 0.0000

240 0.0000 0.0000 0.0000 0.0193 6.8004 4.0000

250 0.0000 0.0000 0.0000 0.0048 6.2563 4.0000

260 0.0000 0.0000 0.0000 0.0000 4.6938 8.0000

270 0.0000 0.0000 0.0000 0.0000 2.5209 0.0000

280 0.0000 0.0000 0.0000 0.0000 0.9837 0.0000

290 0.0000 0.0000 0.0000 0.0000 0.3226 0.0000

300 0.0000 0.0000 0.0000 0.0000 0.0664 4.0000

310 0.0000 0.0000 0.0000 0.0000 0.0127 8.0000

320 0.0000 0.0000 0.0000 0.0000 0.0095 4.0000

330 0.0000 0.0000 0.0000 0.0000 0.0000 4.0000

340 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

350 0.0000 0.0000 0.0000 0.0000 0.0000 4.0000

360 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

370 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

380 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

390 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

400 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

410 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

420 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

430 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

440 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

450 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

460 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

470 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

480 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Proportion of group (%) 33.80 20.73 2.80 24.18 18.48 0.01

