Queensland University of Technology - QUT ePrintseprints.qut.edu.au/16663/1/Gregory_William_White_Thesis.pdf · 6.2 s77-1 and faa pavement design ... sensitivity analysis design appendix

Faculty of the Built Environment and Engineering

AN INVESTIGATION OF THE AUSTRALIAN LAYERED ELASTIC TOOL FOR FLEXIBLE AIRCRAFT PAVEMENT THICKNESS DESIGN By Gregory William White BE(Civil,Hons 1), MEng(UoN), ME(UNSW), MTech(Pvmts), Grad Cert(App Stats), Cert IV(A&WT), CPEng, MIEAust. With the assistance of: Sinclair Knight Merz For the award of Master of Engineering Submitted for examination in July 2007

Queensland University of Technology

Preliminaries Key Words

An Investigation of the Australian Layered Elastic Tool for Flexible Aircraft Pavement Thickness Design

i

KEY WORDS

Aircraft Pavement Structural Design System.

Layered Elastic Thickness Design.

Flexible Aircraft Pavement.

Sensitivity Analysis.

Proof Rolling.

Material Equivalence.

Preliminaries Publications

An Investigation of the Australian Layered Elastic Tool for

Flexible Aircraft Pavement Thickness Design ii

PUBLICATIONS

The following works have been published based on the research contained in

this thesis.

WHITE, G. (2005). ‘A Sensitivity Analysis of APSDS, an Australian

Mechanistic Design Tool for Flexible Aircraft Pavement Thickness

Determination’. Proceedings First European Aircraft Pavement Workshop. The

National Information and Technology Platform for Infrastructure, Traffic,

Transport and Public Space (CROW). Amsterdam, Netherlands. 11-12 May.

WHITE, G. W. (2005). ‘Selection of Input Parameters for Layered Elastic

Design of Flexible Aircraft Pavements‘. Proceedings 7th International

Conference on the Bearing Capacity of Roads, Railways and Airfields. Paper

Number 49. NTNU, NPRA, NNRA and AVINOR. Trondheim, Norway. 27-29

June.

WHITE, G. W. (2005). ‘Design of Proof Rolling Regimes for Heavy Duty

Aircraft Pavements‘. Proceedings 7th International Conference on the Bearing

Capacity of Roads, Railways and Airfields. Paper Number 26. NTNU, NPRA,

NNRA and AVINOR. Trondheim, Norway. 27-29 June.

WHITE, G. W. (2006). ‘Material Equivalence for Flexible aircraft Pavement

Thickness Design’. Proceedings 2006 Airfield and Highway Pavements

Specialty Conference. Refereed paper number 17121. American Society of

Civil Engineers. Atlanta, United States of America. 1-3 May.

Preliminaries Abstract


iii

ABSTRACT

APSDS is a layered elastic tool for aircraft pavement thickness determination

developed and distributed by Mincad Systems and based on the sister software

Circly. As aircraft pavement thickness determination remains an empirical

science, mechanistic-empirical design tools such as APSDS require calibration

to full scale pavement performance, via the S77-1 curve. APSDS provides the

unique advantage over other tools that it models all the aircraft in all their

wandering positions, negating the need for designers to use pass to cover ratios

and acknowledging that different aircraft have their wheels located at difference

distances from the aircraft centerline.

APSDS requires a range of input parameters to be entered, including subgrade

modulus, aircraft types, masses and passes and a pavement structure. A

pavement thickness is then returned which has 50% design reliability. Greater

levels of reliability are obtained by conservative selection of input values. Whilst

most input parameters have a linear influence on pavement thickness,

subgrade modulus changes have a greater influence at lower values and less

influence at higher values. When selecting input values, designers should

concentrate their efforts on subgrade modulus and aircraft mass as these have

the greatest influence on the required pavement thickness. Presumptive or

standard values are generally acceptable for the less influential parameters.

S77-1 pavement thicknesses are of a standard composition with only the sub-

base thickness varying. Non-standard pavement structures are determined

using the principle of material equivalence and the FAA provides range of

material equivalence factors, of which the mid-range values are most commonly

used. APSDS allows direct modelling of non-standard pavement structures. By

comparing different APSDS pavements of equal structural capacity, implied

material equivalences can be calculated. These APSDS implied material

equivalences lie at the lower end of the ranges published by FAA.

Preliminaries Abstract


Flexible Aircraft Pavement Thickness Design iv

In order to obtain consistence between APSDS and the FAA guidance, the

following material equivalence values are recommended:

• Asphalt for Crushed Rock. 1.3.

• Crushed Rock for Uncrushed Gravel. 1.2.

• Asphalt for Uncrushed Gravel. 1.6.

Proof rolling regimes remain an important part of the design and construction of

flexible aircraft pavements. Historically, designers relied on Bousinesq’s

equation and the assumption of point loads on semi-finite homogenous

materials to determine proof rolling regimes using stress as the indicator of

damage. The ability of APSDS to generate stress, strain and deflection at any

depth and any location across the pavement allows these historical

assumptions to be tested. As the design of a proof rolling regime is one of

comparing damage indicators modelled under aircraft loads to those under

heavy roller loads, the historical simplifications are generally valid for practical

design scenarios. Where project specific data is required, APSDS can readily

calculate stresses induced by proof rollers and aircraft at any location and depth

for comparison.

APSDS is a leading tool for flexible aircraft pavement thickness determination

due to its flexibility, transparency and being free from bias. However, the

following possible areas for improvement are considered worthy of future

research and development:

• Improvements to the user interface.

• Ability to model aircraft masses as frequency distributions.

• Ability to copy stress with depth data to Excel™ spreadsheets.

• Ability to perform parametric runs.

• Inclusion of a reliability based design module.

Preliminaries Table of Contents


v

TABLE OF CONTENTS

Section Page

KEY WORDS ...................................................................................................................I PUBLICATIONS ..............................................................................................................II ABSTRACT ....................................................................................................................III TABLE OF CONTENTS ................................................................................................. V LIST OF TABLES ......................................................................................................... VII LIST OF FIGURES...................................................................................................... VIII LIST OF ABBREVIATIONS........................................................................................... IX STATEMENT OF ORIGINAL AUTHORSHIP................................................................ XI ACKNOWLEDGEMENTS............................................................................................. XII 1. INTRODUCTION...................................................................................................1

1.1 General ........................................................................................................................1 1.2 The Early Days ............................................................................................................ 1 1.3 The Original CBR Method............................................................................................ 1 1.4 US Corps of Engineer Full Scale Aircraft Tests........................................................... 2 1.5 Material Equivalence Factors ...................................................................................... 4 1.6 The ICAO Pavement Rating System........................................................................... 5 1.7 Layered Elastic Design ................................................................................................ 6 1.8 New Generation Large Aircraft .................................................................................... 9 1.9 Future Developments ................................................................................................10 1.10 Aims and Methods .....................................................................................................12

2. AIRCRAFT PAVEMENT STRUCTURAL DESIGN SYSTEM..............................15 2.1 General ......................................................................................................................15 2.2 Inception and Development .......................................................................................15 2.3 Overview and Operation ............................................................................................17 2.4 Advantages and Benefits...........................................................................................26 2.5 Potential Improvements .............................................................................................28 2.6 Summary....................................................................................................................31

3. VALIDATION OF APSDS....................................................................................33 3.1 General ......................................................................................................................33 3.2 Validation Process .....................................................................................................33 3.3 Analysis of Results ....................................................................................................35 3.4 Summary....................................................................................................................36

4. INPUT PARAMETER SELECTION.....................................................................37 4.1 General ......................................................................................................................37 4.2 Input Parameters .......................................................................................................37 4.3 Subgrade Strength.....................................................................................................37 4.4 Aircraft Wander..........................................................................................................41 4.5 Aircraft Mass..............................................................................................................42 4.6 Aircraft Tyre Pressure................................................................................................43 4.7 Number of Passes .....................................................................................................43 4.8 Asphalt Modulus ........................................................................................................44 4.9 Pavement Structure ...................................................................................................45 4.10 Design Traffic Mix ......................................................................................................46

Preliminaries Table of Contents


Flexible Aircraft Pavement Thickness Design vi

4.11 Summary ................................................................................................................... 47 5. SENSITIVITY ANALYSIS ................................................................................... 49

5.1 General...................................................................................................................... 49 5.2 Investigation Undertaken........................................................................................... 49 5.3 Sensitivity Analysis.................................................................................................... 52 5.4 Analysis of Results .................................................................................................... 62 5.5 Summary ................................................................................................................... 63

6. MATERIAL EQUIVALENCE ............................................................................... 65 6.1 General...................................................................................................................... 65 6.2 S77-1 and FAA Pavement Design ............................................................................ 65 6.3 Investigation undertaken ........................................................................................... 67 6.4 Practical Pavement Equivalences............................................................................. 69 6.5 Isolated pavement equivalences............................................................................... 80 6.6 Thickness Comparison Examples............................................................................. 84 6.7 Summary ................................................................................................................... 88

7. DESIGN OF PROOF ROLLING REGIMES........................................................ 91 7.1 General...................................................................................................................... 91 7.2 Design of Proof Rolling Regimes .............................................................................. 91 7.3 Australian Proof Rolling Fleet.................................................................................... 92 7.4 Damage Indicator Calculation ................................................................................... 92 7.5 Investigation Undertaken........................................................................................... 94 7.6 Proof Rolling Regime Design .................................................................................. 101 7.7 Practical Limitations ................................................................................................ 106 7.8 Examples of Application.......................................................................................... 107 7.9 Summary ................................................................................................................. 111

8. SUMMARY AND CONCLUSIONS ................................................................... 113 8.1 General.................................................................................................................... 113 8.2 Summary ................................................................................................................. 113 8.3 Conclusions............................................................................................................. 115

APPENDIX 1. S77-1 THICKNESS RESULTS APPENDIX 2. SENSITIVITY ANALYSIS DESIGN APPENDIX 3. SENSITIVITY ANALYSIS RESULTS APPENDIX 4. MATERIAL EQUIVALENCE DESIGN APPENDIX 5. MATERIAL EQUIVALENCE RESULTS APPENDIX 6. DAMAGE INDICATORS WITH DEPTH APPENDIX 7. PROOF ROLLING REGIMES BIBLIOGRAPHY

Preliminaries List of Tables


vii

LIST OF TABLES

Table Name Page

Table 1 Chicago failure criteria. ........................................................................26 Table 2 Input Parameters. ................................................................................34 Table 3 Aircraft Wander Standard Deviation. ...................................................42 Table 4 Typical asphalt moduli. ........................................................................45 Table 5 Aircraft Information...............................................................................50 Table 6 Input Parameters. ................................................................................51 Table 7 Normalised Linear Influence and Importance ......................................62 Table 8 FAA Material Equivalence Guidance. ..................................................67 Table 9 Number of Practical Equivalence Determinations................................70 Table 10 Design Parameter Values for Practical Equivalence. ..........................70 Table 11 Summary Statistics for Practical Equivalence......................................73 Table 12 Recommended Material Equivalences. ...............................................79 Table 13 Design Parameters for Isolated Equivalence.......................................81 Table 14 Equivalence Examples Input Parameters. ...........................................85 Table 15 Equivalence Examples Summary Statistics.........................................87 Table 16 Proof Rolling Regimes for B767, B747 and F111. .............................109

Preliminaries List of Figures


Flexible Aircraft Pavement Thickness Design viii

LIST OF FIGURES

Figure Name Page

Figure 1 US Corps of Engineers CBR Curve....................................................... 3 Figure 2 S77-1 versus APSDS Thicknesses. .................................................... 35 Figure 3 S77-1 versus APSDS Differences. ...................................................... 36 Figure 4 Pavement Structure............................................................................. 51 Figure 5 General Model Results ........................................................................ 54 Figure 6 General Model Residuals .................................................................... 55 Figure 7 Specific Model Results ........................................................................ 56 Figure 8 Residuals for General and Specific Subgrade Models for B747 ......... 57 Figure 9 Residuals for General and Specific Subgrade Models for B767 ......... 57 Figure 10 Residuals for General and Specific Subgrade Models for B737 ......... 58 Figure 11 Thickness Ratio Consistency. ............................................................. 59 Figure 12 Relative Influence of Design Inputs for B747. ..................................... 60 Figure 13 Relative Influence of Design Inputs for B767 ...................................... 60 Figure 14 Relative Influence of Design Inputs for B737. ..................................... 61 Figure 15 Standard S77-1 Pavement Structure................................................... 66 Figure 16 Practical Equivalence for Asphalt and Crushed Rock. ........................ 72 Figure 17 Practical Equivalence for Crushed Rock and Uncrushed Gravel. ....... 72 Figure 18 Practical Equivalence for Asphalt and Uncrushed Gravel. .................. 73 Figure 19 Summary of Asphalt and Crushed Rock Equivalences ....................... 75 Figure 20 Summary of Crushed Rock and Uncrushed Gravel Equivalences ...... 75 Figure 21 Summary of Asphalt and Uncrushed Gravel Equivalences................. 76 Figure 22 Practical Equivalence Results ............................................................. 78 Figure 23 Practical Equivalence Residuals ......................................................... 79 Figure 24 Isolated Equivalence Residuals........................................................... 82 Figure 25 Effect of modulus ratio, thickness and location on equivalence. ......... 83 Figure 26 B737 Vertical Stress with depth for various pavements. ..................... 95 Figure 27 B737 Vertical Strain with depth for various pavements. ...................... 96 Figure 28 B737 Vertical Deflection with depth for various pavements. ............... 97 Figure 29 Comparison of Pavement and Single Material Stresses. .................... 99 Figure 30 Asphalt thickness and modulus effects. ............................................ 100 Figure 31 Allowable Macro Roller Tyre Pressures and Masses. ....................... 102 Figure 32 Allowable Test Rig Roller Tyre Pressures and Masses..................... 102 Figure 33 Porter Supercompactor Tyre Pressures and Masses........................ 103 Figure 34 Vertical Stress with Depth for Various Rollers................................... 103 Figure 35 Macro Roller Vertical Stress with Depth at various roller masses. .... 104 Figure 36 Vertical Stresses with Depth for various Aircraft. .............................. 105 Figure 37 B737 proof rolling regime. ................................................................. 108 Figure 38 B767 proof rolling regime. ................................................................. 110 Figure 39 B747 proof rolling regime. ................................................................. 110 Figure 40 F111 proof rolling regime................................................................... 111

Preliminaries List of Abbreviations


ix

LIST OF ABBREVIATIONS

ACN. Aircraft Classification Number.

ANOVA. Analysis of Variance.

APSDS. Aircraft Pavement Structural Design System.

CBR. Californian Bearing Ratio.

CDF. Cumulative Damage Factor.

CSIRO. Commonwealth Scientific and Industrial Research Organisation.

DCP. Dynamic Cone Penetrometer.

DF. Damage Factor.

ESWL. Equivalent Single Wheel Load.

FAA. Federal Aviation Administration (of the USA).

FAC. Federal Airports Corporation (of Australia).

FEDFAA. Finite Element Design Federal Aviation Administration.

FEM. Finite Element Methods.

HIPAVE. Heavy Industrial Pavement Design.

ICAO. International Civil Aviation Organisation.

kPa. Kilopascals.

LCN. Load Classification Number.

Preliminaries List of Abbreviations


Flexible Aircraft Pavement Thickness Design x

LEDFAA. Layered Elastic Design Federal Aviation Administration.

m. Metre.

MAUM. Maximum All Up Mass.

mm. Millimetre.

MPa. Megapascal.

NAPTF. National Airport Pavement Testing Facility.

NIGS. Nose In Guidance System.

PCN. Pavement Classification Number.

PCR. Pass to Coverage Ratio

PRS. Pioneer Road Services.

t. Tonnes.

με. Microstrain.

μm. Micrometre.

Preliminaries Statement of Original Authorship


xi

STATEMENT OF ORIGINAL AUTHORSHIP

The work contained in this thesis has not been previously submitted for a

degree or diploma at any other higher education institution. To the best of my

knowledge and belief, the thesis contains no material previously published or

written by another person except where due reference is made.

Gregory William White BE(Civil,Hons 1), MEng(UoN), ME (UNSW), MTech(Pvmts),

Grad Cert(App Stats), CertIV(A&WT), CPEng, MIEAust.

Preliminaries Acknowledgements


Flexible Aircraft Pavement Thickness Design xii

ACKNOWLEDGEMENTS

I would like to thank the following individuals and organisations for their

assistance with this research project. Such an undertaken can not be achieved

by an individual working alone and its completion is a reflection of the level of

support that the following have provided.

• Bruce Rodway of Bruce Rodway and Associates for his assistance with the

technical aspects of this project, access to various historical and technical

documents and his ongoing contribution to the development of my

pavement engineering career.

• Leigh Wardle of MINCAD Systems for his contribution to this project and

technical review of elements of this thesis.

• My QUT supervisor, Dr Andreas Nata-atmadja for his review of this thesis.

• My wife Claire who tolerates my moods, distraction and the time it takes to

undertake such a research program.

• My employer, Sinclair Knight Merz, for the corporate support of this research

project and financial assistance in attending conferences to present the

outcomes.

Without your help, this thesis would never have come to fruition. Thank you all.

Chapter 1 Introduction


1

1. INTRODUCTION

1.1 GENERAL

Aircraft and airports have developed dramatically since the maiden flight of the

Wright brothers at Kitty Hawk in 1903. Aircraft have increased in mass from

hundreds of kilograms to hundreds of tonnes. With this dramatic increase in

aircraft size, the requirement for high strength, flat and smooth airfield operating

surfaces also became a reality. Methods for the reliable design of pavements

for supporting aircraft operations have therefore been developed over a number

of years. The more recent of these design developments include advanced

computer based design tools which are calibrated to the performance of

pavements tested under repeated full scale aircraft loading.

1.2 THE EARLY DAYS

Prior to WWII, aircraft did not generally require any specific airfield to be

provided for operations. These aircraft were generally operated from farm

paddocks or from road pavements. The aircraft were light enough at that time

to not require specifically designed pavements to operate from. Operations

were so few and speeds so low that air traffic control was not necessary.

As aircraft grew in size and with the introduction of higher performance aircraft

associated with the war effort, an aircraft pavement design method was

considered to be necessary. As well as greater pavement thicknesses, the

war-time aircraft started to require smoother and flatter surfaces to operate

from. Increased frequency of operations and operating speeds also required

controlled air space and ground movement on formalised airfields.

1.3 THE ORIGINAL CBR METHOD

Prior to the 1920s, all pavements were designed based on experience alone.

In 1929, the first empirical design method, which incorporated a strength or

bearing test for the assessment of the subgrade, was introduced by the

California Highway Department (Porter, 1950) in the USA.



Flexible Aircraft Pavement Thickness Design 2

In 1942, the empirical road pavement design method, known as the California

Bearing Ratio (CBR) method was adapted to aircraft pavements and

extrapolated to incorporate higher wheel loads (Rodway, 2003). This

adaptation utilised the single elastic layer theory of Boussinesq (1885) and only

considered stress, strain and deflection directly under a single wheel load.

The CBR method of aircraft pavement design is an empirical method that

relates the required pavement thickness for a prescribed number of load

coverages to the CBR assigned to the subgrade under the pavement and the

aircraft wheel load (Rodway, 2003). The CBR design method provides for

increased aircraft loading by increasing the thickness between the subgrade

and the aircraft wheel.

The CBR design method assumes that the pavement fails through accumulated

vertical deformation in the subgrade. This implies that only minimal

deformation occurs within the various pavement layers. As these layers are not

specifically assessed in the design method, designers must assume that high

quality materials are used and adequate compaction is achieved during

construction. Otherwise, these layers may have a significant contribution to the

failure of the pavement, rather than failure by subgrade deformation.

1.4 US CORPS OF ENGINEER FULL SCALE AIRCRAFT TESTS

The CBR design method was further developed by the re-determination of the

empirical relationships through full scale testing from the 1940s to the early

1970s (Barker and Gonzalez, 1994). The last of these tests included the B747

four wheel landing gear and were reported in detail by Ahlvin, et al (1971). The

revised CBR-pavement thickness curve became known as the S77-1 curve

(Pereira, 1977) and this remains the primary empirical relationship to which

today’s computer-based aircraft pavement design tools are calibrated. Whilst it

would be preferable to calibrate directly to the empirical data, the limited

amount of empirical data and requirement for interpretation of the data has led

to all design tools being calibrated against S77-1. This has resulted in greater



3

consistence across the various design tools. The S77-2 curve is shown in

Figure 1.

Figure 1 US Corps of Engineers CBR Curve. 0

1

2

3

4

5

6

70.001 0.01 0.1 1

CBR/Pe

T/Sq

rt(A

c)

Where: CBR = California Bearing Ratio for the subgrade.

Pe = Tire pressure of an equivalent single wheel in PSI.

T = Thickness of pavement required in inches.

Ac = Tire contact area for one wheel in square inches.

To allow the S77-1 design curve to be plotted on a single two dimensional

chart, the tyre pressure was normalised with regards to CBR and the tyre

contact area was normalised with regards to the pavement thickness required

(Ahlvin, 1991). Any combination of tyre pressure and contact area can be

related to a unique single wheel aircraft load.

Factors (known as Alpha Factors) were introduced in 1971 which reduced the

required pavement thickness based on the number of wheels on the aircraft

landing gear and the number of coverages to be designed for. These Alpha

Factors were introduced to offset the finding that the damage caused by

multiple wheel landing gear was less than previously modelled under the




Equivalent Single Wheel Load (ESWL). This over statement of ESWL damage

is a result of the over estimation of wheel interaction caused by adopting

deflection as the measure of ‘equivalent’ rather than stress or strain (Rodway,

2000).

Whilst Alpha Factors were introduced for aircraft with up to 24 wheels in total,

only those with 1 to 4 wheels per landing gear were used in practice as no

commercial aircraft then had more than four wheels on any one landing gear.

The only wheel configuration with more wheels included in the full scale testing

was that of the 24-wheeled military C5A. This aircraft was initially considered

as two 12-wheeled gears (each comprising two actual 6-wheel gears behind

each other) but was subsequently amended for design purposes to be modeled

as separate 6-wheel gears. As the full scale testing did not incorporate landing

gear configurations in the conventional dual tridem arrangement, the extension

of the Corps’ full scale test results to the new large aircraft (A380 and B777)

was considered too great an extrapolation.

The concept of the Pass to Cover Ratio (PCR) was also introduced to enable a

logical conversion between aircraft passes and coverages based on the aircraft

wheel configuration and the spread of aircraft across the width of the pavement

(Rodway, 2003b).

1.5 MATERIAL EQUIVALENCE FACTORS

The result of the full scale tests, the S77-1 design curve, relates aircraft load to

pavement thickness required. This thickness is for a ‘standard’ pavement

composition as used in the full-scale tests. It does not take into account the

nature of the actual pavement structure, except for the underlying subgrade

strength. When a designer wishes to determine the required pavement

thickness of an alternate pavement structure, the principle of material

replacement equivalence must be used. The factors used to replace a known

thickness of one pavement material with an equivalent thickness of alternate

material are called ‘material equivalences’ as they relate the required thickness



5

of two difference materials in order to achieve a structurally equivalent

pavement.

The later full scale tests allowed some assessment to be made of the

comparative benefit of pavement materials other than those adopted in the

S77-1 pavement structures. These material equivalences were accepted by

the US Corps of Engineers in 1977 but significantly less than the equivalences

applied to road pavements.

These material equivalences are utilised to convert any pavement structure to

an equivalent thickness of S77-1 pavement, which comprised of 75 mm of

asphalt on 150 mm of fine crushed rock base on variable thickness of natural

gravel sub-base on subgrade of variable CBR (Wardle, et al, 2002). Guideline

material equivalence factors are published by the US Federal Aviation Authority

(FAA) (FAA, 1995). This guide covers a range of materials. However, for most

design scenarios, the equivalences covering fine crushed rock, natural

uncrushed gravel and asphalt are of most interest. The use of these material

equivalence factors is straight forward as demonstrated by Rodway (2003a).

The FAA document provides ranges of equivalence between various pairs of

material. No specific guidance is provided, however, as to which value in the

range is appropriate for any given deign scenario. The basis for the

determination of these factors could not be determined and they are considered

to be a weak link in the CBR design method for pavement structures which

differ significantly from the standard S77-1 test pavement.

1.6 THE ICAO PAVEMENT RATING SYSTEM

Whilst not a pavement design tool, the Aircraft Classification Number –

Pavement Classification Number (ACN – PCN) system for pavement strength

rating is a significant contributor to aircraft pavement engineering’s history. The

ACN – PCN system was introduced by the International Civil Aviation

Organisation (ICAO) in 1981 as the standard system for rating the strength of

aircraft pavements (CROW, 2003). The ACN is defined as twice the wheel load




in tonnes, which on a single wheel, inflated to 1.25 MPa, would cause

pavement damage equal to that caused by the aircraft’s actual multi-wheel gear

at its actual gear load and its actual tyre pressure (Rodway, 2003c). The PCN,

however, remains an airport owner derived value which is essentially an

advertisement to aircraft operators as to which aircraft are welcome to operate

at an unrestricted frequency from the airfield. The PCN should be selected to

be equal to the largest ACN of all the aircraft (at their respective masses) which

the airport owner will allow to operate in an unrestricted (from a pavement

strength view) manner.

With around 75% of the world’s airports utilising the ACN – PCN system (Loizos

and Charonitis, 2004), this system has largely replaced previous systems of

reporting and assessing aircraft pavement strength, such as the Load

Classification Number (LCN). The ACN derivation does not require the actual

pavement thickness or structure to be known, making the ACN of any aircraft

essentially independent of the actual pavement it is to operate on. It does

however depend upon the subgrade strength category and whether the

pavement is of flexible or rigid construction. Guidelines are generally available

which relate ratios of differing ACNs to relative amounts of pavement damage

induced. This relationship is not consistent for all aircraft and is not linear. Two

aircraft with an ACN ratio of 1.5 will have a damage ratio close to nine

(Defence, 2003a). The actual damage ratio is dependent upon the actual

pavement thickness required by the specific aircraft being considered.

1.7 LAYERED ELASTIC DESIGN

The first mechanistic-empirical design methods were developed in the 1950s

(Huang, 1993). The first, computer based layered elastic design tool for

pavements was developed in 1963 and reported by Warren and Dieckmann,

1963). This program was based on Burmister’s layered theory (Burmister,

1943).

With the increases in computer power in the 1980s and 1990s, layered elastic

design methods became commonly available to pavement designers. The



7

adoption of layered elastic design methods requires pavement structures to be

modelled as finitely thick and infinitely long/wide layers of elastic materials.

Each layer of material may be divided into sub-layers, each of uniform elastic

stiffness (modulus). Each material’s assigned modulus depends on both the

pavement material as well as its location within the pavement (as modulus of

granular pavement materials is dependent upon the stress conditions applied to

them) (Holtz and Kovacs, 1981). In 1975 a method of dividing layers into sub-

layers of uniform modulus and assignment of modulus values was developed

(Barker and Brabston, 1977). This method is understood to be used by all

layered elastic aircraft pavement design tools.

Mechanistic-empirical design allows the removal of the empirical load versus

thickness curve. However, one or more failure criteria are required to relate the

modelled single load stress, strain or other damage indicator, to the number of

allowable load applications of that magnitude. The modes of failure modelled

generally include vertical deformation in the subgrade (rutting) and tensile

cracking of all bound layers (fatigue). Of these, the subgrade deformation

(rutting) mode is generally the critical failure mechanism for aircraft pavements.

Failure criteria for layered elastic design tools are generally developed by

calibration against the results of the S77-1 design curve to provide a tie to

reality. This should result in the various tools returning essentially the same

thickness requirements.

Layered Elastic Design Federal Aviation Administration (LEDFAA) is the FAA’s

layered elastic design tool. LEDFAA was originally released in 1995 and

updated in 2004. The 2004 updated included the following changes (Hayhoe,

et al, 2004):

• The strain-repetitions failure criterion became independent of the subgrade

modulus.

• Full scale test data for six wheel aircraft were added to the failure criterion

calibration.




• The sensitivity of the model was reduced with respect to changes in aircraft

passes.

• All wheels were used for the strain calculations instead of just a single

gear’s wheels.

Whilst LEDFAA allows significant flexibility in the input of various pavement

design parameters, it lacks transparency. One cannot change the failure

criteria and the stresses, strains and deflections are not readily visible. Also, as

the FAA required LEDFAA to produce the same thicknesses as the chart-based

CBR methods, the resultant pavement thicknesses are ‘corrected’ to provide

consistent outputs within the range of traffic mixes considered in the

development of the failure criteria.

Aircraft Pavement Structural Design System (APSDS) is the Australian layered

elastic design tool for aircraft pavements and is based on the road pavement

design tool CIRCLY (MINCAD, 2000). CIRCLY, was developed by the

Commonwealth Scientific and Industrial Research Organisation, Australia

(CSIRO) in the 1970s (Wardle, 1976) and commercialised by MINCAD Systems

in the 1980s.

APSDS calibration processes are detailed by Wardle, et al (2001) and this

calibration is considered compulsory for aircraft pavement design. APSDS

offers the advantage of being able to be tailored by the designer, as well as

including the explicit modelling of aircraft wander. Unlike LEDFAA, APSDS

provides the designer with complete flexibility in the selection of all input

parameters and failure criteria as well as providing ready access to all the

calculated stresses, strains and deflections.

Layered elastic design tools such as APSDS include the ability to generate

damage indicator (stress, strain or deflection) with depth curves (MINCAD,

2000). These damage indicators with depth can be utilised for detailed analysis

of modelled pavement behavior. They can also be used for other purposes,

such as the determination of proof rolling regimes during new pavement



9

construction. Similarly, comparative assessments of stresses or strains with

depth can reveal the ordinal relative damage caused by two or more aircraft

with seemingly different loading regimes.

1.8 NEW GENERATION LARGE AIRCRAFT

Increasing congestion and predicted growth in air travel influenced the

development of new larger aircraft. The demand for larger aircraft lead Boeing

to design the B777 and Airbus to design the A380. Both of these new large

aircraft include six wheel (in a dual tridem arrangement) landing gear (Drenth,

2002). The B777 was introduced into service in the 1990s whilst the A380

maiden voyage occurred in April 2005.

The extrapolation of the original US Corps of Engineers full scale test result to

the B777 and A380 was considered beyond justification (Rodway, 2003). As a

result, a new phase of full scale aircraft pavement testing was planned. The

National Airport Pavement Test Facility (NAPTF) in Atlantic City, USA, aimed at

developing new design procedures for B777 and A380 aircraft (Drenth, 2002),

was constructed in the 1990s. Testing at the facility continues and to date has

included preliminary testing as well as flexible and rigid pavement performance

tests.

In addition to the US efforts, a program of testing of various A380 wheel

configurations and their comparison to B777 and B747 aircraft have

commenced at Toulouse Blagnac airport in France. The study includes static

and repeated load testing of various pavements of flexible and rigid

construction (Petitjean, et al, 2002). The pavement experimental program at

Toulouse was designed to correlate the extrapolated finite element and layered

elastic theoretical pavement response to full scale A380 loadings (Fabre, 2005).

Prior to the introduction of these large aircraft, designers accepted that the

various landing gear for a particular aircraft had little or no interaction. That is,

the damage caused by one landing gear was sufficiently isolated from the

damage caused by the other landing gears to ignore them. Whilst the fact that




S77-1 has Alpha curves for up to 24 wheels indicates that the Corps allowed for

gear interaction to be modelled, this was when pavement design was based on

deflection criteria. As vertical strains erode much quicker than vertical

deflections (as one moves horizontally away from the point of load application)

strain based design methods imply less interaction than deflection based

methods would.

The large number of gears and wheels, the close proximity of the various

landing gear and the large mass of the B777 and A380, has seen this premise

be revisited and some design methods such as the FAA’s LEDFAA 1.3, now

utilise all aircraft wheels for design purposes (Hayhoe, et al, 2004). There is

currently no justification for modelling all the wheels of these aircraft, which

results in significantly thicker pavement designs.

A study of comparative subgrade vertical strain under six and four wheel gear

loadings found that subgrade response is more complex than traditional layered

elastic analysis allows. Temperature, wander, accumulated damage and

position of previous loading were all found to affect the recovered and un-

recovered strain under the next load cycle (Hayhoe and Garg, 2002).

1.9 FUTURE DEVELOPMENTS

The introduction of the large B777 and A380 aircraft provide challenges into the

future. The following developments are expected to be issues for flexible

aircraft pavement designers in the near future.

1.9.1 Finite Element Methods

As computer power increases and research into modelling pavement structures

by Finite Element Methods (FEM) improves, the move towards finite element

design methods will continue. Currently, design tools are available which utilise

FEM to calculate the stresses and strains at critical positions in the pavement.

These calculated stresses and strains are, however, generally still related to an

allowable number of load repetitions through empirical performance criteria.



11

Whilst it would be advantageous to develop a fully mechanistic design tool, this

is considered to be unlikely in the foreseeable future. A fully mechanistic

design tool would be free of empirical relationships and would be expected to

include additional failure mechanisms such as asphalt deformation and granular

material densification. Whilst the computer power and analytical methods are

available for such a design tool, the ability to accurately model the plastic

stress, strain and deformation states of each element in the mesh of each

pavement layer remains the weak link. The variable nature of crushed

aggregates, the difficulty in producing consistent material samples for

characterisation testing and the variability of characterisation testing results

further complicates this challenge. It would be more reasonable to expect that

FEM design tools with elastic material parameters would be developed in the

near future. Such a tool would allow the granular materials’ stress dependence

to be modelled and the modulus values assigned based on the material type as

well as the stress state. As such a model would be restricted to elastic

response of the materials, a failure criterion for plastic deformation of the

subgrade would still be required and would remain an empirical relationship.

1.9.2 Replacement of S77-1 design curve

With additional full scale testing being undertaken at Atlantic City as well as

Toulouse, the generation of a replacement S77-1 design curve would be

appropriate. This replacement curve would include the impact on flexible

aircraft pavements of the B777 and A380 aircraft which impose aircraft loading

regimes that greatly exceed the reliability of the original full scale testing of the

US Corps of Engineers. Following the ratification of a replacement S77-1

curve, re-calibration of design tools such as APSDS would be required.

1.9.3 Modelling of alternate materials

The characterisation of pavement materials such as cemented base and sub-

base layers continues (White and Gnanendran, 2005). Improved methods of

determining the modulus of these materials and improved fatigue life models




are expected to find their way into APSDS and other layered elastic design

tools.

1.10 AIMS AND METHODS

1.10.1 Aims

The aim of this research was to identify and provide potential solutions to a

number of weaknesses in the current operation and use of APSDS. This

overarching aim has resulted in a number of sub-aims that include:

• Review the existing software and identify potential improvements.

• Validate the software to confirm its suitability for aircraft pavement design.

• Present general guidance to designers on the selection of input parameters.

• Determine which of the input parameters that pavement thickness is most

and least sensitive to.

• Provide material equivalence factors that are implied by APSDS and

compare them to those recommended by the FAA.

• Develop a methodology for determining proof rolling regimes for aircraft

pavement construction using the stress with depth function of APSDS.

1.10.2 Methods

In achieving these aims, a range of methods have been employed. Literature

searches have been undertaken and the empirical basis of aircraft pavement

thickness determination established. A review of the software was conducted

based on experience with its use for practical engineering purposes.

Significant numbers of parametric runs have been performed to calculate many

pavement thicknesses for a range of aircraft, subgrades and other input

parameters. These parametric runs were designed to allow each of the aims of

the research to be achieved. The runs were generally developed using



13

statistical methods of experimental design. Statistical analysis of the pavement

thicknesses calculated was employed in each stage of the investigation. This

provided for statistically sound conclusions to be drawn.

Stress, strain and deflection with depth data was calculated using appropriate

functions within APSDS. This data was generated for aircraft and common

proof rollers so that proof rolling could be determined by comparing the effects

of the two loads.




Chapter 2 Aircraft Pavement Structural Design System


15

2. AIRCRAFT PAVEMENT STRUCTURAL DESIGN SYSTEM

2.1 GENERAL

APSDS is a layered elastic design tool for the thickness determination of

flexible aircraft pavements. APSDS is based on the road thickness design tool

Circly, which was developed in Australia in the 1970s. Whilst a tool with many

advantages, APSDS also has room for improvement. The inception and

development of Circly is presented along with the implementation of APSDS.

The inputs and outputs are described along with the calibration of the software

to empirical full scale testing. Advantages over other aircraft pavement

thickness design tools are presented as well as areas for potential future

developments.

2.2 INCEPTION AND DEVELOPMENT

2.2.1 Origins

The first mechanistic-empirical design methods were developed in the 1950s.

An Australian layered elastic tool was developed in the 1970 and became

known as Circly.

The Circly layered elastic algorithm was developed by Gerrard and Harrison

(1971) at the CSIRO. This program allowed an extension of Boussinesq’s

(1885) work to calculate stresses, strains and deflections at various depths,

induced by circular loads of uniform contact pressure. Gerrard and Harrison’s

work was furthered by Wardle (1976) and the first Circly user’s manual was

published in 1977 (Wardle, 1977). In these early stages, the Circly program

was a main-frame based program and ran at the limits of the then available

computer power.

2.2.2 Circly

In 1988 Circly was commercialised by Mincad Systems (Mincad, 1999). This

early version of the commercialised Circly was a PC DOS based program. The




program Circly, which was a complete design tool, included a modified version

of the layered elastic algorithm of the same name.

Circly was re-released (Version 2.4) as a Windows based program in 1996.

Later in 1996, Version 3 was released and this included many improvements

such as a revised algorithm for the stress and strain calculations as well as

automation of the sub-layering systems for granular materials (Mincad, 1999).

In 1999, Version 4 was released and saw the inclusion of automated thickness

determination options as well as the generation of the Cumulative Damage

Factor (CDF) for multiple layers in one run.

Most recently, Circly Version 5 was released in 2004 (Wardle and Copley,

2004) and included many improvements consistent with the revision of the

Australian road pavement design guide (Austroads, 2004). This version of

Circly also included features for direct input of weigh-in-motion traffic data and

economical analysis of pavement design options based on user defined

construction and maintenance costs (Wardle and Copley, 2004).

2.2.3 APSDS

APSDS was initially developed in response to a request by the Australian

Federal Airports Corporation (FAC). The initial development was funded by

Pioneer Road Services Pty Ltd (PRS) and a prototype computer program was

produced by PRS’s Ian Rickards. Whilst the user interface and some inputs

were modified to suit the requirements of aircraft pavement design, the layered

elastic module is the same Circly algorithm. APSDS was first released by

Mincad Systems in a Windows based version in 1996. The revisions then

closely followed the release of Circly Version 2.4. The current version of

APSDS, Version 4, was released in mid 2000 and is currently under revision.

2.2.4 HIPAVE

Heavy Industrial Pavement Design System (HIPAVE) is a sister program of

APSDS. It is specifically designed to cater for the unique (variable container

mass on standard vehicle/wheel configuration) loading regime of container



17

terminals. HIPAVE is also based on the Circly layered elastic algorithm.

HIPAVE was released as a test version in 2004 (Wardle and Oldfield, 2005).

2.3 OVERVIEW AND OPERATION

APSDS, like most layered elastic tools for flexible pavement thickness design,

calculates indicators of damage induced in the modelled pavement by a single

load application. The single load induced damage indicator is then related to

an allowable number of load repetitions of the same magnitude. This

relationship, known as the performance relationship or failure criterion, remains

an empirical tie to full scale pavement performance.

The use of the program is relatively straightforward. One selects and inputs a

series of parameters and then the software generates the stresses and strains

induced in the pavement. The effects of all aircraft in the traffic mix are

determined and a CDF is computed for each nominated transverse distance

from the centerline. If the CDF computed is 1.0, then the pavement is modelled

to fail at the end of the nominated design life. If the CDF exceeds 1.0, the

pavement is modelled to fail before the design life has expired.

Due to the accurate nature of the inputs and outputs associated with layered

elastic design, there is a risk of users interpreting the results as being similarly

accurate. However, the accuracy of APSDS can not be any better than the

accuracy and interpretation of the full scale testing to which it is calibrated

through the various failure criteria. Users therefore require an understanding of

the appropriateness of the value selected for each of the various inputs. The

limitations of the data to which the program is calibrated and the practical

accuracies that can be expected for the outputs is also important to understand.

2.3.1 Inputs

Some inputs are specific to the design scenario being considered whilst others

are more general in nature and would normally be common to all reasonable

design scenarios. APSDS allows modification of almost all inputs, including

those considered to be standard and not design scenario specific. Some inputs




are stored in libraries within APSDS whilst other information is input for each

design scenario. These are described in the following sections.

2.3.1.1 Library Inputs

APSDS contains two libraries of data, one for layers and the other for loads.

Each is stored as a Microsoft Access database file.

The ‘layers’ database contains material information. The information stored for

each material is dependent upon the material type. Materials include:

• Asphalt.

• Cemented.

• Unbound granular.

• Subgrade.

For each material, the user can assign or modify the modulus and Poissons’

ratio values and choose either isotropic or cross anisotropic conditions. Whilst

asphalt, cemented materials and subgrades are considered to be homogenous

and isotropic, granular materials can be sub-layered to help address the stress

dependency issue. A single modulus can also be assigned to a non-sub-

layered granular material.

The requirement for sub-layering reflects the stress dependence of these

materials and is well documented in literature such as Barker and Brabston

(1975). A number of options for sub-layering of granular materials is available,

however, because APSDS (as with most other pavement design procedures)

relies on calibration to empirical performance data, the sub-layering system

used in design must be the same as that used in the calibration process. In the

case of aircraft pavements, the Barker and Brabston (1975) sub-layering

routine has been accepted as being suitable and was used for the APSDS

calibration process (Wardle, et al, 2001). Therefore, this sub-layering system



19

must be used to ensure consistence between the model and the empirical data

against which the tool was calibrated.

Once any given layer is identified as a material type, the layer is provided with a

thickness as well as a boundary condition (rough or smooth). In the case of

subgrades, the layer is considered to be semi-infinite in the vertical direction.

Each material can be assigned a performance criterion. Current layered elastic

design protocol is to consider the following performance criteria (Huang, 1993):

• Cumulative vertical deformation at the top of the subgrade (rutting).

• Horizontal tensile fatigue initiating at the bottom of bound layers (fatigue).

Other potential failure mechanisms are assumed to be taken into account and

prevented from occurring by suitable material selection and adequate

construction. For example, internal vertical deformation within asphalt is

assumed not to occur through suitable asphalt mix design and compaction

during construction.

APSDS stores aircraft load information in the ‘loads’ library. Whilst a number of

aircraft come built-in to APSDS, additional aircraft are commonly required. The

loads database includes the following database hierarchy:

• Aircraft.

• Load groups.

• Load locations.

‘Aircraft’ are those aeroplanes being considered in any given design scenario.

Unlike the materials which may be encountered, aircraft are clearly defined and

limited in number. For each aircraft, a number of load groups may be

considered. Many aircraft have only two load groups (the nose wheel group

and the main gear groups). Because the main gears are generally assumed

not to interact, only one main gear group is defined and only one half of the




pavement structure is considered. However, some aircraft, such as the B747,

have more than one main gear on each side of the aircraft and the MD-11

aircraft has a significant centrally located belly gear. As some 95% of aircraft

mass is carried by the main gears, the nose gear group is generally ignored in

design. Each modelled load group has a constant contact tyre pressure

assigned and a portion of the total aircraft mass nominated.

For each load group, the actual load locations are also defined. These load

locations represent the location of each of the aircraft tyres. Each aircraft tyre

is assumed to carry an equal share of the load group’s portion of the aircraft

mass.

Whilst it is common to assume a constant contact pressure over the area of

each aircraft tyre, APSDS provides for complex load distributions with non-

constant contact pressure. The complex loading options also provide for

horizontal stresses to be modelled. These are, however, not considered to be

an advantageous addition for aircraft pavement thickness design as subgrade

deformation almost always governs thickness requirements. Therefore,

horizontal stresses are not commonly used.

2.3.1.2 Design Specific Inputs

A number of design specific inputs are required and these are generally not

retained in libraries. Rather, they are stored in an inputs (.cli) file. These

design specific inputs generally define the pavement structure and aircraft

traffic for any design scenario.

Within the pavement structure definition, the following inputs are required:

• Subgrade modulus. The modulus (in MPa) is representative of the elastic

stiffness of the natural ground or fill on which the pavement is to be

constructed. The assignment of subgrade modulus is actually only the

selection of a subgrade material of specific modulus from the ‘materials’

library, rather than an actual modulus entry.



21

• Layer thicknesses and materials. The number of material layers, material

types and thicknesses are all definable. Where a design is being prepared,

the thickness of one layer, usually the sub-base, is determined to meet the

aircraft traffic requirements. Under an existing pavement evaluation

scenario, all layer thicknesses (in mm) are defined. For Barker and

Brabston base and sub-base type materials, the modulus is automatically

generated by the software, and is not selected by the designer.

• Asphalt modulus. Whilst defined in the ‘layers’ database, the selection of

an asphalt which represents, primarily through its modulus (in MPa), the

material characteristics and environmental conditions associated with the

design scenario.

• Cemented material modulus. Where cemented materials are considered,

they too are selected to reflect the materials available for the specific design

scenario even though their modulus (in MPa) is actually defined in the

‘layers’ library.

Aircraft traffic for any given design scenario is stored within the ‘loads’ library.

This allows use of a common traffic spectrum across a wide range of pavement

designs. However, the development of an aircraft traffic spectrum is a design

scenario specific input. The elements of an aircraft traffic spectrum include:

• Aircraft. The actual aircraft to be modelled are selected from the ‘loads’

library.

• Aircraft Mass. Whilst the maximum mass of each aircraft (in tonnes) is

commonly input into the ‘loads’ library, often a lesser mass is required for

the design scenario. In some instances, the same aircraft will be modelled

at a number of aircraft masses.

• Aircraft Passes. Each aircraft is assigned a number of aircraft passes.

Aircraft passes is defined as the number of times the aircraft passes a given

cross section of pavement. This is noted as being distinctly different from

coverages, operations or movements.




• Aircraft wander. Aircraft wander across the width of a pavement from one

aircraft pass to the next. Aircraft wander is defined as the standard

deviation (in mm) of the distribution of aircraft centerlines. Whilst different

aircraft may be considered to wander to different extents, the location of the

pavement at the airfield (runway, taxiway or apron) is considered to govern

the degree of wander and therefore a single standard deviation of wander is

assigned for each design scenario. This is applied to all aircraft in the traffic

spectrum.

2.3.2 Layered Elastic Solution

The layered elastic component of any aircraft pavement design tool is the

method for the calculation of the damage indicators (stresses, strains and

deflections) at pre-determined locations, induced by a single load application.

APSDS uses the Circly algorithm for this purpose. The Circly algorithm is

based on integral transform methods and Bessel functions. This algorithm

computes the principal as well as shear stresses, strains and deflections.

Whilst some previous design methods have used stress and deflection as the

indicator of damage, APSDS uses strain in an effort to alleviate the

overstatement of wheel interaction associated with using stress as the damage

indicator.

The calculated strains of greatest interest are those that occur at points where

performance criteria have been assigned. This is generally the vertical

compressive strain at the top of the subgrade as well as the horizontal tensile

strain at the bottom of the bound layers.

The important unique feature of APSDS is that subgrade strain, or alternative

damage indicator, is computed at all nominated points across the pavement

width in order to capture all damage contributions from all the aircraft, in all their

wandering positions.

Each of the calculated single load event strains is used to calculate an

allowable number of repetitions of that same strain magnitude. This



23

relationship between induced strain and allowable number of strain repetitions

is the failure criterion. Whilst other design tools, such as LEDFAA 1.3, have a

single, modulus independent, failure criterion for subgrade rutting (Garg, et al,

2005), APSDS has a separate failure criterion for each subgrade modulus. The

general form of the failure criteria is detailed in Equation 1.

N = (k/ε)b ..............................................................................................Equation 1

Where: N = allowable number of repetitions of strain E.

k = a material constant.

b = damage exponent of the material.

ε = the load induced strain.

More complex forms of the failure criteria are applied to most bound materials.

The damage factor is then calculated based on the modelled and allowable

number of load repetitions of the calculated magnitude of strain using Miner’s

Law. Miner’s Law is detailed as Equation 2.

Damage Factor (DF) = n/N ..................................................................Equation 2

Where: n = modelled number of load repetitions of a given magnitude.

N = allowable number of load repetitions of the same magnitude.

The damage contribution by each aircraft load at each wandering position is

then summed into the CDF for each location across the pavement width. The

pavement is assumed to have reached its end-of-life when the CDF equals 1.0.

2.3.3 Outputs

With all input parameters assigned, the designer runs the software and a range

of computations are performed and a range of outputs are generated.

However, prior to this, the designer is able to select the coordinates and format

of the outputs. Any range of coordinates can be selected for the location of

damage indicator calculation and a range of damage indicators can be selected




for graphical output. In addition, an option to design the required thickness of a

given pavement layer can be used.

Following the operation of the software, the following outputs are generated:

• Printable results file. The output (.clo) file contains the output from the

analysis.

• Job summary file. For record retention, the job summary text file (.txt)

provides a summary of the inputs and outputs. This includes the pavement

structure, aircraft traffic spectrum and CDFs for each pavement layer with

an assigned performance criterion.

• Raw results file. The raw results file (.prn) contains the stresses, strains

and deflections generated by the Circly algorithm.

• Plot files. The DFs for each aircraft and CDF are transferred to a Microsoft

Excel™ spreadsheet for the designated pavement layer. These CDFs are

then used to generate a plots at the selected locations across the width of

the pavement as well as the contribution to the total CDF attributed to each

aircraft load in the traffic spectrum.

In addition to these computer file outputs, the CDFs of the pavement layers with

failure criteria assigned are also displayed within the software. Where the

design layer thickness option is utilised, the determined pavement thickness is

also shown.

2.3.4 Empirical Basis

As described above, the relationship between the induced strain (or alternate

damage indicator) and the allowable number of repetitions of the same

magnitude of strain is known as the material performance relationship or failure

criterion. These failure criteria are generally material modulus specific and

provide the tie between the mechanistic element of the design process and ‘real

life’. For asphalt and cemented materials, relationships based on material

specific testing can be utilised. However, for subgrade materials, the failure



25

criteria are based on the results of the full scale testing conducted by the US

Corps of Engineers during the 1940s to 1970s. The combined outcome of the

US Corps of Engineers’ full scale tests is known as the S77-1 design curve as

reported by Pereira (1977). It is to this curve, following adjustment to thickness

for the Corps’ Alpha factors, that APSDS and most other flexible aircraft

pavement design tools are calibrated. The S77-1 curve is shown in Figure 1. It

is recognized that the S77-1 curve is empirical in nature, however it remains the

best international reference for designers and provides a common basis for the

calibration of all current aircraft pavement thickness design methodologies.

2.3.5 Calibration

APSDS is based on the empirical relationships between damage by a single

load application and the number of repetitions until failure. The software must

therefore be calibrated against the original empirical performance relationships

by generation of appropriate failure criteria. For traditional flexible pavements

the most common governing failure criterion is vertical deformation (rutting) of

the subgrade (Rodway and Wardle, 1998). The calibration of the APSDS

subgrade failure criteria to the S77-1 design curve is detailed in Wardle, et al

(2001). Use of these calibrated failure criteria (known as the Chicago Criteria)

is essential to obtaining consistence between APSDS and the S77-1 design

method.

The calibrated subgrade failure criteria are all of the form of Equation 1. The

Chicago Criteria are shown in Table 1 for common subgrade moduli.

Whilst the Chicago Criteria provide a best fit to the S77-1 design curve, which in

turn is a best fit to the combined data from the full scale testing effort,

discrepancies between the S77-1 curve and APSDS (when calibrated with the

Chicago Criteria) occur. Such discrepancies are not unexpected and are

generally minor. This discrepancy is believed to be the result of deflection

being used as the performance indicator in the S77-1 curve whilst strains are

utilised in APSDS (Wardle, et al, 2001).




Table 1 Chicago failure criteria.

Subgrade Modulus (MPa) k b 30 0.0032 9.5 40 0.0032 9.8 50 0.0031 10.3 60 0.0030 10.9 70 0.0029 11.7 80 0.0027 12.6 90 0.0026 13.7

100 0.0024 15.0 110 0.0023 16.4 120 0.0021 18.0 130 0.0020 19.7 140 0.0020 21.6 150 0.0020 23.6

2.3.6 Design Reliability

The S77-1 design curve is a best-fit to the full scale test results. The S77-1

curve and therefore the calibrated APSDS program, is expected to return

designs with a reliability of 50% unless the designer applies factors of safety by

using conservative design input parameter values. There are no built-in factors

of safety in either the design tool or the failure criteria.

2.4 ADVANTAGES AND BENEFITS

APSDS has a number of unique characteristics which give it significant

advantage over other flexible aircraft pavement design tools. These

advantages are considered likely to be the reason for its popularity and are

described in the following sections.

2.4.1 Fully Transparent

Every aspect of the system, with the exception of the calculation of the

stresses, strains and deflections, is fully transparent and able to be modified.

Whilst the damage indicator calculations are not available, all of the calculated

values of stress, strain and deflection are visible at all nominated pavement



27

locations and depths. This allows stress with depth and other similar plots to be

readily generated. The modelling of materials is completely flexible in all

aspects. The location, composition and interaction of loads are also completely

visible and adjustable.

This transparency and ability to control all the inputs parameters provides for

rapid assessment of ‘what if’ scenarios. Designers can very rapidly determine

what effect the change of one or more input parameters can have on the

required thickness design or the life of the pavement at the same thickness.

This provides great advantage in considering the reliability of design solutions

and investigation of the impact of selecting certain values for the various input

parameters.

2.4.2 Aircraft Wander

The incorporation of aircraft wander allows the contribution to damage of all

aircraft in the traffic spectrum, in all their wandering positions, to be calculated

at all locations across the pavement. This contrasts with most previous design

methods which computed single maximum values (under a single tyre or

centroid of a single wheel group) of the damage indicator only. It is this feature

that eliminates the need for the traditional pass-to-coverage concept and allows

the designer to specify any degree of aircraft wander (Mincad, 2000).

2.4.3 Cumulative Damage Factor

The calculation and visibility of the CDF at all locations across the pavement

width and the contribution to the CDF of all aircraft in the traffic spectrum is

highly advantageous. This allows the more critical aircraft to be easily identified

as well as revealing the areas of the pavement which are most likely to fail first.

The graphical output of the CDF across the pavement width makes the

interpretation of this information very easy. This allows non-technical staff to

readily interpret the output of the pavement design process.




2.4.4 Thickness Design Option

By utilising the thickness design option, the selected pavement layer is

automatically selected, trialed and adjusted until a CDF of 1.0 is returned. This

allows quick and easy design of pavements without requiring manual trial and

adjustment runs of the software.

2.4.5 Free from Bias

The freedom and flexibility of the software is allowed as it is not intended to

implement any particular or regulated design procedure. Other software, such

as LEDFAA, is designed to automate the FAA chart based design method and

therefore restricts layer thickness and moduli values to those allowed by the

chart-based methods.

Further, programs such as LEDFAA are forced to return design thicknesses

which are consistent with the FAA chart based design method for ‘typical’

aircraft traffic mixes. This means that any difference between the S77-1 and

the layered elastic thicknesses are ‘corrected’ to provide consistency between

the chart-based and layered elastic solutions (Hayhoe, et al, 2004).

APSDS’ freedom from factors of safety or bias means that the designer can

obtain 50% reliability or ‘best-fit’ thickness designs. The designer can then

utilise judgment and experience in selecting input parameters and observing

their effect on the design thickness and subsequent pavement design reliability.

2.5 POTENTIAL IMPROVEMENTS

Whilst the many advantages of APSDS make it a very attractive pavement

design tool, there remains room for improvement within the software. Some of

the potential areas for improvement are detailed in the following sections.

2.5.1 User Interface

Since the conversion of APSDS to a Windows based tool in 1996, the user

interface has become increasingly simple and familiar to users of other



29

Windows-based applications. The format and accessibility of the output is,

however, an area that could be improved.

The basic output for any given design scenario should be printed and stored on

file if replication or confirmation is ever required in the future. The formatting of

the output files are such that this is not readily achievable in an efficient

manner. For example, the output is formatted with a large number of spaces,

rather than tab stops, making reading of any output report difficult as the

columns of data rarely align.

Benefit would also be gained from the ability to cut and paste the computed

stresses, strains and deflections. This would be especially useful where stress

with depth analyses are being undertaken, and the stress at a range of pre-

specified depths below the pavement surface is required to be copied into an

Excel™ spreadsheet or similar application. Currently, to use a spreadsheet

program, one is required to manually enter the data. This is both laborious and

error prone.

2.5.2 Out of Range Calculations

With the ability to input almost any combination of input parameters and

pavement structures, the ability to stretch the range of the reliability of the

design method is also possible. Whilst this in itself is not considered a problem,

the tendency to create non-solvable situations is. For example, the Barker and

Brabston (1975) sub-layering procedures are modelled by mathematical

equations relating the underlying layer’s stiffness and the next layer’s stiffness.

This procedure has a limit to the modulus that can be assigned any given layer.

This limit is not truly reflected in the software and by selecting certain

combinations of material in various layers, one can exceed the automated

limits. In particular, by modelling a layer of natural gravel over a layer of fine

crushed rock, negative modulus values of the natural gravel can be calculated.

This is clearly nonsensical but no ‘out of range’ error message is generated.

The addition of out of range errors in this and other scenarios would be of

benefit.




2.5.3 Parametric Run Automation

When performing a large number of designs or when performing parametric

runs of the software for research or investigatory purposes, one is required to

input the parameters, manually run the software, change the parameters and

continue. There is no automation tool. Such a tool would allow a large range of

parameter combinations to be automatically run without human interaction.

This would potentially save researchers significant time, as well as allowing the

number of parametric runs being performed to be increased and subsequently

increase the number of results and the associated value of the research

conclusions.

2.5.4 Reliability Based Design

The S77-1 design curve is a best fit curve. Therefore, the calibrated APSDS is

a best fit design tool. That is, the model will return a 50% design reliability for

any given set of input parameters where vertical subgrade deformation is the

governing failure mode. This also may not take into account the variability of

assigned material properties. However, the failure criteria for bound materials,

such as cement stabilised and asphalt materials, are generally not a best fit

curve as they have been developed with in-built factors of safety based on

laboratory and field performance. This mixing of best fit and higher reliability

failure criteria is not considered appropriate but is generally accepted on the

basis that subgrade deformation is commonly the governing failure mode.

The calibration of APSDS to the best fit S77-1 curve means that designers are

required to increase the reliability of their designs through the selection of

conservative input parameters. A more formal approach to design reliability

could be achieved through the re-calibration of the failure criteria to a modified

version of the S77-1 curve with 90% (or some other) level of reliability assigned.

Alternatively, a Monte-Carlo or other simulation could be developed which

would allow the designer to gain an appreciation of the design outcome’s

probability of success and the gain in reliability achieved with any given

increase in pavement thickness. Given the advantage provided by the



31

unbiased nature of the software, the latter is considered to be the preferred

approach.

2.5.5 Aircraft Mass Distributions

Aircraft in APSDS are assigned a specific operating mass. Whilst any given

aircraft can be assigned any specific mass, modelling of two masses for the

same aircraft (say landing mass and take off mass) requires that the aircraft be

modelled as two separate aircraft of the same type. With the introduction of a

container mass distribution input tool for HIPAVE (Wardle and Oldfield, 2005), it

would be relatively simple to incorporate an aircraft mass distribution input for

APSDS. This would allow more accurate modelling of the range of aircraft

operating masses to be incorporated, where that information is available to the

designer.

2.6 SUMMARY

APSDS is a layered elastic design tool for flexible aircraft pavement thickness

determination which is based on the road pavement design tool Circly. The

designer inputs a range of design parameters and the software perform a

number of calculations and produces design outputs. The calculations

performed are the determination of a damage indicator which is then related to

an allowable number of magnitudes of that load. This relationship is known as

the failure criteria and provides the tool a tie to full scale empirical test results.

Whilst APSDS offers many advantages, there are specific issues which could

also be improved to make the tool even more valuable to designers.

The advantages that APSDS holds over other design tools for flexible aircraft

pavements are many. These include being fully transparent, being free from

bias and uniquely catering for aircraft wander to avoid to PCR concept. Areas

where the tool could be improved in the future include:

• Improvement of the user interface.

• Provision of out of range calculations where appropriate.




• Allowing automation of parametric runs for research purposes.

• Incorporation of a reliability based design output.

• Allowing input of variable aircraft masses for a single load group.

Chapter 3 Validation of APSDS


33

3. VALIDATION OF APSDS

3.1 GENERAL

To confirm the applicability of this investigation, which included using APSDS to

generate pavement thicknesses, a validation was required to confirm its

operation. APSDS comes ready to use from MINCAD Systems and requires

little set-up. However, APSDS does not come with the Chicago Criteria built-in.

It was therefore necessary to enter these calibration constants and perform a

validation of the software.

3.2 VALIDATION PROCESS

In order to validate the software, the following steps were undertaken:

• Entering the Chicago Criteria calibration constants.

• Selection of inputs.

• Calculation of a number of pavement thicknesses using APSDS.

• Calculation of equivalence pavement thicknesses using S77-1.

• Comparison of thicknesses generated by the two methods.

Each of these steps is discussed in the following sections.

3.2.1 The Chicago Criteria

Wardle, et al (2001) provides subgrade calibration constants for APSDS at

subgrade moduli values of 30, 60, 100 and 150 MPa. Formulae are provided to

allow the calculation of calibration constants at other subgrade modulus values.

These formulae were utilised to calculate the calibration constants contained in

Table 1. These values were entered into APSDS and new subgrade materials

created which utilised these calibration constants.




3.2.2 Selection in Inputs

The validation was performed following the bulk of the research presented in

this thesis. This meant that the validation was considered to be a confirmatory

process more than an active validation. The input parameters were therefore

selected from the inputs adopted for the various investigations undertaken as

part of this project, specifically the sensitivity analysis.

The inputs parameters selected are detailed in Table 2.

Table 2 Input Parameters.

Design input parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150

Aircraft Type Not Applicable B747, B767, B737 Aircraft Mass % of maximum 60, 80, 100

Aircraft Passes Number 5000, 10000, 20000

3.2.3 Calculation of APSDS thicknesses

The APSDS pavement thicknesses were adopted from those calculated for

other stages of this investigation based on the input parameters detailed above

and using the Chicago Criteria.

3.2.4 Calculation of S77-1 thicknesses

S77-1 thicknesses were calculated using the software COMFAA. These were

recorded and entered into an Excel™ spreadsheet. The COMFAA determined

S77-1 thicknesses are contained in Appendix 1.

3.2.5 Comparison of APSDS and S77-1

Figure 2 shows the APSDS thicknesses against the S77-1 thicknesses. This

figure shows general agreement between the two design tools.



35

Figure 2 S77-1 versus APSDS Thicknesses.

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600 1800 2000S77-1 Thickness (mm)

APS

DS

Thi

ckne

ss (m

m)

B747 B767 B737 Unity

3.3 ANALYSIS OF RESULTS

The residuals are shown in Figure 3. These show that the magnitude of the

difference between S77-1 and APSDS was up to 90 mm for the 108 design

scenarios considered. The mean difference was 36 mm (6.7% of the S77-1

thickness) whilst the median difference was 33 mm (4.8% of the S77-1

thickness).

This analysis shows that APSDS has generally good agreement (R2 = 0.82)

with S77-1 when the Chicago Criteria are used. This analysis has been

performed for B737, B767 and B747 aircraft which span the range of common

commercial jet aircraft in Australia.




Figure 3 S77-1 versus APSDS Differences.

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100 120

Run

Res

idua

l (m

m)

3.4 SUMMARY

A validation of APSDS was performed by comparing thickness calculated from

this software to those calculated from the original S77-1 empirical design curve.

The comparison covered a range of 108 design scenarios, including medium to

large passenger jet aircraft in Australia and a wide range of subgrade moduli.

The analysis showed good general agreement between APSDS and S77-1 with

a median difference of 36 mm (or 6.7% of the S77-1 thickness).

Based on this analysis, it is considered that S77-1 is confirmed as being a valid

tool for aircraft pavement thickness design. This serves to validate the use of

the software for the remaining research presented in this thesis.

Chapter 4 Input Parameter Selection


37

4. INPUT PARAMETER SELECTION

4.1 GENERAL

APSDS, like all computer-based design tools, is only a tool for the conversion of

design input parameters to design outputs. In the case of flexible aircraft

pavement thickness design, the outputs are pavement layer thicknesses or an

indication of pavement adequacy for a given thickness. The selection of input

parameters, which are appropriate is therefore the focus of the designer.

4.2 INPUT PARAMETERS

The inputs required to conduct an aircraft pavement design in APSDS are:

• Subgrade modulus. In MPa.

• Aircraft wander. As a standard deviation of wander in mm.

• Aircraft data. Including mass (in t), tyre pressure (in MPa) and number of

passes.

• Pavement structure. Including the type and thickness of each layer as well

as the modulus for materials which are not automatically sub-layered by the

Barker and Brabston (1975) method. For flexible pavements, this is

generally only the asphalt surface layer.

Appropriate input parameter value selection for any design scenario, should

concentrate on the parameters which have the greatest influence on the

required pavement thickness. The selection of an appropriate value of each

input parameter is described in the following sections.

4.3 SUBGRADE STRENGTH

The purpose of a pavement is to protect the subgrade from the loads imposed

by aircraft and other traffic (Pereira, 1977). The loads are applied to the

pavement surface through the aircraft tyres and then the pavement layers

spread the load until the stresses and strains induced by the load are small




enough to be accommodated by the next lower layer. The deepest portion of

the pavement structure is the subgrade and therefore pavement design focuses

on the load which can be accommodated by the subgrade material. It is

however acknowledged that in reality, damage accumulation can occur within

the pavement layers.

The development of the S77-1 design curves by the US Corps of Engineers in

the 1960s and 1970s expressed subgrade strength by the CBR. CBR is a

dimensionless unit calculated as being the resistance of a soil to the penetration

of a standard piston, as a percentage of the resistance offered by a reference

material (Californian Limestone) (DOD, 1964).

The actual field CBR test is cumbersome, expensive and for existing

pavements, requires significant disturbance of the insitu structures. Therefore,

a number of alternate test methods have been developed in order to simplify the

field work whilst maintaining some correlation to the original test method (Holtz

and Kovacs, 1981). Alternatives to the insitu field CBR test, commonly

available in Australia, include:

4.3.1 Laboratory CBR

Whilst this is a less expensive and relatively simple test, the problem of

obtaining a sample which is representative of the moisture conditions, density

and soil structure in the field is problematic. Soaked (usually 4 or 7 days) and

unsoaked tests are available with varying degrees of overpressure.

4.3.2 Dynamic Cone Penetrometer

The Dynamic Cone Penetrometer (DCP) is a device designed for field

determination of subgrade stiffness which is measured through resistance to

penetration of a standard cone. This cone is dynamically penetrated by the

dropping of a standard weight over a standard height. Guidance for the

conversion of penetration (blows per mm of penetration) to subgrade CBR is

provided but this conversion was derived for fine grained cohesive soils only



39

(AS 1289, 1997). Similar penetrometers are available in other countries under

different names.

4.3.3 Associated material characteristics

By measuring associated material characteristics, an indicative CBR can be

assigned by comparison to the CBR of materials with similar properties.

Commonly used characteristics are the particle size distribution and the

plasticity of the fines (Holtz and Kovacs, 1981).

Of these, the laboratory CBR is the most common test for the determination of

material CBR on green field sites, where materials will be moistened and

compacted and therefore representation of field conditions at the time of

sampling is not appropriate. For existing pavement investigations, the

remolding of laboratory samples to an appropriate density and moisture content

is common and is often supplemented by insitu DCP tests.

It is normal to soak a CBR sample for four days prior to conducting the CBR test

(Huang, 1993). Common Australian practice has been to either adopt the four

day soaked test result or, where existing pavements are available on the same

site, test at the equilibrium moisture content identified under the existing

pavements.

US Corps of Engineer practice is to conduct laboratory CBR tests in a soaked

state, at a range of densities. The design CBR is then read from a plot of

density versus CBR, for a density equivalent to 95% of the maximum density.

The US Corps of Engineers also allow an un-soaked CBR determination in arid

regions (Ahlvin, 1991). Recent US FAA guidelines stipulate the use of a four-

day soaked test for laboratory CBR determination. This is based on the

premise that subgrades reach near saturation under pavements within about

three years of construction (FAA, 1989). The four-day soaked CBR test does

not, however, take into account the pore pressure state of the subgrade under

the pavement.




Take two specimens of identical subgrade material compacted to the same

density at precisely the same moisture content. One sample is retained at zero

pore pressure whilst the other has a negative pore pressure applied. The

sample with negative pore pressure would behave as a significantly stiffer and

stronger subgrade than the zero pore pressure sample. Similarly, a sample

with positive pore pressure would perform more poorly than both samples.

Pore pressures are generally induced in subgrade materials by the relative

height of the water table to the material. No method for incorporating pore

pressure into subgrade CBR selection was identified. Engineering judgment

and experience must be applied in this regard or it must be nominated.

Regardless of the method of selection of subgrade strength in terms of CBR, it

must be converted to a modulus for use in APSDS. The conversion from CBR

to modulus utilised is an inherent part of the S77-1 design model and was

formalised by Barker and Brabston (1975). The conversion is shown in

Equation 3.

M = 10 × CBR...................................................................................... Equation 3

Where: M = Modulus of the Subgrade in MPa

CBR = Californian Bearing Ratio of the Subgrade as a percentage

Whilst other methods for converting from CBR to modulus are available, the

current version of APSDS was calibrated using this conversion. Therefore, this

empirical conversion must also be used for practical purposes.

Given the high influence of subgrade CBR on thickness required, the selection

of an appropriate subgrade CBR is critical to pavement design. This is

especially the case for low subgrades where a change of one CBR unit can

have a great impact on pavement thickness.



41

4.4 AIRCRAFT WANDER

Unlike road and highway pavements, aircraft pavements are subjected to a

significant transverse distribution of loads. This distribution of loads is

commonly referred to as aircraft wander. An issue related to aircraft wander is

that aircraft have significantly different wheel configurations, and therefore, even

at zero aircraft wander, the point of load application transversely across the

pavement can be significantly different for different aircraft types. The effect of

aircraft wheel configuration and aircraft wander combine to distribute damage

across the width of the aircraft pavement and effectively increases the service

life compared to that which would be expected under channelised traffic.

APSDS caters for aircraft wander by applying the nominated number of load

repetitions across the width of the pavement, based on a nominated standard

deviation of aircraft wander, assuming traffic is normally distributed (MINCAD,

2000). The incorporation of aircraft wander into aircraft pavement design tools

negates the requirement to utilise PCR. PCRs are necessary to relate passes

to coverages for other design tools such as LEDFAA (FAA, 1995a) and the

FAA’s chart based methods (FAA, 1995).

A number of studies have been undertaken to measure the actual wander of

aircraft on pavements. These studies have concluded that the wander of

aircraft changes with the pavement area being considered. For example,

aircraft on a runway will land and takeoff with a greater degree of wander

across the pavement than aircraft moving slowly along a straight taxiway

pavement. Under marshal or Nose In Guidance Systems (NIGS) aircraft

parking on aprons, or at aerobridges, would be expected to have the smallest

degree of wander.

Table 3 provides the findings of two studies regarding the degree of aircraft

wander on different areas of aircraft pavement. They are considered

appropriate where site or project specific information is not available, which it

rarely is.




Table 3 Aircraft Wander Standard Deviation.

Pavement Area HoSang (1975) US Army/Air Force (1988) Runway 1800 mm – 3400 mm 1550 mm Taxiway 800 mm – 1800 mm 770 mm

Whilst no specific literature was located, MINCAD (2000) suggests that 200 mm

may be an appropriate standard deviation of wander for parking positions. The

following wander standard deviations are commonly used in Australia:

• Runway. 1550 mm

• Taxiway. 773 mm

• Apron. 200 mm

4.5 AIRCRAFT MASS

Each aircraft has a measurable and exact mass at which it operates on any

given area of aircraft pavement. In addition, all aircraft have published,

certified, maximum operating masses, referred to as the Maximum All Up Mass

(MAUM). Aircraft rarely operate at their MAUM and therefore, to utilise their

MAUM in pavement design is a conservative approach, especially given their

high influence on pavement thickness. Mass can vary significantly for any given

aircraft make, type and variant. In commercial operations, additional weight

implies greater fuel burn and therefore more expensive operations. Also, at

many airfields, large aircraft cannot operate at their MAUM due to runway

length requirements on takeoff.

APSDS allows the input of any aircraft mass. Therefore the effect of different

assumed operating masses can be readily assessed. The mass should be

selected to be within the range of operating masses for the design aircraft and

should be based on some sensible estimate of the likely mass for the majority of

operations. Aircraft operators record aircraft masses for each and every flight

and therefore the actual information is available but may need to be



43

summarised or combined into a number of operations of aircraft at one or two

typical or characteristic masses.

4.6 AIRCRAFT TYRE PRESSURE

Just as each aircraft is certified to operate at a published MAUM, it is also

published with a standard operating tyre pressure. However, in practice, aircraft

maintainers will adjust the tyre pressure to provide an appropriate mass/tyre

pressure combination. This is done to limit the amount by which a tyre deforms

during operations. APSDS allows the input of any tyre pressure for each

aircraft being designed for. However, it is common practice to adopt the

standard operating tyre pressure at all operating weights of the aircraft. This is

a slightly conservative approach to pavement design. Tyre pressures generally

have little effect on pavement thickness required but do cause problems within

the asphalt surfacing.

4.7 NUMBER OF PASSES

The number of aircraft passes is the number of times the design aircraft travels

past any given cross section of aircraft pavement during the design life. This is

distinctly different from coverages, operations, movements and departures. The

number of passes of each of the design aircraft must be determined based on:

• Design life of the pavement. Typically 10 or 15 years is adopted for

flexible aircraft pavements based on the time between asphalt overlays

being required due to environmental degradation.

• Configuration of the pavement. The ratio between departures and passes

will be affected by the airfield layout, including the number of runways,

parallel taxiway and parking arrangements.

• Traffic growth. Like road traffic, aircraft traffic is assumed to grow over

time with an annual growth rate of 3% being a reasonable approximation (in

Australia) in the absence of project specific information.




APSDS allows any number of passes to be assigned for each aircraft

considered in the design traffic.

4.8 ASPHALT MODULUS

As for all materials used to model aircraft pavements in APSDS, asphalt is

assigned a modulus. This modulus is considered to be an elastic resilient

modulus. The measurement of asphalt modulus is not an exact science. Its

measurement is expensive and time consuming and is generally not justified on

a project basis (Sukumaran, et al, 2002). Unlike base and sub-base materials,

which have an automated method for modulus assignment within APSDS

(based on Barker and Brabston (1975)) asphalt moduli are assigned by the

designer for each design scenario.

Asphalt modulus varies with pavement temperature, load duration, asphalt age

and induced confining stress. Therefore, any particular asphalt mix will exhibit a

large range of moduli during its life. However, a constant asphalt modulus (per

design scenario) is required by APSDS.

Procedures are available which relate air temperature to pavement

temperature, and in conjunction with bitumen penetration data, to asphalt

modulus. One method was developed by Heukelom and Klomp (1964) and

described in Brabston, et al (1975). Due to the cost associated with such

methods, it is normal for designers to assume a typical value of asphalt

modulus. Table 4 provides some guidance on typical asphalt moduli values in

various Australian environmental conditions. Given the low influence of asphalt

modulus on pavement thickness, adoption of presumptive or typical values is

generally appropriate.



45

Table 4 Typical asphalt moduli.

Environment Moduli Asphalt in northern and tropical regions.

Young asphalt in moderate regions. 1000 MPa

Mature asphalt in moderate regions. Young asphalt in southern and alpine regions.

2000 MPa

Mature asphalt in southern and alpine regions. 3000 MPa

4.9 PAVEMENT STRUCTURE

The pavement structure is clearly a design specific issue and guidance can not

readily be provided as to what pavement structure is suitable in the various

design environments one might encounter. Therefore, the following issues are

identified for consideration only.

4.9.1 Cemented materials

Whilst cemented materials are available and have been used on Australia

aircraft pavement design practice, they are less common. The concern with

cemented materials is their tendency to crack, due to local and environmental

factors, and the potential for cracks to reflect into the bound asphalt layer.

Where cemented materials have been used, they have commonly been overlain

by an unbound granular layer which acts as a stress dissipater and retards the

reflection of cracks into the asphalt surface.

4.9.2 Asphalt thickness

The thickness of asphalt surfacing in Australian aircraft pavement design

practice is generally 40 mm to 60 mm as this provides a generally economical

pavement structure. In the USA and other countries, thicker asphalt layers are

common. However, a significant number of Australian pavements that have

been subject to multiple overlays have 200 mm or more of asphalt.




4.9.3 Base course thickness

Base course materials are commonly utilised in thicknesses of between

100 mm and 400 mm, depending on the size of the aircraft. The larger the

aircraft the thicker the base course required to protect to sub-base material from

over stressing.

4.9.4 Fill layers

Fill layers have been used in instances where great thicknesses are required

over the subgrade. This is generally associated with weak subgrades or where

the finished surface level greatly exceeds the natural surface level and full

pavement depth is governed by geometric requirements rather than pavement

strength.

4.10 DESIGN TRAFFIC MIX

The aircraft traffic mix or spectrum is clearly a design specific issue. Little

guidance can therefore be provided. The aircraft traffic spectrum includes the

following elements which are discussed for consideration only.

4.10.1 Aircraft Variants

Aircraft often have a number of variants. These variants can have significantly

different load characteristics. For example, the B737-100 has a maximum mass

of 45.4 t and tyre pressure of 1.02 MPa. In contrast, the B737-800 has a mass

of 79.2 t and a tyre pressure of 1.30 MPa. These two variants of the B737 also

have slightly different wheel configurations, with the space between the dual

tyres of the B737-300 being 775 mm but 864 mm for the B737-800. Further,

the B737-500, which has a maximum mass of 60.8 t and tyre pressure of

1.34 MPa, has the B737-300’s wheel spacing.

4.10.2 Masses and Tyre Pressures

As previously discussed, the mass and tyre pressure of the aircraft in the traffic

mix is required. Any number of masses and tyre pressures can be entered by



47

each additional combination requires an additional entry in the aircraft load

table. It is therefore normal for designers to adopt the standard tyre pressure

and to rationalise all aircraft traffic to one or two representative masses.

4.10.3 Number of Aircraft Passes

APSDS allows any number of passes to be assigned for each aircraft

considered in the design traffic. These should be selected based on information

from the airport operator.

4.11 SUMMARY

The use of APSDS is relatively simple but if the input parameters are not

appropriately selected, gross errors in the resulting design thickness can occur.

Therefore, the following input parameters should be appropriately selected

based on the design scenario and experience:

• Subgrade Strength.

• Aircraft Wander.

• Aircraft Mass.

• Aircraft Tyre Pressure.

• Number of Passes.

• Asphalt Modulus.

The aircraft traffic mix and pavement composition (base course thickness and

asphalt thickness) must also be determined. When a designer selects these

input parameters, effort should be concentrated on the parameters that have

the greatest influence on pavement thickness required. Less effort or

conservative estimates would be generally acceptable for the less influential

parameters. To determine the relative influence of the various input

parameters, a sensitivity analysis of APSDS is required.




Chapter 5 Sensitivity Analysis


49

5. SENSITIVITY ANALYSIS

5.1 GENERAL

The key to successful aircraft pavement design using APSDS is the selection of

input parameters. With a general guide for the selection of the main parameters

provided, a designer may ask which of these to concentrate on. Using the

Pareto principle (Lawson and Erjavec, 2001), the parameters which should be

concentrated on are those which have the greatest influence on the outcome.

An understanding of the sensitivities of flexible aircraft pavement thickness to

the various input parameters is therefore desired.

5.2 INVESTIGATION UNDERTAKEN

An investigation was undertaken to determine the effect of the various input

parameters on the total thickness of flexible aircraft pavements. The

investigation included the parametric operation of the program under a range of

reasonable values of each input parameter. The combination of these input

parameters resulted in some impractical pavement solutions. Therefore, these

investigations should not be used as the basis of any pavement design.

During these investigations, some aspects of the input parameters were held

constant. These constants are discussed below.

5.2.1 Aircraft Traffic

For this investigation three aircraft were selected to represent the range of

medium to large domestic and international passenger jet aircraft currently in

operation. These were the B737, B767 and B747. The selected aircraft, their

MAUM and standard tyre pressure, are shown in Table 5. The selection of

Boeing aircraft is representative of their current dominance in the Australian

aviation industry. However, the analysis is equally applicable to similarly sized

alternate aircraft such as the Airbus A340, A300 and A320.




The B747 has outer and inner main landing gears. These gears are modelled

separately in APSDS and their separate contributions to pavement damage are

summed. The B777 and the A380 were specifically excluded from the analysis

as their six-wheel landing gear configurations were not included in the

calibration of the program to the S77-1 design curves (Wardle, et al, 2001) and

therefore the subgrade failure criteria do not adequately model these aircraft.

Table 5 Aircraft Information.

Aircraft MAUM (t) Standard Tyre Pressure (kPa) B747-400 397 1380 B767-300 180 1240 B737-800 79 1360

5.2.2 Pavement Structure

The standard pavement structure utilised during the testing in the US by the

Corps of Engineers to develop the S77-1 design procedure was (Pereira, 1977):

• 75 mm asphalt.

• 150 mm P209 (fine crushed rock base).

• Variable thickness of P154 (natural gravel sub-base).

• Variable CBR subgrade.

P209 (crushed aggregate base course) and P154 (sub-base course) are US

FAA specifications for airfield pavement materials (FAA, 1989). For this

investigation, the pavement structure illustrated in Figure 4 was adopted.



51

Figure 4 Pavement Structure.

5.2.3 Input Parameters

For this sensitivity analysis, values of the various input parameters required by

the program were selected to span the range normally encountered in practice.

The combination of parameter values for any given run was not necessarily

giving valid results, with some combinations returning non-solutions

(theoretically negative thicknesses of sub-base). The input parameters and the

values adopted for this investigation one detailed in Table 6.

Table 6 Input Parameters.

Design input parameter Units Values Subgrade Modulus (SM) MPa 30, 60, 100, 150

Aircraft Wander (W) mm 200, 800, 1400, 2000 Aircraft Mass (M) % of maximum 60, 80, 100

Tyre Pressure (TP) % of standard 80, 90, 100 Aircraft Passes (P) Number 5000, 10000, 20000

Asphalt Modulus (AM) MPa 1000, 2000, 3000 Asphalt Thickness (AT) mm 20, 40, 100 Base Thickness (BT) mm 100, 300, 500

It is noted that the Aircraft Mass were set to percentages of the MAUM of each

aircraft and that Tyre Pressures were set to percentages of the standard tyre

pressure for each aircraft.

20, 40 or 100 mm of asphalt of modulus 1000, 2000 or 3000 MPa

100, 300 or 500 mm of P209 B&B Base

Variable thickness (mm) of P154 B&B Sub-base

Variable CBR (%) Subgrade

Note: ‘B&B’ denotes a sub-

layering and modulus

assignment method in

accordance with Barker

and Brabston (1975).




5.3 SENSITIVITY ANALYSIS

The sensitivity analysis undertaken was based on statistical experimental

design and analysis methods. In particular, the analysis included linear

regression modelling and Analysis of Variance (ANOVA) tools (Lawson and

Erjavec, 2001). The statistical analysis of all data was performed using the tool

MINITAB (MINITAB, 2000). The sensitivity analysis is described in the following

sections.

5.3.1 Investigation Design

Initially, every combination of input parameters values was intended to be

utilised and for each, a total pavement thickness determined. However, for the

input parameter levels detailed in Table 6, this would require 42 × 36 = 11,664

runs of the program, for each aircraft considered, to cover all combinations.

Therefore, a fractional analysis was designed to allow the main effects and

influences of the parameters on total pavement thickness to be determined with

only 512 runs of the program, for each aircraft. The number of runs, 512, was

selected as a reasonable number that could be performed whilst allowing clear

identification of each input’s influence on pavement thickness. The parametric

run design is contained in Appendix 2.

5.3.2 Parametric Runs

Each of the 512 combinations of input parameter values was used to generate a

pavement thickness in APSDS for each of the three aircraft. Each run was

performed using the ‘determine design thickness’ function of the program for the

sub-base course and then the Total Thickness in mm of pavement was

calculated by adding the relevant thickness of asphalt and base course to the

sub-base thickness returned.

The total thickness of pavement was recorded for each run and then input into

MINITAB for analysis. The sub-base thicknesses ranged from ‘Not Applicable’

(where the pavement was more than sufficient without any sub-base course) up

to 1657 mm (a 1,777 mm total pavement thickness). Where a theoretically



53

negative sub-base thickness was returned for the B747 aircraft, the base and

asphalt thicknesses were amended to require some sub-base thickness.

Where B737 or B767 aircraft returned a theoretically negative sub-base

thickness for the B747 adopted base and asphalt thicknesses, a ‘Not

Applicable’ result was recorded. In total, 81 runs required changes to the base

and asphalt thickness for the B747. For the B767 and B737, 22 and 43 runs of

the program returned a ‘Not Applicable’ respectively. The results from the

parametric runs are contained in Appendix 3.

5.3.3 Simple Linear Regressions

Initially, simple linear regressions were performed on the total pavement

thickness for each aircraft. This was aimed at determining the consistency

between sensitivity of the pavement thickness to the various aircraft considered.

The linear regression models detailed as Equations 4 to 6 were derived for the

B747, B767 and B737 respectively.

TTB747 =1145 - 6.65 × SM - 0.0349 × W + 5.80 × M - 1.24 × TP + 0.00409 × P

- 0.0318 × AM - 0.797 × AT - 0.260 × BT (R2 = 0.81)..........................Equation 4

TTB767 = 1038 - 5.93 × SM - 0.0370 × W + 5.67 × M - 1.34 × TP + 0.00327 × P


TTB737 = 837 - 4.62 × SM - 0.0321 × W + 4.61 × M - 0.564 × TP + 0.00309 × P


Where: TTBXXX = Total thickness (for aircraft type)

SM = Subgrade modulus in MPa

W = Standard deviation of aircraft wander in mm

TP = Tyre pressure in MPa

P = Aircraft passes

AM = Asphalt modulus in MPa

AT = Asphalt thickness in mm

BT = Base course thickness in mm




The R2 (coefficient of determination) values are indicators of the goodness of fit

of the data to the linear models. The results are plotted against their modelled

values in Figure 5. The line of unity is also shown.

Figure 5 General Model Results

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600 1800 2000

APSDS thickness (mm)

Mod

elle

d th

ickn

ess

(mm

)


The residuals for each model are shown in Figure 6, plotted against the order of

the runs. This figure clearly shows the non-linear nature of the data and the

associated positive residuals for subgrade modulus of 30 (first 128 runs) and

150 (last 128 runs). Residuals generally had a magnitude of less than 200 mm

with some as large as 400 mm.



55

Figure 6 General Model Residuals

-300

-200

-100

0

100

200

300

400

500

0 128 256 384 512

Run

Res

idua

l (m

m)

B747 B767 B737

5.3.4 Separate Subgrade Linear Regressions

For each aircraft, four additional linear regressions were performed. These

provided linear relationships between pavement thickness and the input

parameters for each subgrade modulus. For the B767 aircraft, the regression

models are expressed as Equations 7 to 10. The APSDS thicknesses are

plotted against in modelled thicknesses in Figure 7. Each model’s residuals are

plotted against the general subgrade model (Equation 4 to Equation 6) residuals

in Figure 8, Figure 9 and Figure 10 for the B747, B767 and B737 respectively.

TT30 = 151 - 0.0376 × W + 13.8 × M - 0.374 × TP + 0.00847 × P - 0.0304 × AM

- 0.687 × AT - 0.204 × BT (R2 = 0.99) .................................................Equation 7

TT60 = 188 - 0.0447 × W + 7.64 × M - 0.420 × TP + 0.00563 × P - 0.0254 × AM

- 0.521 × AT - 0.205 × BT (R2 = 0.99) .................................................Equation 8

TT100 = 232 - 0.0148 × W + 4.01 × M - 0.606 × TP + 0.0023 × P - 0.0171 × AM

- 0.454 × AT - 0.158 × BT (R2 = 0.98) .................................................Equation 9




TT150 = 178 - 0.0143 × W + 2.99 × M - 0.910 × TP + 0.0012 × P - 0.0126 × AM

- 0.463 × AT - 0.158 × BT (R2 = 0.99) ...............................................Equation 10

Where: TTxx = Total thickness (for subgrade modulus for B767)

SM = Subgrade Modulus in MPa

W = Standard deviation of aircraft Wander in mm

TP = Tyre Pressure in MPa

P = Aircraft Passes

AM = Asphalt Modulus in MPa

AT = Asphalt Thickness in mm

BT = Base course Thickness in mm

Figure 7 Specific Model Results

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 200 400 600 800 1000 1200 1400 1600 1800 2000APSDS thickness (mm)

Mod

elle

d th

ickn

ess

(mm

)




57

Figure 8 Residuals for General and Specific Subgrade Models for B747

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 128 256 384 512

Run

Res

idua

l (m

m)

General Subgrade model Specific Subgrade Models


-500

-400

-300

-200

-100

0

100

200

300

400

500

0 128 256 384 512Run

Res

idua

l (m

m)






-500

-400

-300

-200

-100

0

100

200

300

400

500

0 128 256 384 512

Run

Res

idua

l (m

m)


Figure 8 to Figure 10 show that the adoption of four specific subgrade models

reduced the maximum residuals from around 400 mm to 70 mm for all three

aircraft considered. This is combined with improved R2 values for the subgrade

specific models, indicating that pavement thickness is, generally, linear with

respect to all input parameters (when subgrade modulus is removed).

5.3.5 Consistence across Aircraft

An assessment of the consistency of pavement thickness with regard to the

input parameters across the three aircraft types was performed by calculating

the ratio of pavement thickness between each pair of aircraft (B747 and B737,

B747 and B767 as well as B767 and B737) against the pavement thickness

(average for the aircraft in the ratio) with all other factors held constant.

Figure 11 illustrates these ratios for the three aircraft considered in this analysis.



59

Figure 11 Thickness Ratio Consistency.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Average Pavement Thickness (mm)

Thic

knes

s R

atio

B747 to B767 B747 to B737 B767 to B737

Figure 11 shows that the ratios between pavement thicknesses required for the

various aircraft are relatively consistent for all other combinations of the input

parameters. Therefore, the sensitivity of pavement thickness to the input

parameters is considered to be essentially independent of the aircraft being

considered. With consistence across aircraft confirmed, the examination of

sensitivities could be undertaken.

5.3.6 Normalised Sensitivities

To determine the comparative influence of the input parameters on the total

pavement thickness, each parameters’ values (ranging from the smallest to

greatest reasonable value) were given a scale ranging from one to five (1 =

minimum, 3 = average , 5 = maximum). This allowed comparison of all input

parameters on a single chart. These ‘normalized’ parameters were plotted on

the same axis against the total pavement thickness with all other parameters

held constant. The relative influence of the normalised parameters can be

inferred from the relative slope of the resulting lines, which are illustrated in

Figure 12, Figure 13 and Figure 14 for the B747, B767 and B737 aircraft

respectively.




Figure 12 Relative Influence of Design Inputs for B747.

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6

Normalised Input Value

Tota

l Pav

emen

t Thi

ckne

ss (m

m)

Subgrade Modulus Aircraft Wander Aircraft Mass Tyre PressureAircraft Passes Asphalt Modulus Asphalt Thickness Base Thickness

Figure 13 Relative Influence of Design Inputs for B767

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6


Tota

l Pav

emen

t Thi

ckne

ss (m

m)




61

Figure 14 Relative Influence of Design Inputs for B737.

0

200

400

600

800

1000

1200

1400

1600

0 1 2 3 4 5 6


Tota

l Pav

emen

t Thi

ckne

ss (m

m)


It can be seen from Figure 12 to Figure 14 that the relative influence of the input

parameters on total pavement thickness is consistent for all three aircraft

considered. It can also be seen that the subgrade modulus has the greatest

influence on pavement thickness (demonstrated by the greatest slope or

gradient).

5.3.7 Relative Influence

The gradient of each line represents the change in the modelled pavement

thickness resulting from a unit change in that input parameter’s normalised

value. Each gradient represents the relative ‘influence’ of that input parameter

on pavement thickness. The modelled linear influences of all input parameters

are summarised for each aircraft in Table 7. It is noted that the influence of

subgrade modulus is taken as the average gradient over the full length of the

curved line based on a straight line between the two ends.




Table 7 Normalised Linear Influence and Importance

Influence Importance Factor 1 normalised unit equals B747 B767 B737 B747 B767 B737

Subgrade Modulus

30 MPa 200 178 139 43.4 40.2 54.6

Aircraft Wander 450 mm 16 17 14 4.7 5.2 8.0 Aircraft Mass 10 % 58 57 46 14.6 14.8 21.4 Tyre Pressure 5 % 6 7 3 1.6 1.8 1.3 Aircraft Passes 3750 15 12 12 4.0 3.3 5.6

Asphalt Modulus

500 MPa 16 16 13 2.0 2.1 3.1

Asphalt Thickness

20 mm 16 16 14 4.1 4.4 6.7

Base Thickness 100 mm 26 23 21 5.8 5.1 8.4

Table 7 also contains an ‘importance’ value for each input parameter for each

aircraft model. Importance is used to express the statistical significance of the

parameter on the pavement thickness and is a measure of the probability that

the input parameter could be removed from the model. The larger the

importance (the t-statistics from the test for the hypothesis that the coefficient is

equal to zero) the more significant the parameter is in the model and the greater

the analysis suggests that it should not be removed.

5.4 ANALYSIS OF RESULTS

From the analysis undertaken, the input parameters which are most significant

in the linear models for total pavement thickness are subgrade modulus and

aircraft mass. Aircraft wander, aircraft passes, asphalt thickness and base

course thickness are also important whilst tyre pressure and asphalt modulus

are essentially insignificant (as expected).

The relative importance and influence of the input parameters on the total

pavement thickness is consistent for all three aircraft considered. This is shown

by the summary in Table 7 and confirmed by the thickness ratio plot in

Figure 11. Given that these aircraft all have differing wheel configurations and

span the breadth of size of medium to large jet aircraft currently in operation



63

(excluding the B777 and A380) this analysis is considered to be generally

applicable to all medium to heavy jet aircraft. Further, its general application to

all medium to heavy jet aircraft suggests its application to combinations of

aircraft (traffic mixes) for which pavement thickness is governed by one or more

medium to large aircraft within the mix.

With the exception of subgrade modulus, the influence of the various input

parameters on the total pavement thickness is essentially linear as shown in

Figure 12 to Figure 14. In the case of subgrade modulus, a small change is far

more influential on pavement thickness at low subgrade modulus values than at

higher ones. Therefore, a general linear model covering all subgrade values is

not appropriate. Linear models developed for specific subgrade modulus,

however, are far more accurate as all other input parameters influence

pavement thickness in a generally linear manner. This is demonstrated by the

comparison of general and specific model residuals in Figure 8 to Figure 10.

5.5 SUMMARY

An analysis was conducted to determine the sensitivity of APSDS calculated

pavement thicknesses to the various input parameters required. Each input

parameter was varied over the range of commonly encountered values.

Designers should concentrate their efforts on the determination of subgrade

modulus and aircraft mass, as these input parameters have the greatest

influence on the total pavement thickness. Less effort should be spent on the

other influential parameters, and the use of reasonably conservative estimates

are generally appropriate. Presumptive values of tyre pressure and asphalt

modulus are usually adequate because these factors have only minor impact on

computed pavement thickness when failure of the pavement is governed by

subgrade deformation.

Total pavement thickness is essentially linearly responsive to all the program

inputs except for subgrade modulus. The relationship between subgrade




modulus and pavement thickness is clearly nonlinear. Modulus changes are

more influential at lower values than at higher ones.

The sensitivity of total pavement thickness to the various input parameters is

essentially consistent for all three medium to large jet aircraft considered.

Because these aircraft cover the range common medium to large jet aircraft in

current use, this sensitivity analysis is also considered to be applicable to all

medium to large jet aircraft and aircraft traffic mixes containing significant

numbers of at least one medium to large jet. Therefore, for all design traffic

scenarios, the design inputs which should be given the most attention by the

designer are subgrade modulus and aircraft mass.

Whilst not the most influential input parameters, pavement composition (asphalt

thickness and base course thickness) are important input parameters. Where

consistence between APSDS and FAA design procedures (which are based on

material thickness equivalences instead of layered elastic methods) is desired,

the APSDS implied material equivalence is critical.

Chapter 6 Material Equivalence


65

6. MATERIAL EQUIVALENCE

6.1 GENERAL

The S77-1 design curve provides the total pavement thickness required. This

thickness, however, is deemed to comprise of a standard S77-1 pavement

structure. Where alternate pavement structures are considered, their

equivalent thicknesses are determined using material equivalence principles.

Material equivalence factors required to perform these conversions are

contained in the FAA’s guide to aircraft pavement thickness design (FAA,

1995). The FAA guide provides ranges of equivalence factors between various

materials and these ranges are quite broad. Designers therefore tend to adopt

the mid-range values for most applications.

Layered elastic design tools have generally been calibrated to the S77-1 design

curve. These layered elastic design tools commonly use an automated sub-

layering routine which was developed by Barker and Brabston (1975) to divide

each granular material layer into a number of sub-layers and assign a modulus

value to each. Two values of equivalence could be selected from with the FAA

range and result is significantly different total pavement thicknesses.

There was believed to be an inconsistency between the FAA mid-range values

of material equivalence and those implied by layered elastic design using

Barker and Brabston sub-layering techniques. This study provides more

accurate material equivalences for crushed rock base course, uncrushed gravel

sub-base and asphalt, with the aim of providing consistence with APSDS

implied equivalences. These recommended new material equivalence values

could be included in future updates of the FAA guidance.

6.2 S77-1 AND FAA PAVEMENT DESIGN

Aircraft pavement thickness design originated as, and continues to be, an

empirical based design method. Even when so-called mechanistic design tools

are used, the performance relationship, or failure criterion, remains an empirical

relationship developed from full scale testing results. The failure criterion is a




mathematical relationship between the damage indicator (commonly stress,

strain or deflection) modelled under a single load event and the number of

allowable repetitions of that level of loading. The current design methods are

therefore more appropriately termed mechanistic-empirical.

For flexible aircraft pavement design, the governing failure mode is usually

vertical subgrade deformation (rutting). The empirical performance relationship

for subgrade deformation was derived from full scale testing conducted by the

US Corps of Engineers and reported by Pereira (1977). The relationship

between aircraft loading, subgrade strength and pavement thickness required is

known as the S77-1 curve and this remains the empirical basis for most flexible

aircraft pavement design tools today.

The S77-1 curve provides a pavement thickness of a pre-determined

composition. The standard S77-1 pavement structure is shown in Figure 15.

P401, P209 and P154 are standard designations for the described materials,

utilised by the FAA for design and specification purposes (FAA, 1995).

Figure 15 Standard S77-1 Pavement Structure.

Where other pavement structures are considered, they must be converted to

the equivalent thickness of S77-1 pavement. Material equivalence factors are

provided in the FAA design guide (FAA, 1995) as detailed in Table 8. The

guide also provides equivalence factors for others materials including lean mix

concrete, soil cement and cemented crushed rock.

75 mm of 1400 MPa Asphalt (P401)

150 mm of Crushed Rock (P209)

Variable Uncrushed Gravel (P154)

Variable CBR subgrade



67

Table 8 FAA Material Equivalence Guidance.

1 mm of this material Is equivalent to the following thickness (mm)

Of this material

Asphalt (P401) 1.2 to 1.6 Crushed rock (P209) Crushed rock (P209) 1.2 to 1.8 Uncrushed gravel (P154)

Asphalt (P401) 1.7 to 2.3 Uncrushed gravel (P154)

The FAA documentation provides little guidance on when the low, medium and

high values in the various ranges detailed in Table 8 should be used. In

practice, for materials at the same relative density, a range of equivalences

would be expected due to:

• Differences in the material quality. A good quality fine crushed rock

would be more beneficial, in comparison to a standard uncrushed gravel,

than a poor fine crushed rock would be. Therefore, a good fine crushed

rock would have a greater equivalent thickness of standard uncrushed

gravel than what the same thickness of a poor fine crushed rock would.

• Stress conditions. Given the stress dependent nature of granular

materials the equivalence between two materials would be expected to vary

depending on the loading applied as well as the depth within the pavement

that the replacement occurs. Both of these factors will affect the stress

conditions under which the material is required to perform.

Generally, without better guidance, designers will utilise the mean value of the

range of equivalences. This study examines the material equivalences implied

by APSDS and examines their consistence with the FAA guidance.


The investigation undertaken was designed to meet the following objectives:

• Confirm any inconsistence between S77-1 and APSDS pavement thickness

when adopting the mid-range of the FAA equivalence ranges.




• Determine alternate or specific equivalence factors to provide improved

consistence.

• Investigate the cause of any variability in the APSDS implied equivalences.

• Confirm the suitability of the recommended equivalence factors by

performing a number of example calculations.

As the investigation evolved, it comprised of three main stages. In all stages,

the general approach was to perform a number of parametric operations of

APSDS and determine the APSDS implied equivalence factors before

comparing them to the FAA provided values. The three stages of the

investigation were:

• Practical pavement equivalences. The material equivalences implied

from designing various practical or typical pavement structures was

determined. Typical pavements were determined for a range of typical

medium to large aircraft on commonly encountered subgrade conditions.

Different combinations of layer thicknesses were determined, each able to

cater for the modelled number of aircraft passes.

• Isolated pavement equivalences. In order to isolate layer properties from

aircraft and pavement variables, single wheel load was applied and granular

pavement layers were not sub-layered. Materials were modelled as

homogenous materials of a pre-determined modulus and compared to

materials of other moduli values. Pavement thicknesses were determined

so that the vertical compressive strains modelled at the top of the subgrade

were equal to those modelled by a standard layer thickness. The aim of this

portion of the study was to examine the replacement material properties

(modulus, thickness and location) that affect the implied material

equivalence.

• Equivalence Examples. A number of pavement structures were designed

directly by APSDS and by S77-1 and the two pavement thicknesses were

compared using the FAA mid-range equivalences and the recommended



69

equivalence factors. This was designed to confirm the appropriateness of

the recommended equivalence factors as well as demonstrating their

application.

The details of each stage of the investigation are described in the following

sections.

6.4 PRACTICAL PAVEMENT EQUIVALENCES

In order to assess material equivalence for practical use, the APSDS implied

equivalences were determined for common and realistic design scenarios. This

analysis is detailed as follows.

6.4.1 Aircraft Traffic

For this stage of the investigation, three aircraft were selected to represent the

range of medium to large domestic and international passenger jet aircraft

currently in operation in Australia. The selected aircraft, their maximum mass

and standard tyre pressure are shown in Table 5 for consistence with the

sensitivity analysis previously discussed.

6.4.2 Pavement Structure

For this investigation, the pavement structure illustrated in Figure 4 was

adopted. This pavement structure is that utilised for the sensitivity analysis

previously discussed. A consistent pavement structure was selected to allow

re-use of the raw data collected during the sensitivity analysis’ parametric runs

of APSDS.

The number of Asphalt versus Crushed Rock and asphalt versus Uncrushed

Gravel equivalence determinations for each aircraft considered is detailed in

Table 9. For these parametric runs, the ‘design layer thickness’ option was

utilised for the uncrushed gravel layer. Where crushed rock versus asphalt

equivalence was required, a constant uncrushed gravel thickness was needed.

This was not available from the sensitivity analysis data. Therefore the crushed

rock thickness was selected as the ‘design layer thickness’.




Table 9 Number of Practical Equivalence Determinations.

Aircraft Equivalence

B747-400 B767-300 B737-800 Asphalt and Crushed Rock 128 122 109

Crushed Rock and Uncrushed Gravel 245 223 202 Asphalt and Uncrushed Gravel 164 155 141

The difference in the number of equivalence determinations for each aircraft

exists as a result of some pavements not returning a positive pavement layer

thickness for the layer being designed. This was most pronounced for the

lighter B737 aircraft, which requires the thinnest pavement of the three aircraft.

6.4.3 Design Parameters

The values of each of the parameters considered in the parametric runs of

APSDS are detailed in Table 10. The combination of input parameters for each

parametric run of APSDS was derived using the Plackett-Burman method of

statistical experimental design (Lawson and Erjavec, 2001). The parametric

design is contained in Appendix 4 and the results are contained in Appendix 5.

Table 10 Design Parameter Values for Practical Equivalence.

Parameter Units Values Subgrade Modulus MPa 30, 60, 100, 150

Aircraft Wander Mm 200, 800, 1400, 2000 Aircraft Mass % of maximum 60, 80, 100 Tyre Pressure % of standard 80, 90, 100 Aircraft Passes Number 5000, 10000, 20000

Asphalt Modulus MPa 1000, 2000, 3000 Asphalt Thickness Mm 20, 40, 100

Crushed rock Thickness Mm 100, 200, 400

6.4.4 Material Equivalence

Material equivalence was determined for each pair of parametric runs where all

design parameters were identical, with the only difference being the



71

thicknesses of the two materials being considered. The equivalences were

calculated using Equation 11.

EA/B = (TA - TA2)/(TB2 - TB1) .................................................................Equation 11

Where: EA/B = Thickness of A that is equivalent to 1 mm of B

TA1 = Thickness of material A in pavement 1

TA2 = Thickness of material A in pavement 2

TB1 = Thickness of material B in pavement 1

TB2 = Thickness of material B in pavement 2

Where pavement 1 and pavement 2 are considered to be equivalent in

structural capacity and are identical in all aspects except for the thicknesses of

material A and material B. Equation 11 was utilised as it provides for the

thickness of one material that can be directly replaced by another material and

result in the same structural capacity pavement.

Graphical representations of the calculated material equivalence for the three

aircraft considered are shown in Figure 16, Figure 17 and Figure 18, for the

Asphalt and Crushed rock, Crushed rock and Uncrushed gravel and Asphalt

and Uncrushed Gravel respectively. Figure 16 to Figure 18 also contain the

minimum, maximum and mid-range value of the material equivalence guidance

provided by FAA (FAA, 1995).




Figure 16 Practical Equivalence for Asphalt and Crushed Rock.

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0 20 40 60 80 100 120 140

Run

Equi

vale

nce

Rat

io

B747 B767 B737 FAA Max FAA Ave FAA Min

Figure 17 Practical Equivalence for Crushed Rock and Uncrushed Gravel.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 50 100 150 200 250

Run

Equi

vale

nce

Rat

io




73

Figure 18 Practical Equivalence for Asphalt and Uncrushed Gravel.

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

0 20 40 60 80 100 120 140 160

Run

Equi

vale

nce

Rat

io


These figures show that the material equivalence implied by layered elastic

design tools is consistently at the lower range of the FAA guidance for the

materials considered. Summary statistics for the three equivalences are shown

in Table 11.

Table 11 Summary Statistics for Practical Equivalence.

Statistic Asphalt and

Crushed Rock Crushed Rock and Uncrushed

Gravel

Asphalt and Uncrushed

Gravel Mean 1.33 1.19 1.57

Standard Deviation 0.17 0.04 0.21 Coefficient of Variation 12.7% 3.0% 13.3%

Maximum 2.10 1.32 2.50 Upper Quartile 1.37 1.21 1.65

Median 1.30 1.19 1.51 Lower Quartile 1.22 1.17 1.45

Minimum 0.90 1.04 1.15 Range 1.20 0.28 1.35

Inter-quartile range 0.15 0.04 0.20




As a check, the equivalence between Asphalt and Crushed Rock, when

multiplied by that for Crushed Rock and Uncrushed Gravel, should equal that

for Asphalt and Uncrushed Gravel. Based on the mean equivalences

presented in Table 11, this is 1.33 × 1.19 = 1.58, which is very close to 1.57.

Some impractical equivalences are returned such as 0.90 for the equivalence

between Asphalt and Crushed Rock as shown in Figure 16. This implies that

replacing a certain material (Asphalt) with a less stiff material (Crushed Rock)

will reduce the overall pavement thickness. This is not sensible and is the

result of anomalies created by the automatic sub-layering and stiffness

assignment caused by slight changes in the layer thicknesses requiring

different numbers of sub-layers.

Significant variability in the material equivalence is observed, especially for

thicker pavements, which generally relate to low subgrade modulus values.

Further analysis was required to explain the cause of this variance. This

included the preparation of box and whisker plots for each material equivalence

for each aircraft. These are shown in Figure 19 (Asphalt and Crushed

Rock),Figure 20 (Crushed Rock and Natural Gravel) and Figure 21 (Asphalt

and Natural Gravel).



75

Figure 19 Summary of Asphalt and Crushed Rock Equivalences

0.80

1.00

1.20

1.40

1.60

1.80

2.00

2.20

B747 B767 B737

Aircraft

Equi

vale

nce

Figure 20 Summary of Crushed Rock and Uncrushed Gravel Equivalences

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

B747 B767 B737

Aircraft

Equi

vale

nce




Figure 21 Summary of Asphalt and Uncrushed Gravel Equivalences

1.00

1.20

1.40

1.60

1.80

2.00

2.20

2.40

2.60

B747 B767 B737

Aircraft

Equi

vale

nce

Figure 19 to Figure 21 shows that whilst the range of equivalences is large (eg.

1.20 for Asphalt and Crushed Rock), the inter-quartile range (which represents

the range of the central 50% of values) is quite low (eg. 0.15 for Asphalt and

Crushed Rock).

The aircraft type (B747, B767 and B737) was not a statistically significant

predictor of material equivalence. This is clearly shown in the similarity

between the three box and whisker plots contained in each of Figure 19 to

Figure 21. As the equivalences are not generally affected by the aircraft and

therefore further analysis considers the combined data only.

A number of linear regressions were performed on the combined aircraft data

utilised to determine the various practical material equivalences. These

regressions showed that subgrade modulus, asphalt modulus, uncrushed

gravel thickness and crushed rock thickness were generally statistically

significant predictors of material equivalence. These significant parameters can

all be related to the thickness and modulus of the various layers in the

pavement structure.



77

The regressions also showed that aircraft wander, aircraft mass, number of

passes and tyre pressure were not statistically significant. These factors are

independent of the pavement composition and materials.

From the linear regressions performed, simple models for the prediction of

material equivalence were determined. These are detailed in Equation 12 (for

asphalt versus crushed rock), Equation 13 (for crushed rock versus uncrushed

gravel) and Equation 14 (for asphalt versus uncrushed gravel).

ECR/AC = 1.14 + 0.00099 × SM + 0.00014 × AM +0.00025 × ST

(R2 = 0.36) ........................................................................................Equation 12

EUG/CR = 1.20 – 0.00045 × SM + 0.00012 × AT (R2 = 0.34)................Equation 13

EUG/AC = 1.62 – 0.00311 × SM + 0.00014 × AM + 0.00047 × BT

(R2 = 0.49) .........................................................................................Equation 14

Where: ECR/AC = Thickness of CR which is equivalent to 1 mm of AC.

EUG/CR = Thickness of UG which is equivalent to 1 mm of CR.

EUG/AC = Thickness of UG which is equivalent to 1 mm of AC.

SM = Subgrade Modulus in MPa

AM = Asphalt Modulus in MPa

AT = Asphalt Thickness in mm

BT = Base Thickness in mm

ST = Sub-base Thickness in mm

CR = Crushed Rock

UG = Uncrushed Gravel

AC = Asphalt Concrete

The calculated equivalence and modelled equivalence values are shown in

Figure 22. The line of unity is also shown.




Figure 22 Practical Equivalence Results

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2Calculated Equivalence

Mod

elle

d E

quiv

alen

ce

Asphalt versus Crushed Rock Crushed Rock versus Natural GravelAspahlt versus Natural Gravel Unity

The residuals from the linear regressions performed to generate these

prediction models were examined. The residuals are shown for each pair of

materials in Figure 23. Analysis of residuals from the linear regressions

showed no evidence that the residuals were not distributed normally with a

mean close to zero. This suggests that the underlying assumptions of the

linear regressions were not contradicted and the analysis and its findings were

therefore appropriate.



79

Figure 23 Practical Equivalence Residuals

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 100 200 300 400 500 600 700

Order

Res

idua

l

Aspahlt versus Crushed Rock Crushed Rock versus Uncrushed Gravel Asphalt versus Uncrushed Gravel

6.4.5 Recommended Material Equivalences

Based on the analysis undertaken and the premise that the consistence across

the range of aircraft considered in this study suggests consistence across all

medium to large commercial aircraft, the material equivalences detailed in

Table 6 are recommended. The equivalences should be considered in place of

the broader ranges currently detailed in the FAA design guide (FAA, 1995) for

the conversion of non-standard pavement structures to the equivalent thickness

of standard S77-1 pavement (or vice versa). It is noted that the recommended

equivalence factors presented in Table 12 are generally close to the lower

value in each of the FAA recommended ranges.

Table 12 Recommended Material Equivalences.

Equivalence Symbol Value FAA range Asphalt and Crushed Rock ECR/AC 1.3 1.2 to 1.6

Crushed Rock and Uncrushed Gravel EUG/CR 1.2 1.2 to 1.8 Asphalt and Uncrushed Gravel EUG/AC 1.6 1.7 to 2.3




Whether the use of these equivalence factors will result in thinner or thicker

pavements than those obtained using FAA’s mid-range values is case specific.

Where an asphalt thickness greater than 75 mm (the thickness in the standard

S77-1 pavement) is designed, the revised equivalence factors will result in a

thicker pavement. Where an asphalt thickness of less than 75 mm is designed,

a thinner pavement results. Where a 75 mm asphalt thickness is designed,

there would be no difference as there is no need to use an equivalence factor.

The same trends would result for non-standard thicknesses of crushed rock.

6.5 ISOLATED PAVEMENT EQUIVALENCES

To explain the variability in the APSDS implied equivalences, the material

properties were isolated and uniform material moduli values were adopted. In

order to obtain uniform moduli values Barker and Brabston sub-layered

materials were omitted in favour of homogenous, single modulus layers. This

analysis is less applicable to typical design situations than the previous analysis

but was undertaken to explain the variance in the observed practical

equivalences. The analysis is detailed as follows.

6.5.1 Aircraft Traffic and Pavement Structure

In order to isolate the material properties and their effects, a simple wheel load

was utilised in the analysis. This simple load consisted of a 20 t load on a

single wheel of 1.25 MPa tyre pressure. In order to further isolate the material

effects, a single load application was assessed and vertical strain at the

subgrade level was utilised to determine the equivalence of various structures.

As the performance criteria for all subgrade materials in APSDS are based on

vertical subgrade strains, this approach is equivalent to the application of a

constant number of repetitions of the simple wheel load.

The reference material adopted was a homogenous layer with a modulus of

500 MPa which is close to the average maximum allowed by the Barker and

Brabston method for Crushed Rock (690 MPa) and Uncrushed Gravel

(275 MPa). For this material, the reference strains were calculated for each of

the subgrade moduli values considered.



81

The reference strains were:

• 30 MPa subgrade. 685 με.




6.5.2 Design Parameters

With the simplified aircraft traffic and pavement structure, the only factors to

consider were the subgrade modulus and replacement material layer. The

replacement material factors considered were the thickness, modulus and

location of the replacement material. The design parameters considered are

detailed in Table 13.

Table 13 Design Parameters for Isolated Equivalence.


Replacement Modulus MPa 50, 100, 250, 750, 1000, 2000, 4000 Replacement Thickness mm 100, 200, 400, full depth Replacement Location Type Top, bottom, full depth

6.5.3 Material Equivalence

The resulting 196 equivalence determinations were statistically analysed to

assess the factors which affected the equivalence of materials of variable

modulus. The analysis determined that the most influential predictor of material

equivalence was the ratio between the original and replacement material

moduli. The thickness of the replacement layer and its location within the

pavement were also found to be somewhat significant, but less so than the

modulus ratio. The resulting recommended model for the determination of

material equivalence is shown as Equation 15. Equation 16 includes a modulus




ratio squared terms also. Another version, which includes the position of the

replacement layer is shown as Equation 17.

EA/B = 0.822 + 0.186 × MR (R2 = 0.69)...............................................Equation 15

EA/B = 0.715 + 0.323 × MR - 0.017 × MR2 (R2 = 0.72)........................Equation 16

EA/B = 0.964 + 0.186 × MR - 0.284 × Top (R2 = 0.75) ........................Equation 17

Where: EA/B = Thickness of A that is equivalent to 1 mm of B.

MR = Modulus of Material B/Modulus of Material A.

Top = 1 when at the top and 0 when at the bottom

The residuals for the simplest of the three models (Equation 15) are shown in

Figure 24.

Figure 24 Isolated Equivalence Residuals.

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 20 40 60 80 100 120 140 160 180Run

Res

idua

l (m

m)

Figure 25 illustrates the influence of modulus ratio, location of replacement and

replacement thickness on determined material equivalence. The simplest

model (Equation 15) is also shown in this figure.



83

Figure 25 Effect of modulus ratio, thickness and location on equivalence.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 1 2 3 4 5 6 7 8 9

Modulus Ratio

Equi

vale

nce

100 mm at top 200 mm at top 400 mm at top 100 mm at bottom200 mm at bottom 400 mm at bottom

Subgrade modulus was specifically determined as being not statistically

significant with no significant improvement in the prediction models when the

various subgrade values were incorporated.

This isolated analysis of material equivalence does not improve upon the

recommended practical equivalences presented in Table 12. It does, however,

explain the variability in equivalences derived from practical design scenarios

and determines the factors which influence the layered elastic implied

equivalence factors.

The dominant factor of influence on material equivalence is the modulus ratio.

The relationship between equivalence and modulus ratio is approximately

linear. Whether the replacement occurs at the top or the bottom of a pavement

structure and the thickness of the replacement are both less influential but still

statistically significant. The subgrade is not statistically significant for material

equivalence. Based on this analysis, the recommended material equivalence

factors detailed in Table 12 could be adopted knowing that the observed

variability has been analysed and explained. It can also be concluded that




making an improvement to the lower part of a pavement structure produces a

greater increase in pavement life than making the same improvement further up

because of the greater equivalence (on average of 0.3) of the improved

material at that pavement location.

6.6 THICKNESS COMPARISON EXAMPLES

A number of example calculations were undertaken in order to demonstrate the

application of the revised equivalence factors as well as to determine the

factors which have a statistically significant affect on the difference in pavement

thickness returned using the mid-range FAA values and the recommended

values for equivalence.

As an example of the calculation, the S77-1 pavement thickness is first

determined. For 20,000 passes of a 397 t B747 on a pavement with subgrade

CBR 3, a standard S77-1 pavement thickness of 1720 mm is required. This

figure is obtained from the FAA’s COMFAA program and requires the

conversion of aircraft passes to coverages. In this case a PCR of 1.75 is used

for the B747.

A non-standard pavement thickness is determined using APSDS. In this case,

50 mm of Asphalt on 350 mm of Crushed Rock on 1290 mm of Uncrushed

Gravel. This is a total pavement thickness of 1690 mm which is 30 mm thinner

than the standard S77-1 pavement thickness.

The non-standard pavement structure is converted to an equivalent thickness of

S77-1 pavement. In this example, the mid-range equivalence values

recommended by FAA are used. Equally valid would be the conversion of the

S77-1 pavement structure to an equivalent thickness of the non-standard (the

APSDS) pavement with the Uncrushed Gravel thickness being the only

difference. Firstly, the deficiency or excess of Asphalt is calculated and the

equivalent thickness of Crushed Rock is determined. The equivalent thickness

of Crushed Rock is the difference between the S77-1 and the non-standard

pavement’s Asphalt thickness multiplied by the equivalence factor for



85

converting Asphalt to Crushed Rock. That is, (50 - 75) × 1.4 = -35 mm (in this

case a deficiency). The effective thickness of Crushed Rock is then calculated

(350 - 35 = 315 mm). The deficiency or excess of effective Crushed Rock is

then calculated and converted to an equivalent thickness of Uncrushed Gravel.

That is (315-150) × 1.5 = 248 mm. This equivalent Uncrushed Gravel thickness

is added to the actual Uncrushed Gravel of the equivalent non-standard

pavement. That is 248 + 1290 = 1538 mm. The total S77-1 pavement

thickness therefore becomes 75 + 150 + 1538 = 1763 mm. This thickness can

be compared to the actual S77-1 determined thickness of 1720 mm. A

difference of 43 mm.

The same conversion can be made for the non-standard pavement to an

equivalent S77-1 pavement thickness using the recommended equivalence

factors from Table 12. For this example, this is detailed in Equation 18.

((50-75) × 1.3 + (350-150)) × 1.2 + 1290 = 1716 mm ........................Equation 18

The equivalent thickness using the revised equivalence factors is only 4 mm

thinner than the actual S77-1 determined thickness. This is significantly less

different than that determined using the FAA mid-range equivalence factors.

A total of 324 such examples were performed with the FAA mid-range factors

and the recommended equivalence factors detailed in Table 12. These

examples covered the subgrade moduli, aircraft, aircraft masses and aircraft

passes detailed in Table 14.

Table 14 Equivalence Examples Input Parameters.


Aircraft Nil B747, B767, B737 Aircraft Mass % 100, 80, 60

Aircraft Passes Number 5000, 10000, 20000




For each combination of the inputs detailed in Table 14, the S77-1 pavement

thickness required was determined from COMFAA. For these thickness

determinations, the aircraft passes were converted to aircraft coverages using

the following PCRs which can be adopted from a range of literature or

calculated from first principles:

• B747. 1.75.

• B767. 1.90.

• B737. 3.70.

For each of the combinations of input parameters, three combinations of

Asphalt and Crushed Rock thickness were considered. In all cases, a standard

S77-1 pavement structure (75 mm Asphalt and 150 mm Crushed Rock) was

included. This allowed an evaluation of the level of agreement between the

S77-1 and APSDS thicknesses provided by the calibration process. The two

other pavement structures were selected at random and were generally within

the realm of practical pavement solutions. The Asphalt thickness ranged from

30 to 300 mm. The Crushed Rock thickness ranged from 80 mm to 600 mm.

Following the determination of the non-standard pavement thickness from

APSDS, each was converted to the S77-1 equivalent thickness using firstly the

mid-range FAA equivalence factors and then the recommended replacement

factors detailed in Table 12. The resulting magnitudes of the differences were

analysed using statistical techniques, primarily the generation of means and

standard deviations, as well as linear regressions. In order to remove the

influence of the accuracy of the calibration of APSDS to the S77-1 pavement

thicknesses, the equivalent pavement thicknesses were corrected (by

subtracting the difference between the APSDS and S77-1 thickness for the

standard pavement structure) and re-analysed. Table 15 details the relevant

summary statistics.



87

Table 15 Equivalence Examples Summary Statistics.

Difference between S77-1/FAA and APSDS Thickness (mm) Statistic Uncorrected

FAA mid-range Uncorrected

Recommended Corrected

FAA mid-range Corrected

Recommended Average 48 36 45 7 Std Dev 34 23 33 7 Median 41 32 36 6

Maximum 199 96 165 55

From Table 15, it is clear that the recommended equivalence factors detailed in

Table 12 provide for a closer agreement between S77-1 and APSDS returned

pavement thickness for the aircraft and design scenarios considered. When the

differences are corrected for the difference between S77-1 and APSDS

thicknesses for a standard S77-1 pavement structure, the revised equivalence

factors provide agreement with an average difference of 7 mm. The current

FAA mid-range equivalences have an average difference of 45 mm. The

maximum difference was reduced from 165 mm to 55 mm when using the

recommended equivalences.

This agreement, to an average of 7 mm, is significantly better than the

agreement commonly obtained between the S77-1 and APSDS thicknesses for

a standard S77-1 pavement structure. This implies that the calibration of

APSDS to S77-1 creates significantly more variability than the conversion to a

non-standard pavement structure does. This is considered to be the optimum

solution from a material equivalence point of view. The recommendation to

adopt the recommended equivalence factors presented in Table 12 in order to

achieve closer agreement between S77-1 and APSDS thickness

determinations is therefore reinforced.

Linear regressions performed on the differences determined when using the

FAA mid-range and recommended equivalence factors were performed. A

simple linear regression was performed and the residuals were analysed and

confirmed to not contravene the assumptions underlying the validity of the

statistical analysis. These regressions determined that the aircraft type, aircraft

mass and aircraft passes were all non-significant factors for the difference




between S77-1 and APSDS equivalent pavement thicknesses using the

recommended equivalence factors. The subgrade modulus was, however, a

statistically significant determinant. This is in apparent contrast to subgrade not

being significant when the non-sub-layered equivalences were determined.

This apparent contrast results from the influence of subgrade modulus on sub-

layer modulus when using the Barker and Brabston sub-layering regime. For

example, for a 1000 mm thick layer of crushed rock under a B737 aircraft load,

the lowest sub-layer moduli value can range from 116 MPa to 360 MPa for

underlying subgrade CBRs of 3% and 15% respectively. The apparent

influence of subgrade modulus is therefore explained by the subgrade’s impact

on the lower sub-layers’ modulus values. The subgrade modulus has a

significant impact on the lowest sub-layer’s modulus when using the Barker and

Brabston sub-layered and modulus assignment method. The modulus values

in turn impact on the implied material equivalence values as material modulus

is the most influential factor on material equivalence.

6.7 SUMMARY

When determined using S77-1, standard pavement structures are converted to

an equivalent structural thickness of non-standard composition using

equivalence factors. The FAA provides a range for equivalences of a number

of pavement materials. APSDS offers the advantage of direct thickness

determination without the need to separately apply equivalence factors.

Material quality is accounted for in the sub-layering modulus assignment

routines. Inconsistencies have been noted between the equivalent S77-1

thicknesses (after applying conversion using the FAA’s mid-range equivalence

factors) and directly determined APSDS designed pavements for the same

design scenario. It was found that:

• Inconsistence results between S77-1 and APSDS pavement thicknesses

when the FAA’s mid-range equivalence factors are used to convert non-

standard pavement structures.



89

• Recommended equivalence factors, which are generally at the lower end of

the FAA recommended ranges, are:

o Asphalt for Crushed Rock. 1.3.

o Crushed Rock for Uncrushed Gravel. 1.2.

o Asphalt for Uncrushed Gravel. 1.6.

• These equivalence factors are applicable to all medium to large jet aircraft

or traffic mixes governed by their presence in the fleet mix.

• Some variability exists in the implied APSDS equivalence factors. This is

largely explained by the influence of the Barker and Brabston sub-layering

regime and the location of the replacement layer in the pavement structure.

• The isolated pavement material investigation shows that the modulus ratio

of the original and the replacement material is the main influence on the

APSDS implied equivalence.

• Examples show that the recommended replacement equivalence factors

generally provide superior consistence between APSDS and S77-1

pavement thicknesses than the current FAA mid-range values do.

• The FAA should review the material equivalence factors contained in their

design guide, in light of the findings from the investigation undertaken. It is

acknowledged that the correctness of the APSDS implied equivalence

factors can not be confirmed. However, the FAA acknowledges that their

material equivalence guidance is highly questionable and APSDS implied

equivalence factors would at least provide consistence between the two

methods.




Chapter 7 Design of Proof Rolling Regimes


91

7. DESIGN OF PROOF ROLLING REGIMES

7.1 GENERAL

Proof rolling of heavy duty aircraft pavements during their construction is

generally practiced in Australia. With the introduction of large commercial

aircraft, such as the B767 and B747, extra heavy duty proof rolling equipment

was designed and built by the Australian Commonwealth Department of

Housing and Construction from the 1950s.

The aim of proof rolling these heavy duty pavements is to expose the various

layers to a level of ‘damage’ (indicated by calculated stress, strain or deflection)

that is slightly greater than the maximum expected service ‘damage’, prior to

constructing the next layer of the pavement structure. By proving pavements in

this manner, the variability of the structural strength of the pavement is

significantly reduced, allowing thinner pavements to be constructed with equal

reliability.

7.2 DESIGN OF PROOF ROLLING REGIMES

The design of proof rolling regimes therefore comprises two steps:

• Calculating the values of the chosen indicator of damage at various depths

through the pavement layers.

• Selection of a proof rolling regime (mass and tyre pressure combination) to

be applied to the various layers of the pavement structure such that the

calculated maximum service damage indicator value is just exceeded.

APSDS has the ability to calculate normal and shear stresses, strains and

deflections at any location defined by the user. These indicators of damage

can be determined for any desired depths below the pavement surface.




7.3 AUSTRALIAN PROOF ROLLING FLEET

The Australian Department of Defence owns eleven pneumatic-tyred heavy

aircraft pavement rollers. The first two of these rollers were purchased and

imported from the USA in the 1950s (Brown, 1966). These rollers, known as

Marco rollers, were capable of applying up to 50 t on four wheels with a tyre

pressure of up to 1.4 MPa. The Commonwealth then constructed, a number of

additional rollers, based on the US roller design, which became known as

Macro rollers.

One of these Macro rollers was converted to 50 t on two wheels, with tyre

pressures up to 1.65 MPa. The roller was designed to produce stresses

comparable to those induced by heavier commercial aircraft and high tyre

pressure military jets. This roller was known as the Test Rig. At around the

same time, the Commonwealth also constructed a number of 200 t rollers on

four wheels, with up to 1 MPa tyre pressure, known as the Porter

Supercompactor. Only one Porter Supercompactor remains in service in

Australia today. These Porter Supercompactors were specifically designed for

the compaction of deep dredged-sand fills and for proving of subgrades to large

depths.

7.4 DAMAGE INDICATOR CALCULATION

The layered elastic component of APSDS is used for the calculation of the

indicators of damage (stress, strain or deflection) modelled by a single load

application. Many other layered elastic aircraft pavement design tools are also

available for the generation of these pavement damage indicators.

During each design scenario APSDS calculates the stresses, strains and

deflections of the pavement at a range of depths, as well as at user defined

lateral and longitudinal coordinates. The ability to view all damage indicators

calculated at all pavement locations is not available in all layered elastic tools

and is one advantage of APSDS. This provides for the ability to easily generate

plots of stress, strain and deflection against depth under the aircraft wheels or

between aircraft wheels.



93

In developing a methodology for the design of proof rolling regimes, the

damage indicator options include:

• Stress, strain or deflection as the indicator of pavement damage caused by

aircraft and rollers.

• Use of the actual pavement structure or a simple single layer of material.

• Use of actual or representative subgrade modulus value for all subgrades.

• Calculation of the damage indicator directly under a tyre or at the centre of a

wheel gear, or both.

7.4.1 Traditional Approach

Prior to the development of APSDS and other layered elastic pavement design

tools, proof rolling regimes were developed using stress as the damage

indicator. Standard charts for aircraft and various proof rollers were compared

to determine the proof rolling regime. Standard charts were used as their

generation was time consuming and these charts were generally developed

using Boussinesq’s (1885) formula for stress in a single elastic layer imposed

by a simple static load. The use of stress curves generated by single point

loads and uniform, single layer, pavement structures was not by choice but due

to the lack of any more accurate tool being available at the time. Practitioners

hoped that the forced simplifications were valid but this assumption remained

untested.

7.4.2 APSDS Generated Damage Indicators

With the advent of layered elastic design tools, the ability to generate stresses,

strains and deflections at a range of depths for complex loads and complex

pavement structures is readily available. Therefore, the options for comparing

aircraft and roller induced ‘damage’ is markedly expanded.





An investigation was undertaken to assess the options for the design of proof

rolling regimes using layered elastic methods. APSDS was utilised to generate

various damage indicators with depth. The preferred damage indicator, and

pavement composition was investigated as detailed in the following sections.

7.5.1 Deflection, Stress and Strain

To compare the relative merits of using stress, strain or deflection as the

indicator of damage for proof rolling regimes, stresses, strains and deflections

were calculated under a B737 aircraft (between the tyres and directly under one

tyre) and plotted against depth for the following pavement structures:

• 1000 mm crushed rock base course material on CBR 6.

• 1000 mm crushed rock base course material on CBR 15.

• 1000 mm natural gravel sub base material on CBR 6.

• 1000 mm natural gravel sub base material on CBR 15.

The damage indicators with depth data is contained in Appendix 6. The

resulting plots of damage indicator with depth are shown in

Figure 26 to Figure 28 for stress, strain and deflection respectively.



95

Figure 26 B737 Vertical Stress with depth for various pavements.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

Crushed rock on CBR 6 Under Wheel Crushed rock on CBR 6 Centre of GearCrushed rock on CBR 15 Under Wheel Crushed rock on CBR 15 Centre of GearNatural Gravel on CBR 6 Under Wheel Natural Gravel on CBR 6 Centre of GearNatural Gravel on CBR 15 Under Wheel Natural Gravel on CBR 15 Centre of Gear

From Figure 26 it can be seen that stress at the pavement surface is equal to

the tyre pressure (under a wheel) and zero between two tyres. At depth (in this

case below 0.8 m), stresses beneath and between the wheels are similar in all

cases. Irrespective of the pavement material adopted and the subgrade

strength selected, the stresses are similar at all depths.




Figure 27 B737 Vertical Strain with depth for various pavements.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

-1000 -500 0 500 1000 1500 2000 2500 3000 3500 4000Strain (uE)

Dep

th (m

)


From Figure 27, it can be seen that strains vary significantly with pavement

material as well as subgrade strength. Strains also show complex relationships

to depth and are less consistent than stress. They cannot readily be related to

aircraft loading (tyre pressure and load) at either the surface or at depth.

Further, at changes in pavement layers and sub-layers, calculated strains

increase sharply due to a continuously and smoothly decreasing stress and an

immediate (discontinuous) decrease in modelled material modulus.



97

Figure 28 B737 Vertical Deflection with depth for various pavements.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Deflection (mm)D

epth

(m)


Deflections with depth are shown in Figure 28 to be simple in their shape but

vary significantly with subgrade strength and pavement material. There is also

comparatively small difference in the deflection at the top of the pavement to

that at depth.

Based on the analysis of Figure 26 to Figure 28, stress is selected as being the

preferred method for indicating damage in the design of proof rolling regimes.

Stress is selected as it provides the following advantages:

• Easy to visualise and understand compared to strain.

• Equal to tyre pressure at the pavement surface.

• Related to load per landing gear at depth.

• Essentially equal for all modelled subgrade strengths and granular

pavement materials.

• Essentially equal, at depth, under the tyre and in the centre of a multiple

wheel landing gear.




• Decreases smoothly with increased depth from a maximum value at the

surface.

It is also concluded from Figure 26 that stresses should be calculated directly

under a tyre only. At the surface, the stress induced under a tyre is significantly

higher than that at the centre of the landing gear. At depth the under-tyre and

centre-gear stresses converge and whilst the centre-gear stress does exceed

the under-tyre stress at depth, it is essentially equal for comparative purposes.

The additional effort required to compare the greater of the under-tyre and

centre-gear stresses is not considered warranted.

7.5.2 Pavement Composition

Using stress under the tyre as the most appropriate indicator of damage, the

influence of pavement structure was considered. From Figure 26, it can be

seen that there is virtually no difference in the stress with depth for base or sub-

base materials on either a strong (CBR 15) or weaker (CBR 6) subgrade. The

damage indicators with depth data is contained in Appendix 6. The resulting

stress with depth plots are shown in Figure 29 with the equivalent plot for a

typical B737 capable pavement. The B737 pavement consisted of:

• 50 mm asphalt of 1500 MPa.

• 200 mm crushed rock base course material.

• 550 mm natural gravel sub-base material.

• CBR 6 subgrade.



99

Figure 29 Comparison of Pavement and Single Material Stresses.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Stress (MPa)D

epth

(m)

Pavement on CBR 6 Crushed rock on CBR 6 Natural gravel on CBR 6

Significant variations from the B737 pavement adopted for the generation of

Figure 29 were also assessed. This focused on the asphalt layer and included

a higher modulus asphalt option (4000 MPa) and a thicker (200 mm – with the

sub-base reduced to maintain a consistent total pavement thickness) asphalt

layer option. A combined high modulus, thick asphalt option was also

assessed. The comparison of the stress with depth for each asphalt option is

illustrated in Figure 30.




Figure 30 Asphalt thickness and modulus effects.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

50 mm 1500 MPa 50 mm 4000 MPa 200 mm 1500 MPa 200 mm 4000 MPa

Figure 29 and Figure 30 confirm the suggestion from Figure 26 that pavement

structure (material and subgrade strength) have little impact on the stress with

depth.

When it is considered that the proof rolling regime design is a comparison of

relative stress induced by aircraft and roller, the influence of materials or

pavement structure becomes even less important, as long as the same

pavement structure is adopted for both the aircraft and roller stress calculations.

Therefore, for practical purposes, a standard pavement of 1000 mm of crushed

rock base course on CBR 6 subgrade is selected for stress with depth

calculations. This selection is justified by:

• All materials having an essentially negligible differential effect.

• The relative or comparative (aircraft to roller) stress being more important

than the accuracy of any absolute stress values calculated.

• Base material having a modulus approximately equal to the mean of the

moduli of asphalt and subgrade.



101

• CBR 6 being typical of many pavement subgrades at airports in Australia.

When absolute stresses or far from typical pavement structures are required, a

customised pavement may be justified for the determination of stress with

depth. Such a case may be the 200 mm thick of 4000 MPa asphalt surface

layer option shown in Figure 30. However, as the roller and the aircraft stress

with depth would be similarly affected by the non-standard pavement, it would

be inconsequential to use a single layer pavement in most practical

circumstances. Where required, customised stress with depth plots can readily

be generated for any pavement structure using APSDS. The customised

pavement structure must, however, be adopted for both the design aircraft and

the proposed proof rollers.

7.6 PROOF ROLLING REGIME DESIGN

Using the methodology developed above, proof rolling regimes can be

developed for a range of aircraft. All proof rolling regimes are based on the

determination of mass and tyre pressure combinations for proof rollers which

result in stresses with depth that just exceed those imposed by the design

aircraft during service.

7.6.1 Roller Configurations

There are three specifically designed roller types available in Australia for

proving heavy duty aircraft pavements. More conventional pneumatic-tyred

rollers can also be utilised but are less likely to induce stresses comparable to

those caused by the design aircraft. For each roller, there is a range of

acceptable mass and tyre pressure combinations (Defence, 2003) required to

control tyre distortion. The allowable tyre pressure and roller mass

combinations for the Macro, the Test Rig and the Porter Supercompactor are

shown in Figure 31, Figure 32 and Figure 33.




Figure 31 Allowable Macro Roller Tyre Pressures and Masses.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

10 15 20 25 30 35 40 45 50Total Mass (t)

Tyre

Pre

ssur

e (M

Pa)

ACCEPTABLE

UNACCEPTABLE

Figure 32 Allowable Test Rig Roller Tyre Pressures and Masses.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.7

10 15 20 25 30 35 40 45 50Total Mass (t)

Tyre

Pre

ssur

e (M

Pa)

ACCEPTABLE

UNACCEPTABLE



103

Figure 33 Porter Supercompactor Tyre Pressures and Masses.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200Total Mass (t)

Tyre

Pre

ssur

e (M

Pa)

ACCEPTABLE

UNACCEPTABLE

7.6.2 Roller Generated Stresses

The stress, directly under a tyre, with depth (at maximum mass and tyre

pressure) for each of the three rollers is illustrated in Figure 34.

Figure 34 Vertical Stress with Depth for Various Rollers.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7Stress (MPa)

Dep

th (m

)

50 t Macro 50 t Test Rig 200 t Porter




Figure 34 shows that at the pavement surface, the high tyre pressure of the

Test Rig induces the greatest stress. At depth, the higher wheel load of the

Porter Supercompactor results in the greatest stress. Due to their availability

(through greater numbers), portability and versatility, the Macro is the most

practical roller to use for most projects. Other rollers may be preferred for very

large projects, specific project requirements or where they are locally available.

Based on Figure 31, the maximum allowable roller mass for a range of tyre

pressures can be determined for the Macro roller. The stress with depth curves

for each allowable combination is shown in Figure 35. Figure 35 forms the

basis of the roller induced stresses for a proof rolling regime design. The

damage indicators with depth data is contained in Appendix 6.

Figure 35 Macro Roller Vertical Stress with Depth at various roller masses.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Stress (MPa)

Dep

th (m

)

15 t, 0.4 MPa 19 t, 0.5 MPa 22 t, 0.6 MPa 26 t, 0.7 MPa30 t, 0.8 MPa 33 t, 0.9 MPa 36 t, 1.0 MPa 40 t, 1.1 MPa43 t, 1.2 MPa 47 t, 1.3 MPa 50 t, 1.4 MPa

The ‘kinks’ which can be seen for all rollers configurations at 0.25 m depth are

caused by the large change in sub-layer modulus at this depth. The assigned

change in sub-layer modulus is generated by the Barker and Brabston sub-

layering system which is automated in APSDS.



105

7.6.3 Aircraft Generated Stresses

Stress with depth plots for aircraft are generated by APSDS in a similar manner

to that for the rollers. Figure 36 shows stresses with depth for the following:

• B747 at 397 t and 1.38 MPa tyre pressure. A dual-tandem landing gear.

• B767 at 180 t and 1.24 MPa tyre pressure. A dual-tandem landing gear.

• B737 at 78.5 t and 1.36 MPa tyre pressure. A dual wheel landing gear.

• F111 at 50.8 t and 1.48 MPa tyre pressure. A single wheel landing gear.

The damage indicators with depth data is contained in Appendix 6.

Figure 36 Vertical Stresses with Depth for various Aircraft.

0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5Stress (MPa)

Dep

th (m

)

B737 78.5 t, 1.36 MPa B767 180 t, 1.24 MPaB747 397 t, 1.38 MPa F111 50.8 t, 1.48 MPa

These aircraft were chosen as they span the range of common medium to large

civil and military jet aircraft in terms of landing gear configurations, wheel loads

and tyre pressures.




A proof rolling regime designed for any aircraft mix should accommodate the

envelope of maximum stress induced by all the aircraft in the mix. For the four

aircraft shown in Figure 36, the high tyre pressure of the F111 would govern in

the upper layers whilst the B747’s high mass per landing gear would dominate

at the lower levels and subgrade.

The B767 is approximately half the mass of the B747 but has half the number

of main wheels so induces similar stresses at depth to those of the larger

aircraft. The B747 and B767 aircraft induce pressures at 1.2 m that are

comparable to those induced by the F111 and B737 at around 0.9 m.

7.7 PRACTICAL LIMITATIONS

Each of the materials and layers encountered during the construction of an

aircraft pavement have limits to the stresses they can accommodate.

Therefore, the theoretically required 0.8 MPa tyre pressure rolling of the

subgrade for a B747 aircraft, may not be practical as the subgrade may fail in

shear with such a high tyre pressure being placed directly on this material. In

such circumstances, experience must be applied by the designer and

constructor to minimise the risk of unduly failing pavements and bogging rollers.

The development of the proof rolling regime should therefore take into account

the following general rules.

7.7.1 Sand Subgrades

Sand subgrades should be covered with a layer of granular material to provide

some confinement before rolling and proving.

7.7.2 Weak Clay Subgrades

Often, clay subgrades cannot be significantly improved by compaction because

they are saturated and impermeable. In such cases, proving provides a check

for weak spots only and pavements are designed to accommodate the poor

subgrade conditions.



107

7.7.3 Over Proof Rolling

Clay and other weaker subgrades should be proved with lower tyre pressures

to prevent shear failures under high stresses.

7.8 EXAMPLES OF APPLICATION

A proof rolling regime is to be determined for each of the individual aircraft

whose stress with depth is illustrated in Figure 36. With the adoption of a

standard pavement (1000 mm crushed rock base course material on CBR 6

subgrade) the only pavement specific issue needing to be considered is the

layers (and their thickness) upon which the rollers are to be applied. The depth

from the finished surface level determines the portion of the aircraft induced

stress with depth plot to be considered. These are the stresses that need to be

exceeded by the chosen proof roller for proving that layer of the pavement.

7.8.1 Proof Rolling Regime Design

Example proof rolling regimes have been designed for three common aircraft.

The stress with depth data for these proof rolling regimes is contained in

Appendix 7.

For the B737 aircraft, the assumed pavement structure is as detailed for the

derivation of Figure 29.

Based on the stress with depth plot for the B737 aircraft and the application of

the proof rollers at finished subgrade, top of sub-base and top of base course

levels, the proof rolling regime becomes:

• Subgrade. 22 t at 0.6 MPa.

• Sub-base. 36 t at 1.0 MPa.

• Base. 50 t at 1.4 MPa.




The stress with depth for the B737 aircraft and for the proof rollers (applied at

each pavement layer) is shown in Figure 37. The roller masses and pressures

were selected to allow the roller induced stresses to just exceed the aircraft

induced stresses in each layer being proved. The asphalt surface layer is not

proved because the required degree of compaction is only achievable when the

asphalt mix is at placing temperature, typically around 150°C. Proof rolling at

ambient temperatures would not correct low asphalt density or prove that the

required asphalt density had been achieved during construction.

Figure 37 B737 proof rolling regime.

0.0

0.10.2

0.3

0.40.5

0.6

0.70.8

0.9

1.01.1

1.2

1.31.4

1.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

B737 50 t at 1.4 MPa 36 t at 1.0 MPa 22 t at 0.6 MPa

Proof rolling regimes were also determined for B767, B747 and F111 aircraft. It

is noted that the pavement layer thicknesses needed to be determined in each

case as this determines the levels at which the rollers are applied. Table 16

details the adopted pavement structures and proof rolling regimes for each of

these aircraft (all with a 50 mm of 1500 MPa asphalt surface).



109

Table 16 Proof Rolling Regimes for B767, B747 and F111.

B767 B747 F111 Course

Thickness Roller Thickness Roller Thickness Roller Subgrade NA 19 t

0.5 MPa NA 30 t

0.8 MPa NA 19 t

0.5 MPa Sub-base 500 mm 26 t

0.7 MPa 400 mm 22 t

0.6 MPa 550 mm 30 t

0.8 MPa Base 400 mm 22 t

0.6 MPa 50 t

1.4 MPa

400 mm 26 t 0.7 MPa

50 t 1.4 MPa

200 mm 50 t 1.4 MPa

Two rolling configurations are required for the B767 and B747 base courses as

the Macro roller (at 50 t and 1.4 MPa) cannot match the aircraft induced

stresses at the bottom of the base course when applied at the top. The first of

the two roller configurations is applied to the bottom half of the base course and

the second configuration to the top of the base course. This is appropriate as

the 400 mm of base course would be placed in two layers in order to achieve

adequate compaction.

The rolling regimes and the associated stresses with depth, for the B767, B747

and F111 aircraft, are illustrated in Figure 25, Figure 39 and Figure 40.





0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

B767 50 t at 1.4 MPa 22 t at 0.6 MPa 26 t at 0.7 MPa 19 t at 0.5 MPa


0.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

B747 50 t at 1.4 MPa 26 t at 0.7 MPa 22 t at 0.6 MPa 30 t at 0.8 MPa



111

Figure 40 F111 proof rolling regime.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.11.2

1.3

1.4

1.5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Stress (MPa)

Dep

th (m

)

F111 50 t at 1.4 MPa 30 t at 0.8 MPa 19 t at 0.5 MPa

From Figure 40 it can be seen that the maximum stress induced by the Macro

roller of 1.4 MPa (equal to the highest allowable tyre pressure) cannot equal the

stress induced at the pavement surface by the very high tyre pressure of the

F111 aircraft. However, the spreading of the stress through the asphalt surface

layer is such that the roller applied to the top of the base course produces

almost equal stress (1.40 MPa versus 1.46 MPa) to that induced by the aircraft

from the finished surface. This inability to exceed the very high stresses

induced in the upper layers by high tyre pressure military aircraft is one of the

reasons for the development of the higher tyre pressure Test Rig roller.

However, adequate specification and compaction of the crushed rock base

course just below the asphalt is generally able to provide suitable performance

without the need to fully prove the crushed rock with the higher tyre pressure

roller.

7.9 SUMMARY

Proof rolling remains an important aspect of heavy duty aircraft pavement

construction. Determination of suitable proof rolling regimes should be the

responsibility of pavement designers. In the past, simple equations (based on




single point loads and single elastic layers) and standard plots of stress with

depth were utilised for proof loading regime design. Practitioners hoped that

these simplifications were appropriate. With the availability of stress, strain and

deflection at any position and depth in the pavement, more rigorous analysis is

possible and has indicated the suitability of the traditional assumptions for many

practical design scenarios.

When compared to strain and deflection, stress is the simplest damage

indicator to understand and the most consistent. Stress is therefore the

preferred indicator of damage for proof rolling regime design. Whilst APSDS

allows specific pavement materials to be modelled, comparison of a number of

scenarios has shown that the adoption of a single material on any particular

subgrade can adequately represent any pavement being analysed. A

pavement of 1000 mm of crushed rock on CBR 6 subgrade is recommended as

standard, as this is typical for many Australian design scenarios. The traditional

Boussinesq generated stress charts are also suitable, as long as the same

stress generation method is used for both the roller and the aircraft being

compared.

Regimes are readily able to be developed for proof rolling pavements by

comparing the calculated stresses induced by the aircraft and those calculated

for the proof rolling device for a number of tyre pressure and mass

combinations. Roller configurations that provide modelled stresses just

exceeding the aircraft induced stresses should be selected. Where a thicker

pavement course cannot be rolled to exceed the aircraft induced stresses,

rolling the course in two layers may be required.

In practice, proof rolling regimes must take into account the site constraints.

The rollers are large and expensive to transport and therefore the selection of a

roller must take this into consideration. Also, clays and sands require special

consideration and their proof rolling regimes should be determined by the

methods described in this paper and then checked by experienced personnel

and modified as required.

Chapter 8 Summary and Conclusions


113

8. SUMMARY AND CONCLUSIONS

8.1 GENERAL

A significant investigation into the use of APSDS for the calculation of aircraft

pavement thickness was conducted. This investigation focused on identifying

potential areas of improvement within the software and providing potential

solutions.

8.2 SUMMARY

8.2.1 Aircraft Pavement Design

Aircraft pavement design dates back to around WWII when aircraft increased in

size and complexity at an accelerated rate. This required appropriately

designed and constructed pavements with a sealed and uniformly graded

surface to be provided.

The determination of aircraft pavement thickness remains an empirical science.

The majority of the full scale testing that today’s design tools are reliant was

performed by the US Corps of Engineers in the 1940s and 1950s and

culminated in the publishing of the S77-1 curve. This remains the basis for

calibration of aircraft pavement design tools today.

8.2.2 Overview of APSDS

APSDS is a specialised version of the road pavement design software Circly.

APSDS uses a layered elastic system and has been calibrated to S77-1. As an

mechanistic-empirical tool, APSDS retains a largely empirical approach, albeit

an efficient one.

Whilst a very useful and effective tool for aircraft pavement thickness design,

APSDS contains a number of areas for potential improvement. These have

been investigated and potential improvements have been suggested for future

releases of the software.




8.2.3 Validation of APSDS

The Chicago Criteria represent the current basis for calibration of APSDS. This

series of calibration constants were derived by comparison of pavement

thicknesses calculated by APSDS to those calculated from S77-1 (using

COMFAA) for a range of aircraft types, subgrade moduli and numbers of

aircraft passes.

A comparison between S77-1 and APSDS thicknesses was performed to

confirm that the Chicago Criteria provide a valid tie to the empirical

relationships between materials, loads and pavement thickness.

8.2.4 Selection of Inputs

Each of the input parameters required by APSDS for a pavement design were

described. Each parameter was detailed and guidance provided for their

selection.

8.2.5 Sensitivity Analysis

A statistically designed sensitivity analysis was performed for a range of

common medium to large commercial jet aircraft. This allowed the relative

influence of each input parameter on the required pavement thickness to be

determined.

Commonly accepted relative sensitivities were confirmed and designers were

provided with guidance as to which inputs parameters to focus on defining

accurately during design.

8.2.6 Materials Equivalence

Observations had suggested that the material equivalences implied by APSDS

were not always consistent with the mid-points of the ranges provided by the

FAA. Statistically designed parametric runs were performed to enable many

values of material equivalence to be calculated from similar pavements

designed for the same subgrade modulus and aircraft load. This analysis



115

considered equivalence between asphalt, crushed rock (base) and natural

gravel (sub-base). Practical values of material equivalence were determined

although significant variation in material equivalence values was observed.

Aircraft were replaced by a single wheel load and the pavement structure

simplified to isolate the material stiffness effects on material equivalence. This

less practical analysis provided insight into why the practical material

equivalence values varied and provided confidence in the recommended

practical material equivalence values.

8.2.7 Proof Rolling

In order to assess the traditional methodologies for determining proof rolling

regimes during aircraft pavement construction, stresses, strains and deflections

were calculated by APSDS. These were assessed for different locations (under

versus between wheels), at various levels in the pavement, and for difference

pavement compositions (practical pavements versus uniform materials). Stress

was confirmed as being the most appropriate indicator of damage for the

determination of proof rolling regimes.

A number of stress with depth plots were generated for aircraft and common

proof rollers. These were compared to allow proof roller configurations to be

determined that would adequately prove the pavement layers for their design

aircraft loads. Example proof rolling regimes were determined for a number of

common aircraft.

8.3 CONCLUSIONS

Based on the investigations undertaken, a number of significant conclusions

have been made. These are detailed as follows.

• Aircraft pavement thickness design remains an empirical science with purely

mechanistic tools unlikely to replace mechanistic-empirical tools in the near

future.




• APSDS is the preferred software for aircraft pavement thickness design. It

provides a transparent and very flexible tool that easily provides for ‘what if’

analysis.

• The Chicago Criteria provide for a reasonable fit to S77-1 pavement

thickness requirements and therefore APSDS is a suitable software for

aircraft pavement thickness design using existing knowledge and methods.

• Designers should utilise commonly accepted practice to determine the

values of each and every input parameter for any APSDS design.

• Designers should focus their attention to the very influential input

parameters of subgrade modulus and aircraft mass. Tyre pressure and

asphalt modulus can be assigned presumptive values as they have very

little influence on typical aircraft pavement thicknesses.

• The mid-points of the FAA guidance of material equivalence are not

consistent with the values implied by APSDS. In order to provide for

consistence with APSDS, the FAA should consider adopting the following

material equivalence values:

o Asphalt for Crushed Rock. 1.3.

o Crushed Rock for Uncrushed Gravel. 1.2.

o Asphalt for Uncrushed Gravel. 1.6.

• Proof rolling regimes should be determined using stress as the indicator of

damage with depth. Pavements should be modelled as single layers of

uniform (but sub-layered) material with a presumptive value of subgrade

modulus.

This project investigated the strengths and weaknesses of APSDS as a tool for

aircraft pavement thickness design. The software was validated, methods for

determining proof rolling regimes were developed and implied material

equivalence factors were determined for common pavement materials.

Guidance on input parameter selection was also presented.

Appendix 1 S77-1 Thickness Results


A1 - 1

APPENDIX 1. S77-1 THICKNESS RESULTS

Run SM (MPa) Aircraft M

(%) P

(no.) Thickness

(mm) 1 30 B747 100 5000 1545 2 30 B747 100 10000 1635 3 30 B747 100 20000 1720 4 30 B747 80 5000 1327 5 30 B747 80 10000 1409 6 30 B747 80 20000 1487 7 30 B747 60 5000 1070 8 30 B747 60 10000 1142 9 30 B747 60 20000 1212

10 30 B767 100 5000 1445 11 30 B767 100 10000 1532 12 30 B767 100 20000 1616 13 30 B767 80 5000 1235 14 30 B767 80 10000 1315 15 30 B767 80 20000 1392 16 30 B767 60 5000 993 17 30 B767 60 10000 1061 18 30 B767 60 20000 1130 19 30 B737 100 5000 1058 20 30 B737 100 10000 1124 21 30 B737 100 20000 1186 22 30 B737 80 5000 923 23 30 B737 80 10000 984 24 30 B737 80 20000 1040 25 30 B737 60 5000 769 26 30 B737 60 10000 821 27 30 B737 60 20000 870 28 60 B747 100 5000 931 29 60 B747 100 10000 994 30 60 B747 100 20000 1054 31 60 B747 80 5000 784 32 60 B747 80 10000 835 33 60 B747 80 20000 887 34 60 B747 60 5000 634 35 60 B747 60 10000 672



Flexible Aircraft Pavement Thickness Design A1 - 2


(%) P

(no.) Thickness

(mm) 36 60 B747 60 20000 710 37 60 B767 100 5000 860 38 60 B767 100 10000 920 39 60 B767 100 20000 980 40 60 B767 80 5000 727 41 60 B767 80 10000 774 42 60 B767 80 20000 822 43 60 B767 60 5000 593 44 60 B767 60 10000 628 45 60 B767 60 20000 664 46 60 B737 100 5000 686 47 60 B737 100 10000 733 48 60 B737 100 20000 778 49 60 B737 80 5000 592 50 60 B737 80 10000 632 51 60 B737 80 20000 670 52 60 B737 60 5000 489 53 60 B737 60 10000 521 54 60 B737 60 20000 552 55 100 B747 100 5000 634 56 100 B747 100 10000 672 57 100 B747 100 20000 710 58 100 B747 80 5000 539 59 100 B747 80 10000 572 60 100 B747 80 20000 603 61 100 B747 60 5000 439 62 100 B747 60 10000 463 63 100 B747 60 20000 486 64 100 B767 100 5000 593 65 100 B767 100 10000 628 66 100 B767 100 20000 664 67 100 B767 80 5000 507 68 100 B767 80 10000 536 69 100 B767 80 20000 566 70 100 B767 60 5000 414 71 100 B767 60 10000 436 72 100 B767 60 20000 458 73 100 B737 100 5000 492



A1 - 3


(%) P

(no.) Thickness

(mm) 74 100 B737 100 10000 524 75 100 B737 100 20000 555 76 100 B737 80 5000 423 77 100 B737 80 10000 450 78 100 B737 80 20000 476 79 100 B737 60 5000 351 80 100 B737 60 10000 372 81 100 B737 60 20000 392 82 150 B747 100 5000 472 83 150 B747 100 10000 499 84 150 B747 100 20000 525 85 150 B747 80 5000 406 86 150 B747 80 10000 428 87 150 B747 80 20000 448 88 150 B747 60 5000 332 89 150 B747 60 10000 349 90 150 B747 60 20000 366 91 150 B767 100 5000 444 92 150 B767 100 10000 468 93 150 B767 100 20000 492 94 150 B767 80 5000 382 95 150 B767 80 10000 403 96 150 B767 80 20000 422 97 150 B767 60 5000 316 98 150 B767 60 10000 334 99 150 B767 60 20000 351

100 150 B737 100 5000 376 101 150 B737 100 10000 400 102 150 B737 100 20000 423 103 150 B737 80 5000 329 104 150 B737 80 10000 348 105 150 B737 80 20000 366 106 150 B737 60 5000 265 107 150 B737 60 10000 280 108 150 B737 60 20000 295




Appendix 2 Sensitivity Analysis Design


A2 - 1

APPENDIX 2. SENSITIVITY ANALYSIS DESIGN

Factor Levels Run SM

(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

1 30 2600 60 80 5000 1000 20 100 2 30 2600 60 80 5000 1000 20 300 3 30 2600 60 80 5000 1000 40 100 4 30 2600 60 80 5000 1000 40 500 5 30 2600 60 80 5000 1500 20 300 6 30 2600 60 80 5000 1500 20 500 7 30 2600 60 80 5000 1500 100 100 8 30 2600 60 80 5000 1500 100 300 9 30 2600 60 80 10000 1000 40 100

10 30 2600 60 80 10000 1000 40 500 11 30 2600 60 80 10000 1000 100 300 12 30 2600 60 80 10000 1000 100 500 13 30 2600 60 80 10000 2000 20 100 14 30 2600 60 80 10000 2000 20 300 15 30 2600 60 80 10000 2000 40 100 16 30 2600 60 80 10000 2000 40 500 17 30 2600 60 90 5000 1500 20 300 18 30 2600 60 90 5000 1500 20 500 19 30 2600 60 90 5000 1500 100 100 20 30 2600 60 90 5000 1500 100 300 21 30 2600 60 90 5000 2000 40 100 22 30 2600 60 90 5000 2000 40 500 23 30 2600 60 90 5000 2000 100 300 24 30 2600 60 90 5000 2000 100 500 25 30 2600 60 90 20000 1000 20 100 26 30 2600 60 90 20000 1000 20 300 27 30 2600 60 90 20000 1000 40 100 28 30 2600 60 90 20000 1000 40 500 29 30 2600 60 90 20000 1500 20 300 30 30 2600 60 90 20000 1500 20 500 31 30 2600 60 90 20000 1500 100 100 32 30 2600 60 90 20000 1500 100 300 33 30 2600 80 80 10000 1000 40 100 34 30 2600 80 80 10000 1000 40 500





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

35 30 2600 80 80 10000 1000 100 300 36 30 2600 80 80 10000 1000 100 500 37 30 2600 80 80 10000 2000 20 100 38 30 2600 80 80 10000 2000 20 300 39 30 2600 80 80 10000 2000 40 100 40 30 2600 80 80 10000 2000 40 500 41 30 2600 80 80 20000 1500 20 300 42 30 2600 80 80 20000 1500 20 500 43 30 2600 80 80 20000 1500 100 100 44 30 2600 80 80 20000 1500 100 300 45 30 2600 80 80 20000 2000 40 100 46 30 2600 80 80 20000 2000 40 500 47 30 2600 80 80 20000 2000 100 300 48 30 2600 80 80 20000 2000 100 500 49 30 2600 80 100 5000 1000 20 100 50 30 2600 80 100 5000 1000 20 300 51 30 2600 80 100 5000 1000 40 100 52 30 2600 80 100 5000 1000 40 500 53 30 2600 80 100 5000 1500 20 300 54 30 2600 80 100 5000 1500 20 500 55 30 2600 80 100 5000 1500 100 100 56 30 2600 80 100 5000 1500 100 300 57 30 2600 80 100 10000 1000 40 100 58 30 2600 80 100 10000 1000 40 500 59 30 2600 80 100 10000 1000 100 300 60 30 2600 80 100 10000 1000 100 500 61 30 2600 80 100 10000 2000 20 100 62 30 2600 80 100 10000 2000 20 300 63 30 2600 80 100 10000 2000 40 100 64 30 2600 80 100 10000 2000 40 500 65 30 1000 60 90 5000 1500 20 300 66 30 1000 60 90 5000 1500 20 500 67 30 1000 60 90 5000 1500 100 100 68 30 1000 60 90 5000 1500 100 300 69 30 1000 60 90 5000 2000 40 100 70 30 1000 60 90 5000 2000 40 500 71 30 1000 60 90 5000 2000 100 300



A2 - 3


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

72 30 1000 60 90 5000 2000 100 500 73 30 1000 60 90 20000 1000 20 100 74 30 1000 60 90 20000 1000 20 300 75 30 1000 60 90 20000 1000 40 100 76 30 1000 60 90 20000 1000 40 500 77 30 1000 60 90 20000 1500 20 300 78 30 1000 60 90 20000 1500 20 500 79 30 1000 60 90 20000 1500 100 100 80 30 1000 60 90 20000 1500 100 300 81 30 1000 60 100 10000 1000 40 100 82 30 1000 60 100 10000 1000 40 500 83 30 1000 60 100 10000 1000 100 300 84 30 1000 60 100 10000 1000 100 500 85 30 1000 60 100 10000 2000 20 100 86 30 1000 60 100 10000 2000 20 300 87 30 1000 60 100 10000 2000 40 100 88 30 1000 60 100 10000 2000 40 500 89 30 1000 60 100 20000 1500 20 300 90 30 1000 60 100 20000 1500 20 500 91 30 1000 60 100 20000 1500 100 100 92 30 1000 60 100 20000 1500 100 300 93 30 1000 60 100 20000 2000 40 100 94 30 1000 60 100 20000 2000 40 500 95 30 1000 60 100 20000 2000 100 300 96 30 1000 60 100 20000 2000 100 500 97 30 1000 100 80 5000 1000 20 100 98 30 1000 100 80 5000 1000 20 300 99 30 1000 100 80 5000 1000 40 100

100 30 1000 100 80 5000 1000 40 500 101 30 1000 100 80 5000 1500 20 300 102 30 1000 100 80 5000 1500 20 500 103 30 1000 100 80 5000 1500 100 100 104 30 1000 100 80 5000 1500 100 300 105 30 1000 100 80 10000 1000 40 100 106 30 1000 100 80 10000 1000 40 500 107 30 1000 100 80 10000 1000 100 300 108 30 1000 100 80 10000 1000 100 500





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

109 30 1000 100 80 10000 2000 20 100 110 30 1000 100 80 10000 2000 20 300 111 30 1000 100 80 10000 2000 40 100 112 30 1000 100 80 10000 2000 40 500 113 30 1000 100 90 5000 1500 20 300 114 30 1000 100 90 5000 1500 20 500 115 30 1000 100 90 5000 1500 100 100 116 30 1000 100 90 5000 1500 100 300 117 30 1000 100 90 5000 2000 40 100 118 30 1000 100 90 5000 2000 40 500 119 30 1000 100 90 5000 2000 100 300 120 30 1000 100 90 5000 2000 100 500 121 30 1000 100 90 20000 1000 20 100 122 30 1000 100 90 20000 1000 20 300 123 30 1000 100 90 20000 1000 40 100 124 30 1000 100 90 20000 1000 40 500 125 30 1000 100 90 20000 1500 20 300 126 30 1000 100 90 20000 1500 20 500 127 30 1000 100 90 20000 1500 100 100 128 30 1000 100 90 20000 1500 100 300 129 60 200 80 80 10000 1000 40 100 130 60 200 80 80 10000 1000 40 500 131 60 200 80 80 10000 1000 100 300 132 60 200 80 80 10000 1000 100 500 133 60 200 80 80 10000 2000 20 100 134 60 200 80 80 10000 2000 20 300 135 60 200 80 80 10000 2000 40 100 136 60 200 80 80 10000 2000 40 500 137 60 200 80 80 20000 1500 20 300 138 60 200 80 80 20000 1500 20 500 139 60 200 80 80 20000 1500 100 100 140 60 200 80 80 20000 1500 100 300 141 60 200 80 80 20000 2000 40 100 142 60 200 80 80 20000 2000 40 500 143 60 200 80 80 20000 2000 100 300 144 60 200 80 80 20000 2000 100 500 145 60 200 80 100 5000 1000 20 100



A2 - 5


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

146 60 200 80 100 5000 1000 20 300 147 60 200 80 100 5000 1000 40 100 148 60 200 80 100 5000 1000 40 500 149 60 200 80 100 5000 1500 20 300 150 60 200 80 100 5000 1500 20 500 151 60 200 80 100 5000 1500 100 100 152 60 200 80 100 5000 1500 100 300 153 60 200 80 100 10000 1000 40 100 154 60 200 80 100 10000 1000 40 500 155 60 200 80 100 10000 1000 100 300 156 60 200 80 100 10000 1000 100 500 157 60 200 80 100 10000 2000 20 100 158 60 200 80 100 10000 2000 20 300 159 60 200 80 100 10000 2000 40 100 160 60 200 80 100 10000 2000 40 500 161 60 200 100 90 5000 1500 20 300 162 60 200 100 90 5000 1500 20 500 163 60 200 100 90 5000 1500 100 100 164 60 200 100 90 5000 1500 100 300 165 60 200 100 90 5000 2000 40 100 166 60 200 100 90 5000 2000 40 500 167 60 200 100 90 5000 2000 100 300 168 60 200 100 90 5000 2000 100 500 169 60 200 100 90 20000 1000 20 100 170 60 200 100 90 20000 1000 20 300 171 60 200 100 90 20000 1000 40 100 172 60 200 100 90 20000 1000 40 500 173 60 200 100 90 20000 1500 20 300 174 60 200 100 90 20000 1500 20 500 175 60 200 100 90 20000 1500 100 100 176 60 200 100 90 20000 1500 100 300 177 60 200 100 100 10000 1000 40 100 178 60 200 100 100 10000 1000 40 500 179 60 200 100 100 10000 1000 100 300 180 60 200 100 100 10000 1000 100 500 181 60 200 100 100 10000 2000 20 100 182 60 200 100 100 10000 2000 20 300





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

183 60 200 100 100 10000 2000 40 100 184 60 200 100 100 10000 2000 40 500 185 60 200 100 100 20000 1500 20 300 186 60 200 100 100 20000 1500 20 500 187 60 200 100 100 20000 1500 100 100 188 60 200 100 100 20000 1500 100 300 189 60 200 100 100 20000 2000 40 100 190 60 200 100 100 20000 2000 40 500 191 60 200 100 100 20000 2000 100 300 192 60 200 100 100 20000 2000 100 500 193 60 1800 60 80 5000 1000 20 100 194 60 1800 60 80 5000 1000 20 300 195 60 1800 60 80 5000 1000 40 100 196 60 1800 60 80 5000 1000 40 500 197 60 1800 60 80 5000 1500 20 300 198 60 1800 60 80 5000 1500 20 500 199 60 1800 60 80 5000 1500 100 100 200 60 1800 60 80 5000 1500 100 300 201 60 1800 60 80 10000 1000 40 100 202 60 1800 60 80 10000 1000 40 500 203 60 1800 60 80 10000 1000 100 300 204 60 1800 60 80 10000 1000 100 500 205 60 1800 60 80 10000 2000 20 100 206 60 1800 60 80 10000 2000 20 300 207 60 1800 60 80 10000 2000 40 100 208 60 1800 60 80 10000 2000 40 500 209 60 1800 60 90 5000 1500 20 300 210 60 1800 60 90 5000 1500 20 500 211 60 1800 60 90 5000 1500 100 100 212 60 1800 60 90 5000 1500 100 300 213 60 1800 60 90 5000 2000 40 100 214 60 1800 60 90 5000 2000 40 500 215 60 1800 60 90 5000 2000 100 300 216 60 1800 60 90 5000 2000 100 500 217 60 1800 60 90 20000 1000 20 100 218 60 1800 60 90 20000 1000 20 300 219 60 1800 60 90 20000 1000 40 100



A2 - 7


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

220 60 1800 60 90 20000 1000 40 500 221 60 1800 60 90 20000 1500 20 300 222 60 1800 60 90 20000 1500 20 500 223 60 1800 60 90 20000 1500 100 100 224 60 1800 60 90 20000 1500 100 300 225 60 1800 80 80 10000 1000 40 100 226 60 1800 80 80 10000 1000 40 500 227 60 1800 80 80 10000 1000 100 300 228 60 1800 80 80 10000 1000 100 500 229 60 1800 80 80 10000 2000 20 100 230 60 1800 80 80 10000 2000 20 300 231 60 1800 80 80 10000 2000 40 100 232 60 1800 80 80 10000 2000 40 500 233 60 1800 80 80 20000 1500 20 300 234 60 1800 80 80 20000 1500 20 500 235 60 1800 80 80 20000 1500 100 100 236 60 1800 80 80 20000 1500 100 300 237 60 1800 80 80 20000 2000 40 100 238 60 1800 80 80 20000 2000 40 500 239 60 1800 80 80 20000 2000 100 300 240 60 1800 80 80 20000 2000 100 500 241 60 1800 80 100 5000 1000 20 100 242 60 1800 80 100 5000 1000 20 300 243 60 1800 80 100 5000 1000 40 100 244 60 1800 80 100 5000 1000 40 500 245 60 1800 80 100 5000 1500 20 300 246 60 1800 80 100 5000 1500 20 500 247 60 1800 80 100 5000 1500 100 100 248 60 1800 80 100 5000 1500 100 300 249 60 1800 80 100 10000 1000 40 100 250 60 1800 80 100 10000 1000 40 500 251 60 1800 80 100 10000 1000 100 300 252 60 1800 80 100 10000 1000 100 500 253 60 1800 80 100 10000 2000 20 100 254 60 1800 80 100 10000 2000 20 300 255 60 1800 80 100 10000 2000 40 100 256 60 1800 80 100 10000 2000 40 500





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

257 100 2600 60 90 5000 1500 20 300 258 100 2600 60 90 5000 1500 20 500 259 100 2600 60 90 5000 1500 100 100 260 100 2600 60 90 5000 1500 100 300 261 100 2600 60 90 5000 2000 40 100 262 100 2600 60 90 5000 2000 40 500 263 100 2600 60 90 5000 2000 100 300 264 100 2600 60 90 5000 2000 100 500 265 100 2600 60 90 20000 1000 20 100 266 100 2600 60 90 20000 1000 20 300 267 100 2600 60 90 20000 1000 40 100 268 100 2600 60 90 20000 1000 40 500 269 100 2600 60 90 20000 1500 20 300 270 100 2600 60 90 20000 1500 20 500 271 100 2600 60 90 20000 1500 100 100 272 100 2600 60 90 20000 1500 100 300 273 100 2600 60 100 10000 1000 40 100 274 100 2600 60 100 10000 1000 40 500 275 100 2600 60 100 10000 1000 100 300 276 100 2600 60 100 10000 1000 100 500 277 100 2600 60 100 10000 2000 20 100 278 100 2600 60 100 10000 2000 20 300 279 100 2600 60 100 10000 2000 40 100 280 100 2600 60 100 10000 2000 40 500 281 100 2600 60 100 20000 1500 20 300 282 100 2600 60 100 20000 1500 20 500 283 100 2600 60 100 20000 1500 100 100 284 100 2600 60 100 20000 1500 100 300 285 100 2600 60 100 20000 2000 40 100 286 100 2600 60 100 20000 2000 40 500 287 100 2600 60 100 20000 2000 100 300 288 100 2600 60 100 20000 2000 100 500 289 100 2600 100 80 5000 1000 20 100 290 100 2600 100 80 5000 1000 20 300 291 100 2600 100 80 5000 1000 40 100 292 100 2600 100 80 5000 1000 40 500 293 100 2600 100 80 5000 1500 20 300



A2 - 9


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

294 100 2600 100 80 5000 1500 20 500 295 100 2600 100 80 5000 1500 100 100 296 100 2600 100 80 5000 1500 100 300 297 100 2600 100 80 10000 1000 40 100 298 100 2600 100 80 10000 1000 40 500 299 100 2600 100 80 10000 1000 100 300 300 100 2600 100 80 10000 1000 100 500 301 100 2600 100 80 10000 2000 20 100 302 100 2600 100 80 10000 2000 20 300 303 100 2600 100 80 10000 2000 40 100 304 100 2600 100 80 10000 2000 40 500 305 100 2600 100 90 5000 1500 20 300 306 100 2600 100 90 5000 1500 20 500 307 100 2600 100 90 5000 1500 100 100 308 100 2600 100 90 5000 1500 100 300 309 100 2600 100 90 5000 2000 40 100 310 100 2600 100 90 5000 2000 40 500 311 100 2600 100 90 5000 2000 100 300 312 100 2600 100 90 5000 2000 100 500 313 100 2600 100 90 20000 1000 20 100 314 100 2600 100 90 20000 1000 20 300 315 100 2600 100 90 20000 1000 40 100 316 100 2600 100 90 20000 1000 40 500 317 100 2600 100 90 20000 1500 20 300 318 100 2600 100 90 20000 1500 20 500 319 100 2600 100 90 20000 1500 100 100 320 100 2600 100 90 20000 1500 100 300 321 100 1000 80 80 10000 1000 40 100 322 100 1000 80 80 10000 1000 40 500 323 100 1000 80 80 10000 1000 100 300 324 100 1000 80 80 10000 1000 100 500 325 100 1000 80 80 10000 2000 20 100 326 100 1000 80 80 10000 2000 20 300 327 100 1000 80 80 10000 2000 40 100 328 100 1000 80 80 10000 2000 40 500 329 100 1000 80 80 20000 1500 20 300 330 100 1000 80 80 20000 1500 20 500





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

331 100 1000 80 80 20000 1500 100 100 332 100 1000 80 80 20000 1500 100 300 333 100 1000 80 80 20000 2000 40 100 334 100 1000 80 80 20000 2000 40 500 335 100 1000 80 80 20000 2000 100 300 336 100 1000 80 80 20000 2000 100 500 337 100 1000 80 100 5000 1000 20 100 338 100 1000 80 100 5000 1000 20 300 339 100 1000 80 100 5000 1000 40 100 340 100 1000 80 100 5000 1000 40 500 341 100 1000 80 100 5000 1500 20 300 342 100 1000 80 100 5000 1500 20 500 343 100 1000 80 100 5000 1500 100 100 344 100 1000 80 100 5000 1500 100 300 345 100 1000 80 100 10000 1000 40 100 346 100 1000 80 100 10000 1000 40 500 347 100 1000 80 100 10000 1000 100 300 348 100 1000 80 100 10000 1000 100 500 349 100 1000 80 100 10000 2000 20 100 350 100 1000 80 100 10000 2000 20 300 351 100 1000 80 100 10000 2000 40 100 352 100 1000 80 100 10000 2000 40 500 353 100 1000 100 90 5000 1500 20 300 354 100 1000 100 90 5000 1500 20 500 355 100 1000 100 90 5000 1500 100 100 356 100 1000 100 90 5000 1500 100 300 357 100 1000 100 90 5000 2000 40 100 358 100 1000 100 90 5000 2000 40 500 359 100 1000 100 90 5000 2000 100 300 360 100 1000 100 90 5000 2000 100 500 361 100 1000 100 90 20000 1000 20 100 362 100 1000 100 90 20000 1000 20 300 363 100 1000 100 90 20000 1000 40 100 364 100 1000 100 90 20000 1000 40 500 365 100 1000 100 90 20000 1500 20 300 366 100 1000 100 90 20000 1500 20 500 367 100 1000 100 90 20000 1500 100 100



A2 - 11


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

368 100 1000 100 90 20000 1500 100 300 369 100 1000 100 100 10000 1000 40 100 370 100 1000 100 100 10000 1000 40 500 371 100 1000 100 100 10000 1000 100 300 372 100 1000 100 100 10000 1000 100 500 373 100 1000 100 100 10000 2000 20 100 374 100 1000 100 100 10000 2000 20 300 375 100 1000 100 100 10000 2000 40 100 376 100 1000 100 100 10000 2000 40 500 377 100 1000 100 100 20000 1500 20 300 378 100 1000 100 100 20000 1500 20 500 379 100 1000 100 100 20000 1500 100 100 380 100 1000 100 100 20000 1500 100 300 381 100 1000 100 100 20000 2000 40 100 382 100 1000 100 100 20000 2000 40 500 383 100 1000 100 100 20000 2000 100 300 384 100 1000 100 100 20000 2000 100 500 385 150 200 60 80 5000 1000 20 100 386 150 200 60 80 5000 1000 20 300 387 150 200 60 80 5000 1000 40 100 388 150 200 60 80 5000 1000 40 500 389 150 200 60 80 5000 1500 20 300 390 150 200 60 80 5000 1500 20 500 391 150 200 60 80 5000 1500 100 100 392 150 200 60 80 5000 1500 100 300 393 150 200 60 80 10000 1000 40 100 394 150 200 60 80 10000 1000 40 500 395 150 200 60 80 10000 1000 100 300 396 150 200 60 80 10000 1000 100 500 397 150 200 60 80 10000 2000 20 100 398 150 200 60 80 10000 2000 20 300 399 150 200 60 80 10000 2000 40 100 400 150 200 60 80 10000 2000 40 500 401 150 200 60 90 5000 1500 20 300 402 150 200 60 90 5000 1500 20 500 403 150 200 60 90 5000 1500 100 100 404 150 200 60 90 5000 1500 100 300





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

405 150 200 60 90 5000 2000 40 100 406 150 200 60 90 5000 2000 40 500 407 150 200 60 90 5000 2000 100 300 408 150 200 60 90 5000 2000 100 500 409 150 200 60 90 20000 1000 20 100 410 150 200 60 90 20000 1000 20 300 411 150 200 60 90 20000 1000 40 100 412 150 200 60 90 20000 1000 40 500 413 150 200 60 90 20000 1500 20 300 414 150 200 60 90 20000 1500 20 500 415 150 200 60 90 20000 1500 100 100 416 150 200 60 90 20000 1500 100 300 417 150 200 80 80 10000 1000 40 100 418 150 200 80 80 10000 1000 40 500 419 150 200 80 80 10000 1000 100 300 420 150 200 80 80 10000 1000 100 500 421 150 200 80 80 10000 2000 20 100 422 150 200 80 80 10000 2000 20 300 423 150 200 80 80 10000 2000 40 100 424 150 200 80 80 10000 2000 40 500 425 150 200 80 80 20000 1500 20 300 426 150 200 80 80 20000 1500 20 500 427 150 200 80 80 20000 1500 100 100 428 150 200 80 80 20000 1500 100 300 429 150 200 80 80 20000 2000 40 100 430 150 200 80 80 20000 2000 40 500 431 150 200 80 80 20000 2000 100 300 432 150 200 80 80 20000 2000 100 500 433 150 200 80 100 5000 1000 20 100 434 150 200 80 100 5000 1000 20 300 435 150 200 80 100 5000 1000 40 100 436 150 200 80 100 5000 1000 40 500 437 150 200 80 100 5000 1500 20 300 438 150 200 80 100 5000 1500 20 500 439 150 200 80 100 5000 1500 100 100 440 150 200 80 100 5000 1500 100 300 441 150 200 80 100 10000 1000 40 100



A2 - 13


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

442 150 200 80 100 10000 1000 40 500 443 150 200 80 100 10000 1000 100 300 444 150 200 80 100 10000 1000 100 500 445 150 200 80 100 10000 2000 20 100 446 150 200 80 100 10000 2000 20 300 447 150 200 80 100 10000 2000 40 100 448 150 200 80 100 10000 2000 40 500 449 150 1800 60 90 5000 1500 20 300 450 150 1800 60 90 5000 1500 20 500 451 150 1800 60 90 5000 1500 100 100 452 150 1800 60 90 5000 1500 100 300 453 150 1800 60 90 5000 2000 40 100 454 150 1800 60 90 5000 2000 40 500 455 150 1800 60 90 5000 2000 100 300 456 150 1800 60 90 5000 2000 100 500 457 150 1800 60 90 20000 1000 20 100 458 150 1800 60 90 20000 1000 20 300 459 150 1800 60 90 20000 1000 40 100 460 150 1800 60 90 20000 1000 40 500 461 150 1800 60 90 20000 1500 20 300 462 150 1800 60 90 20000 1500 20 500 463 150 1800 60 90 20000 1500 100 100 464 150 1800 60 90 20000 1500 100 300 465 150 1800 60 100 10000 1000 40 100 466 150 1800 60 100 10000 1000 40 500 467 150 1800 60 100 10000 1000 100 300 468 150 1800 60 100 10000 1000 100 500 469 150 1800 60 100 10000 2000 20 100 470 150 1800 60 100 10000 2000 20 300 471 150 1800 60 100 10000 2000 40 100 472 150 1800 60 100 10000 2000 40 500 473 150 1800 60 100 20000 1500 20 300 474 150 1800 60 100 20000 1500 20 500 475 150 1800 60 100 20000 1500 100 100 476 150 1800 60 100 20000 1500 100 300 477 150 1800 60 100 20000 2000 40 100 478 150 1800 60 100 20000 2000 40 500





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

BT (mm)

479 150 1800 60 100 20000 2000 100 300 480 150 1800 60 100 20000 2000 100 500 481 150 1800 100 80 5000 1000 20 100 482 150 1800 100 80 5000 1000 20 300 483 150 1800 100 80 5000 1000 40 100 484 150 1800 100 80 5000 1000 40 500 485 150 1800 100 80 5000 1500 20 300 486 150 1800 100 80 5000 1500 20 500 487 150 1800 100 80 5000 1500 100 100 488 150 1800 100 80 5000 1500 100 300 489 150 1800 100 80 10000 1000 40 100 490 150 1800 100 80 10000 1000 40 500 491 150 1800 100 80 10000 1000 100 300 492 150 1800 100 80 10000 1000 100 500 493 150 1800 100 80 10000 2000 20 100 494 150 1800 100 80 10000 2000 20 300 495 150 1800 100 80 10000 2000 40 100 496 150 1800 100 80 10000 2000 40 500 497 150 1800 100 90 5000 1500 20 300 498 150 1800 100 90 5000 1500 20 500 499 150 1800 100 90 5000 1500 100 100 500 150 1800 100 90 5000 1500 100 300 501 150 1800 100 90 5000 2000 40 100 502 150 1800 100 90 5000 2000 40 500 503 150 1800 100 90 5000 2000 100 300 504 150 1800 100 90 5000 2000 100 500 505 150 1800 100 90 20000 1000 20 100 506 150 1800 100 90 20000 1000 20 300 507 150 1800 100 90 20000 1000 40 100 508 150 1800 100 90 20000 1000 40 500 509 150 1800 100 90 20000 1500 20 300 510 150 1800 100 90 20000 1500 20 500 511 150 1800 100 90 20000 1500 100 100 512 150 1800 100 90 20000 1500 100 300

Appendix 3 Sensitivity Analysis Results


A3 - 1

APPENDIX 3. SENSITIVITY ANALYSIS RESULTS

Factor Levels B747 B767 B737 Run

SM W M TP P AM AT BT ST TT ST TT ST TT 1 30 2600 60 80 5000 1000 20 100 899 1019 785 905 669 789 2 30 2600 60 80 5000 1000 20 300 661 981 548 868 427 747 3 30 2600 60 80 5000 1000 40 100 861 1001 748 888 632 772 4 30 2600 60 80 5000 1000 40 500 393 933 260 800 159 699 5 30 2600 60 80 5000 1500 20 300 648 968 535 855 413 733 6 30 2600 60 80 5000 1500 20 500 406 926 285 805 187 707 7 30 2600 60 80 5000 1500 100 100 761 961 643 843 539 739 8 30 2600 60 80 5000 1500 100 300 517 917 412 812 284 684 9 30 2600 60 80 10000 1000 40 100 928 1068 811 951 672 812

10 30 2600 60 80 10000 1000 40 500 443 983 326 866 204 744 11 30 2600 60 80 10000 1000 100 300 610 1010 481 881 349 749 12 30 2600 60 80 10000 1000 100 500 359 959 222 822 101 701 13 30 2600 60 80 10000 2000 20 100 940 1060 812 932 687 807 14 30 2600 60 80 10000 2000 20 300 704 1024 588 908 444 764 15 30 2600 60 80 10000 2000 40 100 894 1034 781 921 646 786 16 30 2600 60 80 10000 2000 40 500 406 946 289 829 169 709 17 30 2600 60 90 5000 1500 20 300 649 969 490 810 415 735 18 30 2600 60 90 5000 1500 20 500 406 926 240 760 189 709





SM W M TP P AM AT BT ST TT ST TT ST TT 19 30 2600 60 90 5000 1500 100 100 763 963 610 810 541 741 20 30 2600 60 90 5000 1500 100 300 519 919 364 764 286 686 21 30 2600 60 90 5000 2000 40 100 831 971 681 821 609 749 22 30 2600 60 90 5000 2000 40 500 354 894 204 744 129 669 23 30 2600 60 90 5000 2000 100 300 502 902 350 750 271 671 24 30 2600 60 90 5000 2000 100 500 240 840 104 704 44 644 25 30 2600 60 90 20000 1000 20 100 1033 1153 839 959 754 874 26 30 2600 60 90 20000 1000 20 300 802 1122 610 930 512 832 27 30 2600 60 90 20000 1000 40 100 1000 1140 811 951 716 856 28 30 2600 60 90 20000 1000 40 500 519 1059 325 865 221 761 29 30 2600 60 90 20000 1500 20 300 788 1108 598 918 499 819 30 30 2600 60 90 20000 1500 20 500 544 1064 350 870 246 766 31 30 2600 60 90 20000 1500 100 100 883 1083 703 903 610 810 32 30 2600 60 90 20000 1500 100 300 643 1043 454 854 371 771 33 30 2600 80 80 10000 1000 40 100 1218 1358 1063 1203 837 977 34 30 2600 80 80 10000 1000 40 500 735 1275 596 1136 357 897 35 30 2600 80 80 10000 1000 100 300 882 1282 743 1143 510 910 36 30 2600 80 80 10000 1000 100 500 632 1232 490 1090 252 852 37 30 2600 80 80 10000 2000 20 100 1219 1339 1074 1194 851 971 38 30 2600 80 80 10000 2000 20 300 989 1309 837 1157 610 930 39 30 2600 80 80 10000 2000 40 100 1174 1314 1024 1164 813 953



A3 - 3










A3 - 5


SM W M TP P AM AT BT ST TT ST TT ST TT 82 30 1000 60 100 10000 1000 40 500 490 1030 407 947 236 776 83 30 1000 60 100 10000 1000 100 300 644 1044 569 969 407 807 84 30 1000 60 100 10000 1000 100 500 406 1006 313 913 162 762 85 30 1000 60 100 10000 2000 20 100 986 1106 898 1018 745 865 86 30 1000 60 100 10000 2000 20 300 749 1069 661 981 503 823 87 30 1000 60 100 10000 2000 40 100 938 1078 853 993 702 842 88 30 1000 60 100 10000 2000 40 500 449 989 380 920 203 743 89 30 1000 60 100 20000 1500 20 300 823 1143 743 1063 559 879 90 30 1000 60 100 20000 1500 20 500 592 1112 496 1016 307 827 91 30 1000 60 100 20000 1500 100 100 927 1127 839 1039 666 866 92 30 1000 60 100 20000 1500 100 300 687 1087 610 1010 413 813 93 30 1000 60 100 20000 2000 40 100 1009 1149 919 1059 745 885 94 30 1000 60 100 20000 2000 40 500 525 1065 430 970 245 785 95 30 1000 60 100 20000 2000 100 300 668 1068 595 995 406 806 96 30 1000 60 100 20000 2000 100 500 406 1006 335 935 165 765 97 30 1000 100 80 5000 1000 20 100 1472 1592 1369 1489 1038 1158 98 30 1000 100 80 5000 1000 20 300 1221 1541 1121 1441 802 1122 99 30 1000 100 80 5000 1000 40 100 1427 1567 1325 1465 1006 1146

100 30 1000 100 80 5000 1000 40 500 949 1489 840 1380 512 1052 101 30 1000 100 80 5000 1500 20 300 1216 1536 1107 1427 789 1109 102 30 1000 100 80 5000 1500 20 500 972 1492 863 1383 537 1057








A3 - 7










A3 - 9







SM W M TP P AM AT BT ST TT ST TT ST TT 187 60 200 100 100 20000 1500 100 100 904 1104 802 1002 699 899 188 60 200 100 100 20000 1500 100 300 664 1064 561 961 447 847 189 60 200 100 100 20000 2000 40 100 983 1123 874 1014 776 916 190 60 200 100 100 20000 2000 40 500 497 1037 397 937 278 818 191 60 200 100 100 20000 2000 100 300 646 1046 545 945 431 831 192 60 200 100 100 20000 2000 100 500 395 995 290 890 189 789 193 60 1800 60 80 5000 1000 20 100 516 636 463 583 425 545 194 60 1800 60 80 5000 1000 20 300 274 594 222 542 193 513 195 60 1800 60 80 5000 1000 40 100 484 624 433 573 400 540 196 60 1800 60 80 5000 1000 40 500 27 567 NA NA NA NA 197 60 1800 60 80 5000 1500 20 300 265 585 216 536 184 504 198 60 1800 60 80 5000 1500 20 500 42 562 NA NA NA NA 199 60 1800 60 80 5000 1500 100 100 391 591 338 538 298 498 200 60 1800 60 80 5000 1500 100 300 147 547 95 495 60 460 201 60 1800 60 80 10000 1000 40 100 514 654 458 598 419 559 202 60 1800 60 80 10000 1000 40 500 46 586 NA NA NA NA 203 60 1800 60 80 10000 1000 100 300 194 594 136 536 99 499 204 60 1800 60 80 10000 1000 100 100 430 630 379 579 337 537 205 60 1800 60 80 10000 2000 20 100 531 651 475 595 434 554 206 60 1800 60 80 10000 2000 20 300 288 608 231 551 203 523 207 60 1800 60 80 10000 2000 40 100 499 639 443 583 407 547



A3 - 11


SM W M TP P AM AT BT ST TT ST TT ST TT 208 60 1800 60 80 10000 2000 40 500 33 573 NA NA NA NA 209 60 1800 60 90 5000 1500 20 300 269 589 218 538 188 508 210 60 1800 60 90 5000 1500 20 500 45 565 NA NA NA NA 211 60 1800 60 90 5000 1500 100 100 395 595 341 541 301 501 212 60 1800 60 90 5000 1500 100 300 152 552 100 500 63 463 213 60 1800 60 90 5000 2000 40 100 474 614 423 563 388 528 214 60 1800 60 90 5000 2000 40 500 20 560 NA NA NA NA 215 60 1800 60 90 5000 2000 100 300 140 540 89 489 52 452 216 60 1800 60 90 5000 2000 100 100 383 583 329 529 289 489 217 60 1800 60 90 20000 1000 20 100 581 701 520 640 480 600 218 60 1800 60 90 20000 1000 20 300 341 661 279 599 240 560 219 60 1800 60 90 20000 1000 40 100 549 689 489 629 448 588 220 60 1800 60 90 20000 1000 40 500 77 617 29 569 NA NA 221 60 1800 60 90 20000 1500 20 300 332 652 270 590 231 551 222 60 1800 60 90 20000 1500 20 500 99 619 45 565 21 541 223 60 1800 60 90 20000 1500 100 100 451 651 394 594 354 554 224 60 1800 60 90 20000 1500 100 300 205 605 152 552 111 511 225 60 1800 80 80 10000 1000 40 100 668 808 593 733 546 686 226 60 1800 80 80 10000 1000 40 500 198 738 117 657 68 608 227 60 1800 80 80 10000 1000 100 300 347 747 265 665 217 617 228 60 1800 80 80 10000 1000 100 500 108 708 46 646 NA NA





SM W M TP P AM AT BT ST TT ST TT ST TT 229 60 1800 80 80 10000 2000 20 100 683 803 609 729 561 681 230 60 1800 80 80 10000 2000 20 300 444 764 369 689 321 641 231 60 1800 80 80 10000 2000 40 100 649 789 576 716 526 666 232 60 1800 80 80 10000 2000 40 500 172 712 96 636 48 588 233 60 1800 80 80 20000 1500 20 300 502 822 419 739 365 685 234 60 1800 80 80 20000 1500 20 500 257 777 181 701 123 643 235 60 1800 80 80 20000 1500 100 100 617 817 537 737 481 681 236 60 1800 80 80 20000 1500 100 300 377 777 290 690 232 632 237 60 1800 80 80 20000 2000 40 100 695 835 616 756 560 700 238 60 1800 80 80 20000 2000 40 500 208 748 124 664 75 615 239 60 1800 80 80 20000 2000 100 300 364 764 278 678 219 619 240 60 1800 80 80 20000 2000 100 500 122 722 52 652 NA NA 241 60 1800 80 100 5000 1000 20 100 665 785 596 716 553 673 242 60 1800 80 100 5000 1000 20 300 426 746 357 677 313 633 243 60 1800 80 100 5000 1000 40 100 633 773 565 705 520 660 244 60 1800 80 100 5000 1000 40 500 161 701 91 631 47 587 245 60 1800 80 100 5000 1500 20 300 416 736 348 668 303 623 246 60 1800 80 100 5000 1500 20 500 186 706 113 633 67 587 247 60 1800 80 100 5000 1500 100 100 540 740 467 667 421 621 248 60 1800 80 100 5000 1500 100 300 292 692 221 621 181 581 249 60 1800 80 100 10000 1000 40 100 675 815 601 741 552 692



A3 - 13


SM W M TP P AM AT BT ST TT ST TT ST TT 250 60 1800 80 100 10000 1000 40 500 204 744 126 666 73 613 251 60 1800 80 100 10000 1000 100 300 354 754 274 674 227 627 252 60 1800 80 100 10000 1000 100 500 116 716 47 647 NA NA 253 60 1800 80 100 10000 2000 20 100 691 811 613 733 567 687 254 60 1800 80 100 10000 2000 20 300 451 771 377 697 327 647 255 60 1800 80 100 10000 2000 40 100 656 796 584 724 532 672 256 60 1800 80 100 10000 2000 40 500 180 720 106 646 53 593 257 100 2600 60 90 5000 1500 20 300 138 458 101 421 70 390 258 100 2600 60 90 5000 1500 20 100 378 498 338 458 303 423 259 100 2600 60 90 5000 1500 100 100 253 453 214 414 181 381 260 100 2600 60 90 5000 1500 100 300 26 426 NA NA NA NA 261 100 2600 60 90 5000 2000 40 100 340 480 303 443 269 409 262 100 2600 60 90 5000 2000 40 300 101 441 66 406 37 377 263 100 2600 60 90 5000 2000 20 300 133 453 96 416 65 385 264 100 2600 60 90 5000 2000 20 100 370 490 333 453 299 419 265 100 2600 60 90 20000 1000 20 100 410 530 372 492 337 457 266 100 2600 60 90 20000 1000 20 300 175 495 136 456 103 423 267 100 2600 60 90 20000 1000 40 100 383 523 343 483 308 448 268 100 2600 60 90 20000 1000 40 300 145 485 106 446 74 414 269 100 2600 60 90 20000 1500 20 300 167 487 128 448 96 416 270 100 2600 60 90 20000 1500 20 100 406 526 366 486 331 451





SM W M TP P AM AT BT ST TT ST TT ST TT 271 100 2600 60 90 20000 1500 100 100 284 484 243 443 207 407 272 100 2600 60 90 20000 1500 100 300 52 452 19 419 NA NA 273 100 2600 60 100 10000 1000 40 100 372 512 331 471 298 438 274 100 2600 60 100 10000 1000 40 300 135 475 94 434 65 405 275 100 2600 60 100 10000 1000 100 300 55 455 21 421 NA NA 276 100 2600 60 100 10000 1000 100 100 287 487 246 446 213 413 277 100 2600 60 100 10000 2000 20 100 390 510 350 470 317 437 278 100 2600 60 100 10000 2000 20 300 152 472 112 432 82 402 279 100 2600 60 100 10000 2000 40 100 359 499 319 459 286 426 280 100 2600 60 100 10000 2000 40 300 121 461 81 421 53 393 281 100 2600 60 100 20000 1500 20 300 172 492 131 451 100 420 282 100 2600 60 100 20000 1500 20 100 407 527 368 488 334 454 283 100 2600 60 100 20000 1500 100 100 288 488 244 444 211 411 284 100 2600 60 100 20000 1500 100 300 56 456 21 421 NA NA 285 100 2600 60 100 20000 2000 40 100 375 515 333 473 300 440 286 100 2600 60 100 20000 2000 40 300 135 475 94 434 65 405 287 100 2600 60 100 20000 2000 100 300 45 445 NA NA NA NA 288 100 2600 60 100 20000 2000 100 100 276 476 232 432 199 399 289 100 2600 100 80 5000 1000 20 100 549 669 486 606 462 582 290 100 2600 100 80 5000 1000 20 300 309 629 246 566 224 544 291 100 2600 100 80 5000 1000 40 100 518 658 456 596 432 572



A3 - 15


SM W M TP P AM AT BT ST TT ST TT ST TT 292 100 2600 100 80 5000 1000 40 500 50 590 NA NA NA NA 293 100 2600 100 80 5000 1500 20 300 301 621 238 558 216 536 294 100 2600 100 80 5000 1500 20 500 70 590 NA NA NA NA 295 100 2600 100 80 5000 1500 100 100 422 622 363 563 337 537 296 100 2600 100 80 5000 1500 100 300 184 584 123 523 98 498 297 100 2600 100 80 10000 1000 40 100 542 682 478 618 451 591 298 100 2600 100 80 10000 1000 40 500 71 611 NA NA NA NA 299 100 2600 100 80 10000 1000 100 300 218 618 158 558 134 534 300 100 2600 100 80 10000 1000 100 100 460 660 398 598 372 572 301 100 2600 100 80 10000 2000 20 100 559 679 495 615 469 589 302 100 2600 100 80 10000 2000 20 300 318 638 253 573 230 550 303 100 2600 100 80 10000 2000 40 100 527 667 463 603 437 577 304 100 2600 100 80 10000 2000 40 500 55 595 NA NA NA NA 305 100 2600 100 90 5000 1500 20 300 308 628 247 567 222 542 306 100 2600 100 90 5000 1500 20 500 78 598 26 546 NA NA 307 100 2600 100 90 5000 1500 100 100 429 629 371 571 343 543 308 100 2600 100 90 5000 1500 100 300 192 592 131 531 105 505 309 100 2600 100 90 5000 2000 40 100 511 651 451 591 423 563 310 100 2600 100 90 5000 2000 40 500 42 582 NA NA NA NA 311 100 2600 100 90 5000 2000 100 300 180 580 120 520 93 493 312 100 2600 100 90 5000 2000 100 100 419 619 360 560 332 532





SM W M TP P AM AT BT ST TT ST TT ST TT 313 100 2600 100 90 20000 1000 20 100 605 725 537 657 510 630 314 100 2600 100 90 20000 1000 20 300 366 686 298 618 273 593 315 100 2600 100 90 20000 1000 40 100 574 714 507 647 480 620 316 100 2600 100 90 20000 1000 40 500 102 642 41 581 21 561 317 100 2600 100 90 20000 1500 20 300 356 676 289 609 264 584 318 100 2600 100 90 20000 1500 20 500 125 645 61 581 35 555 319 100 2600 100 90 20000 1500 100 100 478 678 411 611 385 585 320 100 2600 100 90 20000 1500 100 300 235 635 173 573 145 545 321 100 1000 80 80 10000 1000 40 100 462 602 420 560 395 535 322 100 1000 80 80 10000 1000 40 300 222 562 184 524 158 498 323 100 1000 80 80 10000 1000 100 300 143 543 102 502 77 477 324 100 1000 80 80 10000 1000 100 100 382 582 340 540 313 513 325 100 1000 80 80 10000 2000 20 100 479 599 438 558 411 531 326 100 1000 80 80 10000 2000 20 300 238 558 201 521 175 495 327 100 1000 80 80 10000 2000 40 100 448 588 407 547 382 522 328 100 1000 80 80 10000 2000 40 300 205 545 168 508 142 482 329 100 1000 80 80 20000 1500 20 300 264 584 221 541 199 519 330 100 1000 80 80 20000 1500 20 500 40 560 13 533 NA NA 331 100 1000 80 80 20000 1500 100 100 387 587 344 544 317 517 332 100 1000 80 80 20000 1500 100 300 149 549 107 507 80 480 333 100 1000 80 80 20000 2000 40 100 468 608 426 566 399 539



A3 - 17







SM W M TP P AM AT BT ST TT ST TT ST TT 355 100 1000 100 90 5000 1500 100 100 442 642 396 596 370 570 356 100 1000 100 90 5000 1500 100 300 203 603 156 556 130 530 357 100 1000 100 90 5000 2000 40 100 523 663 476 616 449 589 358 100 1000 100 90 5000 2000 40 500 52 592 NA NA NA NA 359 100 1000 100 90 5000 2000 100 300 193 593 145 545 119 519 360 100 1000 100 90 5000 2000 100 100 432 632 385 585 358 558 361 100 1000 100 90 20000 1000 20 100 616 736 564 684 541 661 362 100 1000 100 90 20000 1000 20 300 380 700 325 645 303 623 363 100 1000 100 90 20000 1000 40 100 588 728 534 674 509 649 364 100 1000 100 90 20000 1000 40 500 115 655 65 605 39 579 365 100 1000 100 90 20000 1500 20 300 371 691 317 637 294 614 366 100 1000 100 90 20000 1500 20 500 139 659 86 606 59 579 367 100 1000 100 90 20000 1500 100 100 492 692 438 638 413 613 368 100 1000 100 90 20000 1500 100 300 249 649 200 600 174 574 369 100 1000 100 100 10000 1000 40 100 568 708 517 657 491 631 370 100 1000 100 100 10000 1000 40 500 96 636 50 590 27 567 371 100 1000 100 100 10000 1000 100 300 244 644 198 598 172 572 372 100 1000 100 100 10000 1000 100 500 25 625 NA NA NA NA 373 100 1000 100 100 10000 2000 20 100 584 704 534 654 507 627 374 100 1000 100 100 10000 2000 20 300 344 664 293 613 268 588 375 100 1000 100 100 10000 2000 40 100 552 692 503 643 474 614



A3 - 19


SM W M TP P AM AT BT ST TT ST TT ST TT 376 100 1000 100 100 10000 2000 40 300 309 649 259 599 232 572 377 100 1000 100 100 20000 1500 20 300 376 696 323 643 298 618 378 100 1000 100 100 20000 1500 20 500 144 664 92 612 64 584 379 100 1000 100 100 20000 1500 100 100 497 697 443 643 416 616 380 100 1000 100 100 20000 1500 100 300 254 654 203 603 179 579 381 100 1000 100 100 20000 2000 40 100 577 717 525 665 496 636 382 100 1000 100 100 20000 2000 40 500 103 643 55 595 28 568 383 100 1000 100 100 20000 2000 100 300 243 643 195 595 167 567 384 100 1000 100 100 20000 2000 100 100 487 687 433 633 406 606 385 150 200 60 80 5000 1000 20 100 301 421 273 393 248 368 386 150 200 60 80 5000 1000 20 300 67 387 41 361 21 341 387 150 200 60 80 5000 1000 40 100 272 412 244 384 220 360 388 150 200 60 80 5000 1000 40 300 40 380 17 357 NA NA 389 150 200 60 80 5000 1500 20 300 61 381 36 356 NA NA 390 150 200 60 80 5000 1500 20 100 294 414 267 387 243 363 391 150 200 60 80 5000 1500 100 100 175 375 147 347 122 322 392 150 200 60 80 5000 1500 40 100 266 406 238 378 215 355 393 150 200 60 80 10000 1000 40 100 280 420 252 392 228 368 394 150 200 60 80 10000 1000 40 300 48 388 23 363 NA NA 395 150 200 60 80 10000 1000 100 100 200 400 171 371 146 346 396 150 200 60 80 10000 1000 20 300 75 395 49 369 28 348





SM W M TP P AM AT BT ST TT ST TT ST TT 397 150 200 60 80 10000 2000 20 100 298 418 271 391 247 367 398 150 200 60 80 10000 2000 20 300 65 385 39 359 20 340 399 150 200 60 80 10000 2000 40 100 268 408 241 381 218 358 400 150 200 60 80 10000 2000 40 300 37 377 NA NA NA NA 401 150 200 60 90 5000 1500 20 300 69 389 45 365 22 342 402 150 200 60 90 5000 1500 20 100 301 421 277 397 249 369 403 150 200 60 90 5000 1500 100 100 182 382 157 357 129 329 404 150 200 60 90 5000 1500 40 100 273 413 248 388 221 361 405 150 200 60 90 5000 2000 40 100 267 407 244 384 216 356 406 150 200 60 90 5000 2000 40 300 36 376 16 356 NA NA 407 150 200 60 90 5000 2000 100 100 169 369 143 343 114 314 408 150 200 60 90 5000 2000 20 300 64 384 41 361 19 339 409 150 200 60 90 20000 1000 20 100 324 444 299 419 269 389 410 150 200 60 90 20000 1000 20 300 91 411 66 386 40 360 411 150 200 60 90 20000 1000 40 100 295 435 270 410 242 382 412 150 200 60 90 20000 1000 40 300 63 403 39 379 17 357 413 150 200 60 90 20000 1500 20 300 84 404 60 380 35 355 414 150 200 60 90 20000 1500 20 100 318 438 292 412 264 384 415 150 200 60 90 20000 1500 100 100 199 399 173 373 143 343 416 150 200 60 90 20000 1500 40 100 289 429 264 404 236 376 417 150 200 80 80 10000 1000 40 100 356 496 317 457 293 433



A3 - 21


SM W M TP P AM AT BT ST TT ST TT ST TT 418 150 200 80 80 10000 1000 40 300 116 456 82 422 62 402 419 150 200 80 80 10000 1000 100 300 39 439 NA NA NA NA 420 150 200 80 80 10000 1000 100 100 269 469 235 435 212 412 421 150 200 80 80 10000 2000 20 100 369 489 336 456 312 432 422 150 200 80 80 10000 2000 20 300 133 453 100 420 79 399 423 150 200 80 80 10000 2000 40 100 339 479 306 446 282 422 424 150 200 80 80 10000 2000 40 300 102 442 69 409 50 390 425 150 200 80 80 20000 1500 20 300 147 467 113 433 92 412 426 150 200 80 80 20000 1500 20 100 383 503 349 469 326 446 427 150 200 80 80 20000 1500 100 100 265 465 230 430 206 406 428 150 200 80 80 20000 1500 100 300 35 435 NA NA NA NA 429 150 200 80 80 20000 2000 40 100 349 489 315 455 292 432 430 150 200 80 80 20000 2000 40 300 111 451 78 418 58 398 431 150 200 80 80 20000 2000 100 300 26 426 NA NA NA NA 432 150 200 80 80 20000 2000 100 100 253 453 218 418 195 395 433 150 200 80 100 5000 1000 20 100 384 504 353 473 326 446 434 150 200 80 100 5000 1000 20 300 150 470 118 438 95 415 435 150 200 80 100 5000 1000 40 100 355 495 323 463 297 437 436 150 200 80 100 5000 1000 40 300 121 461 89 429 67 407 437 150 200 80 100 5000 1500 20 300 142 462 111 431 88 408 438 150 200 80 100 5000 1500 20 100 378 498 346 466 320 440





SM W M TP P AM AT BT ST TT ST TT ST TT 439 150 200 80 100 5000 1500 100 100 259 459 226 426 201 401 440 150 200 80 100 5000 1500 100 300 32 432 NA NA NA NA 441 150 200 80 100 10000 1000 40 100 365 505 333 473 307 447 442 150 200 80 100 10000 1000 40 300 131 471 99 439 75 415 443 150 200 80 100 10000 1000 100 300 53 453 24 424 NA NA 444 150 200 80 100 10000 1000 100 100 283 483 250 450 224 424 445 150 200 80 100 10000 2000 20 100 383 503 351 471 325 445 446 150 200 80 100 10000 2000 20 300 148 468 116 436 93 413 447 150 200 80 100 10000 2000 40 100 353 493 321 461 295 435 448 150 200 80 100 10000 2000 40 300 117 457 85 425 63 403 449 150 1800 60 90 5000 1500 20 300 54 374 30 350 NA NA 450 150 1800 60 90 5000 1500 20 100 286 406 259 379 233 353 451 150 1800 60 90 5000 1500 100 100 167 367 139 339 111 311 452 150 1800 60 90 5000 1500 40 100 258 398 231 371 205 345 453 150 1800 60 90 5000 2000 40 100 253 393 227 367 202 342 454 150 1800 60 90 5000 2000 40 300 23 363 NA NA NA NA 455 150 1800 60 90 5000 2000 100 100 153 353 125 325 97 297 456 150 1800 60 90 5000 2000 20 100 282 402 256 376 230 350 457 150 1800 60 90 20000 1000 20 100 308 428 281 401 252 372 458 150 1800 60 90 20000 1000 20 300 76 396 49 369 25 345 459 150 1800 60 90 20000 1000 40 100 280 420 252 392 224 364



A3 - 23


SM W M TP P AM AT BT ST TT ST TT ST TT 460 150 1800 60 90 20000 1000 40 300 48 388 16 356 NA NA 461 150 1800 60 90 20000 1500 20 300 70 390 44 364 21 341 462 150 1800 60 90 20000 1500 20 100 303 423 275 395 247 367 463 150 1800 60 90 20000 1500 100 100 183 383 155 355 126 326 464 150 1800 60 90 20000 1500 40 100 274 414 246 386 219 359 465 150 1800 60 100 10000 1000 40 100 277 417 248 388 222 362 466 150 1800 60 100 10000 1000 40 300 46 386 21 361 NA NA 467 150 1800 60 100 10000 1000 100 100 197 397 167 367 141 341 468 150 1800 60 100 10000 1000 20 100 306 426 277 397 251 371 469 150 1800 60 100 10000 2000 20 100 296 416 267 387 242 362 470 150 1800 60 100 10000 2000 20 300 63 383 37 357 17 337 471 150 1800 60 100 10000 2000 40 100 266 406 238 378 212 352 472 150 1800 60 100 10000 2000 40 300 35 375 NA NA NA NA 473 150 1800 60 100 20000 1500 20 300 75 395 48 368 25 345 474 150 1800 60 100 20000 1500 20 100 308 428 279 399 252 372 475 150 1800 60 100 20000 1500 100 100 189 389 159 359 131 331 476 150 1800 60 100 20000 1500 40 100 279 419 250 390 224 364 477 150 1800 60 100 20000 2000 40 100 274 414 246 386 220 360 478 150 1800 60 100 20000 2000 40 300 43 383 18 358 NA NA 479 150 1800 60 100 20000 2000 100 100 176 376 146 346 117 317 480 150 1800 60 100 20000 2000 20 100 304 424 274 394 249 369





SM W M TP P AM AT BT ST TT ST TT ST TT 481 150 1800 100 80 5000 1000 20 100 412 532 372 492 352 472 482 150 1800 100 80 5000 1000 20 300 176 496 135 455 118 438 483 150 1800 100 80 5000 1000 40 100 383 523 342 482 322 462 484 150 1800 100 80 5000 1000 40 300 146 486 106 446 88 428 485 150 1800 100 80 5000 1500 20 300 168 488 128 448 110 430 486 150 1800 100 80 5000 1500 20 100 406 526 365 485 345 465 487 150 1800 100 80 5000 1500 100 100 288 488 246 446 227 427 488 150 1800 100 80 5000 1500 100 300 55 455 19 419 NA NA 489 150 1800 100 80 10000 1000 40 100 394 534 353 493 333 473 490 150 1800 100 80 10000 1000 40 300 157 497 116 456 99 439 491 150 1800 100 80 10000 1000 100 300 79 479 39 439 24 424 492 150 1800 100 80 10000 1000 100 100 313 513 271 471 251 451 493 150 1800 100 80 10000 2000 20 100 412 532 371 491 352 472 494 150 1800 100 80 10000 2000 20 300 174 494 133 453 116 436 495 150 1800 100 80 10000 2000 40 100 382 522 341 481 321 461 496 150 1800 100 80 10000 2000 40 300 143 483 102 442 85 425 497 150 1800 100 90 5000 1500 20 300 179 499 139 459 119 439 498 150 1800 100 90 5000 1500 20 100 414 534 376 496 353 473 499 150 1800 100 90 5000 1500 100 100 297 497 257 457 234 434 500 150 1800 100 90 5000 1500 100 300 65 465 28 428 NA NA 501 150 1800 100 90 5000 2000 40 100 381 521 341 481 319 459



A3 - 25


SM W M TP P AM AT BT ST TT ST TT ST TT 502 150 1800 100 90 5000 2000 40 300 142 482 103 443 84 424 503 150 1800 100 90 5000 2000 100 300 55 455 20 420 NA NA 504 150 1800 100 90 5000 2000 100 100 286 486 245 445 222 422 505 150 1800 100 90 20000 1000 20 100 444 564 404 524 380 500 506 150 1800 100 90 20000 1000 20 300 206 526 167 487 147 467 507 150 1800 100 90 20000 1000 40 100 414 554 374 514 351 491 508 150 1800 100 90 20000 1000 40 300 178 518 137 477 118 458 509 150 1800 100 90 20000 1500 20 300 201 521 159 479 139 459 510 150 1800 100 90 20000 1500 20 100 437 557 397 517 374 494 511 150 1800 100 90 20000 1500 100 100 320 520 278 478 255 455 512 150 1800 100 90 20000 1500 100 300 86 486 47 447 28 428

Notes

Bold denotes changed parameters to return a positive SB thickness for B747 aircraft.

NA denotes a combination of parameters for which no SB thickness was required to achieve a CDF of less than 1.0.




Appendix 4 Material Equivalence Design


A4 - 1

APPENDIX 4. MATERIAL EQUIVALENCE DESIGN

Practical Crushed Rock versus Uncrushed Gravel


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

1 30 2600 60 80 5000 1000 20 2 30 2600 60 80 5000 1000 40 3 30 2600 60 80 5000 1500 20 4 30 2600 60 80 5000 1500 100 5 30 2600 60 80 10000 1000 40 6 30 2600 60 80 10000 1000 100 7 30 2600 60 80 10000 2000 20 8 30 2600 60 80 10000 2000 40 9 30 2600 60 90 5000 1500 20

10 30 2600 60 90 5000 1500 100 11 30 2600 60 90 5000 2000 40 12 30 2600 60 90 5000 2000 100 13 30 2600 60 90 20000 1000 20 14 30 2600 60 90 20000 1000 40 15 30 2600 60 90 20000 1500 20 16 30 2600 60 90 20000 1500 100 17 30 2600 80 80 10000 1000 40 18 30 2600 80 80 10000 1000 100 19 30 2600 80 80 10000 2000 20 20 30 2600 80 80 10000 2000 40 21 30 2600 80 80 20000 1500 20 22 30 2600 80 80 20000 1500 100 23 30 2600 80 80 20000 2000 40 24 30 2600 80 80 20000 2000 100 25 30 2600 80 100 5000 1000 20 26 30 2600 80 100 5000 1000 40 27 30 2600 80 100 5000 1500 20 28 30 2600 80 100 5000 1500 100 29 30 2600 80 100 10000 1000 40 30 30 2600 80 100 10000 1000 100 31 30 2600 80 100 10000 2000 20 32 30 2600 80 100 10000 2000 40





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

33 30 1000 60 90 5000 1500 20 34 30 1000 60 90 5000 1500 100 35 30 1000 60 90 5000 2000 40 36 30 1000 60 90 5000 2000 100 37 30 1000 60 90 20000 1000 20 38 30 1000 60 90 20000 1000 40 39 30 1000 60 90 20000 1500 20 40 30 1000 60 90 20000 1500 100 41 30 1000 60 100 10000 1000 40 42 30 1000 60 100 10000 1000 100 43 30 1000 60 100 10000 2000 20 44 30 1000 60 100 10000 2000 40 45 30 1000 60 100 20000 1500 20 46 30 1000 60 100 20000 1500 100 47 30 1000 60 100 20000 2000 40 48 30 1000 60 100 20000 2000 100 49 30 1000 100 80 5000 1000 20 50 30 1000 100 80 5000 1000 40 51 30 1000 100 80 5000 1500 20 52 30 1000 100 80 5000 1500 100 53 30 1000 100 80 10000 1000 40 54 30 1000 100 80 10000 1000 100 55 30 1000 100 80 10000 2000 20 56 30 1000 100 80 10000 2000 40 57 30 1000 100 90 5000 1500 20 58 30 1000 100 90 5000 1500 100 59 30 1000 100 90 5000 2000 40 60 30 1000 100 90 5000 2000 100 61 30 1000 100 90 20000 1000 20 62 30 1000 100 90 20000 1000 40 63 30 1000 100 90 20000 1500 20 64 30 1000 100 90 20000 1500 100 65 60 200 80 80 10000 1000 40 66 60 200 80 80 10000 1000 100 67 60 200 80 80 10000 2000 20 68 60 200 80 80 10000 2000 40 69 60 200 80 80 20000 1500 20



A4 - 3


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

70 60 200 80 80 20000 1500 100 71 60 200 80 80 20000 2000 40 72 60 200 80 80 20000 2000 100 73 60 200 80 100 5000 1000 20 74 60 200 80 100 5000 1000 40 75 60 200 80 100 5000 1500 20 76 60 200 80 100 5000 1500 100 77 60 200 80 100 10000 1000 40 78 60 200 80 100 10000 1000 100 79 60 200 80 100 10000 2000 20 80 60 200 80 100 10000 2000 40 81 60 200 100 90 5000 1500 20 82 60 200 100 90 5000 1500 100 83 60 200 100 90 5000 2000 40 84 60 200 100 90 5000 2000 100 85 60 200 100 90 20000 1000 20 86 60 200 100 90 20000 1000 40 87 60 200 100 90 20000 1500 20 88 60 200 100 90 20000 1500 100 89 60 200 100 100 10000 1000 40 90 60 200 100 100 10000 1000 100 91 60 200 100 100 10000 2000 20 92 60 200 100 100 10000 2000 40 93 60 200 100 100 20000 1500 20 94 60 200 100 100 20000 1500 100 95 60 200 100 100 20000 2000 40 96 60 200 100 100 20000 2000 100 97 60 1800 60 80 5000 1000 20 98 60 1800 60 80 5000 1000 40 99 60 1800 60 80 5000 1500 20

100 60 1800 60 80 5000 1500 100 101 60 1800 60 80 10000 1000 40 102 60 1800 60 80 10000 1000 100 103 60 1800 60 80 10000 2000 20 104 60 1800 60 80 10000 2000 40 105 60 1800 60 90 5000 1500 20 106 60 1800 60 90 5000 1500 100





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

107 60 1800 60 90 5000 2000 40 108 60 1800 60 90 5000 2000 100 109 60 1800 60 90 20000 1000 20 110 60 1800 60 90 20000 1000 40 111 60 1800 60 90 20000 1500 20 112 60 1800 60 90 20000 1500 100 113 60 1800 80 80 10000 1000 40 114 60 1800 80 80 10000 1000 100 115 60 1800 80 80 10000 2000 20 116 60 1800 80 80 10000 2000 40 117 60 1800 80 80 20000 1500 20 118 60 1800 80 80 20000 1500 100 119 60 1800 80 80 20000 2000 40 120 60 1800 80 80 20000 2000 100 121 60 1800 80 100 5000 1000 20 122 60 1800 80 100 5000 1000 40 123 60 1800 80 100 5000 1500 20 124 60 1800 80 100 5000 1500 100 125 60 1800 80 100 10000 1000 40 126 60 1800 80 100 10000 1000 100 127 60 1800 80 100 10000 2000 20 128 60 1800 80 100 10000 2000 40 129 100 2600 60 90 5000 1500 20 130 100 2600 60 90 5000 1500 100 131 100 2600 60 90 5000 2000 40 132 100 2600 60 90 5000 2000 20 133 100 2600 60 90 20000 1000 20 134 100 2600 60 90 20000 1000 40 135 100 2600 60 90 20000 1500 20 136 100 2600 60 90 20000 1500 100 137 100 2600 60 100 10000 1000 40 138 100 2600 60 100 10000 1000 100 139 100 2600 60 100 10000 2000 20 140 100 2600 60 100 10000 2000 40 141 100 2600 60 100 20000 1500 20 142 100 2600 60 100 20000 1500 100 143 100 2600 60 100 20000 2000 40



A4 - 5


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

144 100 2600 60 100 20000 2000 100 145 100 2600 100 80 5000 1000 20 146 100 2600 100 80 5000 1000 40 147 100 2600 100 80 5000 1500 20 148 100 2600 100 80 5000 1500 100 149 100 2600 100 80 10000 1000 40 150 100 2600 100 80 10000 1000 100 151 100 2600 100 80 10000 2000 20 152 100 2600 100 80 10000 2000 40 153 100 2600 100 90 5000 1500 20 154 100 2600 100 90 5000 1500 100 155 100 2600 100 90 5000 2000 40 156 100 2600 100 90 5000 2000 100 157 100 2600 100 90 20000 1000 20 158 100 2600 100 90 20000 1000 40 159 100 2600 100 90 20000 1500 20 160 100 2600 100 90 20000 1500 100 161 100 1000 80 80 10000 1000 40 162 100 1000 80 80 10000 1000 100 163 100 1000 80 80 10000 2000 20 164 100 1000 80 80 10000 2000 40 165 100 1000 80 80 20000 1500 20 166 100 1000 80 80 20000 1500 100 167 100 1000 80 80 20000 2000 40 168 100 1000 80 80 20000 2000 100 169 100 1000 80 100 5000 1000 20 170 100 1000 80 100 5000 1000 40 171 100 1000 80 100 5000 1500 20 172 100 1000 80 100 5000 1500 100 173 100 1000 80 100 10000 1000 40 174 100 1000 80 100 10000 1000 100 175 100 1000 80 100 10000 2000 20 176 100 1000 80 100 10000 2000 40 177 100 1000 100 90 5000 1500 20 178 100 1000 100 90 5000 1500 100 179 100 1000 100 90 5000 2000 40 180 100 1000 100 90 5000 2000 100





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

181 100 1000 100 90 20000 1000 20 182 100 1000 100 90 20000 1000 40 183 100 1000 100 90 20000 1500 20 184 100 1000 100 90 20000 1500 100 185 100 1000 100 100 10000 1000 40 186 100 1000 100 100 10000 1000 100 187 100 1000 100 100 10000 2000 20 188 100 1000 100 100 10000 2000 40 189 100 1000 100 100 20000 1500 20 190 100 1000 100 100 20000 1500 100 191 100 1000 100 100 20000 2000 40 192 100 1000 100 100 20000 2000 100 193 150 200 60 80 5000 1000 20 194 150 200 60 80 5000 1000 40 195 150 200 60 80 5000 1500 20 196 150 200 60 80 10000 1000 40 197 150 200 60 80 10000 2000 20 198 150 200 60 80 10000 2000 40 199 150 200 60 90 5000 1500 20 200 150 200 60 90 5000 2000 40 201 150 200 60 90 20000 1000 20 202 150 200 60 90 20000 1000 40 203 150 200 60 90 20000 1500 20 204 150 200 80 80 10000 1000 40 205 150 200 80 80 10000 1000 100 206 150 200 80 80 10000 2000 20 207 150 200 80 80 10000 2000 40 208 150 200 80 80 20000 1500 20 209 150 200 80 80 20000 1500 100 210 150 200 80 80 20000 2000 40 211 150 200 80 80 20000 2000 100 212 150 200 80 100 5000 1000 20 213 150 200 80 100 5000 1000 40 214 150 200 80 100 5000 1500 20 215 150 200 80 100 5000 1500 100 216 150 200 80 100 10000 1000 40 217 150 200 80 100 10000 1000 100



A4 - 7


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

AT (mm)

218 150 200 80 100 10000 2000 20 219 150 200 80 100 10000 2000 40 220 150 1800 60 90 5000 1500 20 221 150 1800 60 90 5000 2000 40 222 150 1800 60 90 20000 1000 20 223 150 1800 60 90 20000 1000 40 224 150 1800 60 90 20000 1500 20 225 150 1800 60 100 10000 1000 40 226 150 1800 60 100 10000 2000 20 227 150 1800 60 100 10000 2000 40 228 150 1800 60 100 20000 1500 20 229 150 1800 60 100 20000 2000 40 230 150 1800 100 80 5000 1000 20 231 150 1800 100 80 5000 1000 40 232 150 1800 100 80 5000 1500 20 233 150 1800 100 80 5000 1500 100 234 150 1800 100 80 10000 1000 40 235 150 1800 100 80 10000 1000 100 236 150 1800 100 80 10000 2000 20 237 150 1800 100 80 10000 2000 40 238 150 1800 100 90 5000 1500 20 239 150 1800 100 90 5000 1500 100 240 150 1800 100 90 5000 2000 40 241 150 1800 100 90 5000 2000 100 242 150 1800 100 90 20000 1000 20 243 150 1800 100 90 20000 1000 40 244 150 1800 100 90 20000 1500 20 245 150 1800 100 90 20000 1500 100




Practical Asphalt versus Uncrushed Gravel


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

BT (mm)

1 30 2600 60 80 5000 1000 100 2 30 2600 60 80 5000 1500 300 3 30 2600 60 80 10000 1000 500 4 30 2600 60 80 10000 2000 100 5 30 2600 60 90 5000 1500 300 6 30 2600 60 90 5000 2000 500 7 30 2600 60 90 20000 1000 100 8 30 2600 60 90 20000 1500 300 9 30 2600 80 80 10000 1000 500

10 30 2600 80 80 10000 2000 100 11 30 2600 80 80 20000 1500 300 12 30 2600 80 80 20000 2000 500 13 30 2600 80 100 5000 1000 100 14 30 2600 80 100 5000 1500 300 15 30 2600 80 100 10000 1000 500 16 30 2600 80 100 10000 2000 100 17 30 1000 60 90 5000 1500 300 18 30 1000 60 90 5000 2000 500 19 30 1000 60 90 20000 1000 100 20 30 1000 60 90 20000 1500 300 21 30 1000 60 100 10000 1000 500 22 30 1000 60 100 10000 2000 100 23 30 1000 60 100 20000 1500 300 24 30 1000 60 100 20000 2000 500 25 30 1000 100 80 5000 1000 100 26 30 1000 100 80 5000 1500 300 27 30 1000 100 80 10000 1000 500 28 30 1000 100 90 5000 1500 300 29 30 1000 100 90 5000 2000 500 30 30 1000 100 90 20000 1000 100 31 30 1000 100 90 20000 1500 300 32 60 200 80 80 10000 1000 500 33 60 200 80 80 10000 2000 100 34 60 200 80 80 20000 1500 300 35 60 200 80 80 20000 2000 500



A4 - 9


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

BT (mm)

36 60 200 80 100 5000 1000 100 37 60 200 80 100 5000 1500 300 38 60 200 80 100 10000 1000 500 39 60 200 80 100 10000 2000 100 40 60 200 100 90 5000 1500 300 41 60 200 100 90 5000 2000 500 42 60 200 100 90 20000 1000 100 43 60 200 100 90 20000 1500 300 44 60 200 100 100 10000 1000 500 45 60 200 100 100 10000 2000 100 46 60 200 100 100 20000 1500 300 47 60 200 100 100 20000 2000 500 48 60 1800 60 80 5000 1000 100 49 60 1800 60 80 5000 1500 300 50 60 1800 60 80 10000 1000 100 51 60 1800 60 80 10000 2000 100 52 60 1800 60 90 5000 1500 300 53 60 1800 60 90 5000 2000 100 54 60 1800 60 90 20000 1000 100 55 60 1800 60 90 20000 1500 300 56 60 1800 80 80 10000 1000 500 57 60 1800 80 80 10000 2000 100 58 60 1800 80 80 20000 1500 300 59 60 1800 80 80 20000 2000 500 60 60 1800 80 100 5000 1000 100 61 60 1800 80 100 5000 1500 300 62 60 1800 80 100 10000 1000 500 63 60 1800 80 100 10000 2000 100 64 100 2600 60 90 5000 1500 100 65 100 2600 60 90 5000 1500 300 66 100 2600 60 90 5000 2000 100 67 100 2600 60 90 5000 2000 300 68 100 2600 60 90 20000 1000 100 69 100 2600 60 90 20000 1000 300 70 100 2600 60 90 20000 1500 100 71 100 2600 60 90 20000 1500 300 72 100 2600 60 100 10000 1000 100





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

BT (mm)

73 100 2600 60 100 10000 1000 300 74 100 2600 60 100 10000 2000 100 75 100 2600 60 100 10000 2000 300 76 100 2600 60 100 20000 1500 100 77 100 2600 60 100 20000 1500 300 78 100 2600 60 100 20000 2000 100 79 100 2600 60 100 20000 2000 300 80 100 2600 100 80 5000 1000 100 81 100 2600 100 80 5000 1500 300 82 100 2600 100 80 10000 1000 100 83 100 2600 100 80 10000 2000 100 84 100 2600 100 90 5000 1500 300 85 100 2600 100 90 5000 2000 100 86 100 2600 100 90 20000 1000 100 87 100 2600 100 90 20000 1500 300 88 100 1000 80 80 10000 1000 100 89 100 1000 80 80 10000 1000 300 90 100 1000 80 80 10000 2000 100 91 100 1000 80 80 10000 2000 300 92 100 1000 80 80 20000 1500 300 93 100 1000 80 80 20000 2000 100 94 100 1000 80 100 5000 1000 100 95 100 1000 80 100 5000 1000 300 96 100 1000 80 100 5000 1500 100 97 100 1000 80 100 5000 1500 300 98 100 1000 80 100 10000 1000 100 99 100 1000 80 100 10000 1000 300

100 100 1000 80 100 10000 2000 100 101 100 1000 80 100 10000 2000 300 102 100 1000 100 90 5000 2000 100 103 100 1000 100 90 20000 1000 100 104 100 1000 100 90 20000 1500 300 105 100 1000 100 100 10000 1000 500 106 100 1000 100 100 10000 2000 100 107 100 1000 100 100 10000 2000 300 108 100 1000 100 100 20000 1500 300 109 100 1000 100 100 20000 2000 100



A4 - 11


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

BT (mm)

110 150 200 60 80 5000 1000 100 111 150 200 60 80 5000 1000 300 112 150 200 60 80 5000 1500 100 113 150 200 60 80 10000 1000 100 114 150 200 60 80 10000 1000 300 115 150 200 60 80 10000 2000 100 116 150 200 60 80 10000 2000 300 117 150 200 60 90 5000 1500 100 118 150 200 60 90 5000 2000 100 119 150 200 60 90 5000 2000 300 120 150 200 60 90 20000 1000 100 121 150 200 60 90 20000 1000 300 122 150 200 60 90 20000 1500 100 123 150 200 80 80 10000 1000 100 124 150 200 80 80 10000 1000 300 125 150 200 80 80 10000 2000 100 126 150 200 80 80 10000 2000 300 127 150 200 80 80 20000 1500 100 128 150 200 80 80 20000 1500 300 129 150 200 80 80 20000 2000 100 130 150 200 80 80 20000 2000 300 131 150 200 80 100 5000 1000 100 132 150 200 80 100 5000 1000 300 133 150 200 80 100 5000 1500 100 134 150 200 80 100 5000 1500 300 135 150 200 80 100 10000 1000 100 136 150 200 80 100 10000 1000 300 137 150 200 80 100 10000 2000 100 138 150 200 80 100 10000 2000 300 139 150 1800 60 90 5000 1500 100 140 150 1800 60 90 5000 2000 100 141 150 1800 60 90 20000 1000 100 142 150 1800 60 90 20000 1000 300 143 150 1800 60 90 20000 1500 100 144 150 1800 60 100 10000 1000 100 145 150 1800 60 100 10000 2000 100 146 150 1800 60 100 10000 2000 300





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

BT (mm)

147 150 1800 60 100 20000 1500 100 148 150 1800 60 100 20000 2000 100 149 150 1800 100 80 5000 1000 100 150 150 1800 100 80 5000 1000 300 151 150 1800 100 80 5000 1500 100 152 150 1800 100 80 5000 1500 300 153 150 1800 100 80 10000 1000 100 154 150 1800 100 80 10000 1000 300 155 150 1800 100 80 10000 2000 100 156 150 1800 100 80 10000 2000 300 157 150 1800 100 90 5000 1500 100 158 150 1800 100 90 5000 1500 300 159 150 1800 100 90 5000 2000 100 160 150 1800 100 90 5000 2000 300 161 150 1800 100 90 20000 1000 100 162 150 1800 100 90 20000 1000 300 163 150 1800 100 90 20000 1500 100 164 150 1800 100 90 20000 1500 300



A4 - 13

Practical Asphalt versus Crushed Rock


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

ST (mm)

1 30 2600 60 80 5000 1000 200 2 30 2600 60 80 5000 1500 400 3 30 2600 60 80 10000 1000 200 4 30 2600 60 80 10000 2000 800 5 30 2600 60 90 5000 1500 400 6 30 2600 60 90 5000 2000 800 7 30 2600 60 90 20000 1000 200 8 30 2600 60 90 20000 2000 400 9 30 2600 80 80 10000 1500 200

10 30 2600 80 80 10000 2000 800 11 30 2600 80 80 20000 1000 400 12 30 2600 80 80 20000 1500 800 13 30 2600 80 100 5000 1500 200 14 30 2600 80 100 5000 2000 400 15 30 2600 80 100 10000 1000 200 16 30 2600 80 100 10000 1500 800 17 30 1000 60 80 5000 1000 400 18 30 1000 60 80 5000 2000 800 19 30 1000 60 80 20000 1000 200 20 30 1000 60 80 20000 1500 400 21 30 1000 60 90 10000 1000 200 22 30 1000 60 90 10000 2000 800 23 30 1000 60 90 20000 1500 400 24 30 1000 60 90 20000 2000 800 25 30 1000 100 80 5000 1000 200 26 30 1000 100 80 5000 2000 400 27 30 1000 100 80 10000 1500 200 28 30 1000 100 80 10000 2000 800 29 30 1000 100 100 5000 1000 400 30 30 1000 100 100 5000 1500 800 31 30 1000 100 100 20000 1500 200 32 30 1000 100 100 20000 2000 400 33 60 200 60 80 10000 1000 200 34 60 200 60 80 10000 1500 400 35 60 200 60 80 20000 1000 400





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

ST (mm)

36 60 200 60 80 20000 2000 400 37 60 200 60 90 5000 1000 200 38 60 200 60 90 5000 1500 400 39 60 200 60 90 10000 1000 200 40 60 200 60 90 10000 2000 400 41 60 200 80 80 5000 1500 400 42 60 200 80 80 5000 2000 200 43 60 200 80 80 20000 1000 200 44 60 200 80 80 20000 2000 400 45 60 200 80 100 10000 1500 200 46 60 200 80 100 10000 2000 400 47 60 200 80 100 20000 1000 400 48 60 200 80 100 20000 1500 200 49 60 1800 60 80 5000 1500 200 50 60 1800 60 80 5000 2000 400 51 60 1800 60 80 10000 1000 200 52 60 1800 60 80 10000 1500 400 53 60 1800 60 90 5000 1000 400 54 60 1800 60 90 5000 2000 200 55 60 1800 60 90 20000 1000 200 56 60 1800 60 90 20000 1500 400 57 60 1800 100 80 10000 1000 200 58 60 1800 100 80 10000 2000 800 59 60 1800 100 80 20000 1500 400 60 60 1800 100 80 20000 2000 800 61 60 1800 100 100 5000 1000 200 62 60 1800 100 100 5000 2000 400 63 60 1800 100 100 10000 1500 200 64 60 1800 100 100 10000 2000 800 65 100 2600 60 80 5000 1000 200 66 100 2600 60 80 5000 1500 200 67 100 2600 60 80 20000 1500 200 68 100 2600 60 80 20000 2000 200 69 100 2600 60 90 10000 1000 200 70 100 2600 60 90 10000 1500 200 71 100 2600 60 90 20000 1000 200 72 100 2600 60 90 20000 2000 200



A4 - 15


(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

ST (mm)

73 100 2600 80 80 5000 1000 200 74 100 2600 80 80 5000 1500 400 75 100 2600 80 80 10000 1000 200 76 100 2600 80 80 10000 2000 200 77 100 2600 80 100 5000 1500 400 78 100 2600 80 100 5000 2000 200 79 100 2600 80 100 20000 1000 200 80 100 2600 80 100 20000 2000 400 81 100 1000 60 80 10000 1500 200 82 100 1000 60 80 10000 2000 200 83 100 1000 60 80 20000 1000 400 84 100 1000 60 80 20000 1500 200 85 100 1000 60 90 5000 1500 200 86 100 1000 60 90 5000 2000 200 87 100 1000 60 90 10000 1000 200 88 100 1000 60 90 10000 1500 200 89 100 1000 100 80 5000 1000 400 90 100 1000 100 80 5000 2000 200 91 100 1000 100 80 20000 1000 200 92 100 1000 100 80 20000 1500 400 93 100 1000 100 100 10000 1000 200 94 100 1000 100 100 10000 2000 400 95 100 1000 100 100 20000 1500 400 96 100 1000 100 100 20000 2000 200 97 150 200 60 80 5000 1000 200 98 150 200 60 80 5000 2000 200 99 150 200 60 80 10000 1500 200

100 150 200 60 80 10000 2000 200 101 150 200 60 90 5000 1000 200 102 150 200 60 90 5000 1500 200 103 150 200 60 90 20000 1500 200 104 150 200 60 90 20000 2000 200 105 150 200 80 80 10000 1000 200 106 150 200 80 80 10000 1500 200 107 150 200 80 80 20000 1000 200 108 150 200 80 80 20000 2000 200 109 150 200 80 100 5000 1000 200





(MPa) W

(mm) M

(%) TP (%)

P (no.)

AM (MPa)

ST (mm)

110 150 200 80 100 5000 1500 200 111 150 200 80 100 10000 1000 200 112 150 200 80 100 10000 2000 200 113 150 1800 60 80 5000 1500 200 114 150 1800 60 80 5000 2000 200 115 150 1800 60 80 20000 1000 200 116 150 1800 60 80 20000 2000 200 117 150 1800 60 90 10000 1500 200 118 150 1800 60 90 10000 2000 200 119 150 1800 60 90 20000 1000 200 120 150 1800 60 90 20000 1500 200 121 150 1800 100 80 5000 1500 200 122 150 1800 100 80 5000 2000 200 123 150 1800 100 80 10000 1000 200 124 150 1800 100 80 10000 1500 400 125 150 1800 100 100 5000 1000 200 126 150 1800 100 100 5000 2000 200 127 150 1800 100 100 20000 1000 200 128 150 1800 100 100 20000 1500 800



A4 - 17

Isolated Material Equivalence


(MPa) RL RM

(MPa) RT

(mm) 1 30 Full 50 Full 2 30 Full 100 Full 3 30 Full 250 Full 4 30 Full 750 Full 5 30 Full 1000 Full 6 30 Full 2000 Full 7 30 Full 4000 Full 8 60 Full 50 Full 9 60 Full 100 Full

10 60 Full 250 Full 11 60 Full 750 Full 12 60 Full 1000 Full 13 60 Full 2000 Full 14 60 Full 4000 Full 15 100 Full 50 Full 16 100 Full 100 Full 17 100 Full 250 Full 18 100 Full 750 Full 19 100 Full 1000 Full 20 100 Full 2000 Full 21 100 Full 4000 Full 22 150 Full 50 Full 23 150 Full 100 Full 24 150 Full 250 Full 25 150 Full 750 Full 26 150 Full 1000 Full 27 150 Full 2000 Full 28 150 Full 4000 Full 29 30 Top 50 100 30 30 Top 50 200 31 30 Top 50 400 32 30 Top 100 100 33 30 Top 100 200 34 30 Top 100 400 35 30 Top 250 100





(MPa) RL RM

(MPa) RT

(mm) 36 30 Top 250 200 37 30 Top 250 400 38 30 Top 750 100 39 30 Top 750 200 40 30 Top 750 400 41 30 Top 1000 100 42 30 Top 1000 200 43 30 Top 1000 400 44 30 Top 2000 100 45 30 Top 2000 200 46 30 Top 2000 400 47 30 Top 4000 100 48 30 Top 4000 200 49 30 Top 4000 400 50 30 Bottom 50 100 51 30 Bottom 50 200 52 30 Bottom 50 400 53 30 Bottom 100 100 54 30 Bottom 100 200 55 30 Bottom 100 400 56 30 Bottom 250 100 57 30 Bottom 250 200 58 30 Bottom 250 400 59 30 Bottom 750 100 60 30 Bottom 750 200 61 30 Bottom 750 400 62 30 Bottom 1000 100 63 30 Bottom 1000 200 64 30 Bottom 1000 400 65 30 Bottom 2000 100 66 30 Bottom 2000 200 67 30 Bottom 2000 400 68 30 Bottom 4000 100 69 30 Bottom 4000 200 70 30 Bottom 4000 400 71 60 Top 50 100 72 60 Top 50 200



A4 - 19


(MPa) RL RM

(MPa) RT

(mm) 73 60 Top 50 400 74 60 Top 100 100 75 60 Top 100 200 76 60 Top 100 400 77 60 Top 250 100 78 60 Top 250 200 79 60 Top 250 400 80 60 Top 750 100 81 60 Top 750 200 82 60 Top 750 400 83 60 Top 1000 100 84 60 Top 1000 200 85 60 Top 1000 400 86 60 Top 2000 100 87 60 Top 2000 200 88 60 Top 2000 400 89 60 Top 4000 100 90 60 Top 4000 200 91 60 Top 4000 400 92 60 Bottom 50 100 93 60 Bottom 50 200 94 60 Bottom 50 400 95 60 Bottom 100 100 96 60 Bottom 100 200 97 60 Bottom 100 400 98 60 Bottom 250 100 99 60 Bottom 250 200

100 60 Bottom 250 400 101 60 Bottom 750 100 102 60 Bottom 750 200 103 60 Bottom 750 400 104 60 Bottom 1000 100 105 60 Bottom 1000 200 106 60 Bottom 1000 400 107 60 Bottom 2000 100 108 60 Bottom 2000 200 109 60 Bottom 2000 400





(MPa) RL RM

(MPa) RT

(mm) 110 60 Bottom 4000 100 111 60 Bottom 4000 200 112 60 Bottom 4000 400 113 100 Top 50 100 114 100 Top 50 200 115 100 Top 50 400 116 100 Top 100 100 117 100 Top 100 200 118 100 Top 100 400 119 100 Top 250 100 120 100 Top 250 200 121 100 Top 250 400 122 100 Top 750 100 123 100 Top 750 200 124 100 Top 750 400 125 100 Top 1000 100 126 100 Top 1000 200 127 100 Top 1000 400 128 100 Top 2000 100 129 100 Top 2000 200 130 100 Top 2000 400 131 100 Top 4000 100 132 100 Top 4000 200 133 100 Top 4000 400 134 100 Bottom 50 100 135 100 Bottom 50 200 136 100 Bottom 50 400 137 100 Bottom 100 100 138 100 Bottom 100 200 139 100 Bottom 100 400 140 100 Bottom 250 100 141 100 Bottom 250 200 142 100 Bottom 250 400 143 100 Bottom 750 100 144 100 Bottom 750 200 145 100 Bottom 750 400 146 100 Bottom 1000 100



A4 - 21


(MPa) RL RM

(MPa) RT

(mm) 147 100 Bottom 1000 200 148 100 Bottom 1000 400 149 100 Bottom 2000 100 150 100 Bottom 2000 200 151 100 Bottom 2000 400 152 100 Bottom 4000 100 153 100 Bottom 4000 200 154 100 Bottom 4000 400 155 150 Top 50 100 156 150 Top 50 200 157 150 Top 50 400 158 150 Top 100 100 159 150 Top 100 200 160 150 Top 100 400 161 150 Top 250 100 162 150 Top 250 200 163 150 Top 250 400 164 150 Top 750 100 165 150 Top 750 200 166 150 Top 750 400 167 150 Top 1000 100 168 150 Top 1000 200 169 150 Top 1000 400 170 150 Top 2000 100 171 150 Top 2000 200 172 150 Top 2000 400 173 150 Top 4000 100 174 150 Top 4000 200 175 150 Top 4000 400 176 150 Bottom 50 100 177 150 Bottom 50 200 178 150 Bottom 50 400 179 150 Bottom 100 100 180 150 Bottom 100 200 181 150 Bottom 100 400 182 150 Bottom 250 100 183 150 Bottom 250 200





(MPa) RL RM

(MPa) RT

(mm) 184 150 Bottom 250 400 185 150 Bottom 750 100 186 150 Bottom 750 200 187 150 Bottom 750 400 188 150 Bottom 1000 100 189 150 Bottom 1000 200 190 150 Bottom 1000 400 191 150 Bottom 2000 100 192 150 Bottom 2000 200 193 150 Bottom 2000 400 194 150 Bottom 4000 100 195 150 Bottom 4000 200 196 150 Bottom 4000 400



A4 - 23

Equivalence Examples


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) 1 30 B747 397 5,000 1.75 2,857 2 30 B747 397 5,000 1.75 2,857 3 30 B747 397 5,000 1.75 2,857 4 30 B747 397 10,000 1.75 5,714 5 30 B747 397 10,000 1.75 5,714 6 30 B747 397 10,000 1.75 5,714 7 30 B747 397 20,000 1.75 11,429 8 30 B747 397 20,000 1.75 11,429 9 30 B747 397 20,000 1.75 11,429

10 30 B747 318 5,000 1.75 2,857 11 30 B747 318 5,000 1.75 2,857 12 30 B747 318 5,000 1.75 2,857 13 30 B747 318 10,000 1.75 5,714 14 30 B747 318 10,000 1.75 5,714 15 30 B747 318 10,000 1.75 5,714 16 30 B747 318 20,000 1.75 11,429 17 30 B747 318 20,000 1.75 11,429 18 30 B747 318 20,000 1.75 11,429 19 30 B747 238 5,000 1.75 2,857 20 30 B747 238 5,000 1.75 2,857 21 30 B747 238 5,000 1.75 2,857 22 30 B747 238 10,000 1.75 5,714 23 30 B747 238 10,000 1.75 5,714 24 30 B747 238 10,000 1.75 5,714 25 30 B747 238 20,000 1.75 11,429 26 30 B747 238 20,000 1.75 11,429 27 30 B747 238 20,000 1.75 11,429 28 30 B767 180 5,000 1.90 2,632 29 30 B767 180 5,000 1.90 2,632 30 30 B767 180 5,000 1.90 2,632 31 30 B767 180 10,000 1.90 5,263 32 30 B767 180 10,000 1.90 5,263 33 30 B767 180 10,000 1.90 5,263 34 30 B767 180 20,000 1.90 10,526 35 30 B767 180 20,000 1.90 10,526





(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) 36 30 B767 180 20,000 1.90 10,526 37 30 B767 144 5,000 1.90 2,632 38 30 B767 144 5,000 1.90 2,632 39 30 B767 144 5,000 1.90 2,632 40 30 B767 144 10,000 1.90 5,263 41 30 B767 144 10,000 1.90 5,263 42 30 B767 144 10,000 1.90 5,263 43 30 B767 144 20,000 1.90 10,526 44 30 B767 144 20,000 1.90 10,526 45 30 B767 144 20,000 1.90 10,526 46 30 B767 108 5,000 1.90 2,632 47 30 B767 108 5,000 1.90 2,632 48 30 B767 108 5,000 1.90 2,632 49 30 B767 108 10,000 1.90 5,263 50 30 B767 108 10,000 1.90 5,263 51 30 B767 108 10,000 1.90 5,263 52 30 B767 108 20,000 1.90 10,526 53 30 B767 108 20,000 1.90 10,526 54 30 B767 108 20,000 1.90 10,526 55 30 B737 79 5,000 3.70 1,351 56 30 B737 79 5,000 3.70 1,351 57 30 B737 79 5,000 3.70 1,351 58 30 B737 79 10,000 3.70 2,703 59 30 B737 79 10,000 3.70 2,703 60 30 B737 79 10,000 3.70 2,703 61 30 B737 79 20,000 3.70 5,405 62 30 B737 79 20,000 3.70 5,405 63 30 B737 79 20,000 3.70 5,405 64 30 B737 63 5,000 3.70 1,351 65 30 B737 63 5,000 3.70 1,351 66 30 B737 63 5,000 3.70 1,351 67 30 B737 63 10,000 3.70 2,703 68 30 B737 63 10,000 3.70 2,703 69 30 B737 63 10,000 3.70 2,703 70 30 B737 63 20,000 3.70 5,405 71 30 B737 63 20,000 3.70 5,405 72 30 B737 63 20,000 3.70 5,405



A4 - 25


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) 73 30 B737 47 5,000 3.70 1,351 74 30 B737 47 5,000 3.70 1,351 75 30 B737 47 5,000 3.70 1,351 76 30 B737 47 10,000 3.70 2,703 77 30 B737 47 10,000 3.70 2,703 78 30 B737 47 10,000 3.70 2,703 79 30 B737 47 20,000 3.70 5,405 80 30 B737 47 20,000 3.70 5,405 81 30 B737 47 20,000 3.70 5,405 82 60 B747 397 5,000 1.75 2,857 83 60 B747 397 5,000 1.75 2,857 84 60 B747 397 5,000 1.75 2,857 85 60 B747 397 10,000 1.75 5,714 86 60 B747 397 10,000 1.75 5,714 87 60 B747 397 10,000 1.75 5,714 88 60 B747 397 20,000 1.75 11,429 89 60 B747 397 20,000 1.75 11,429 90 60 B747 397 20,000 1.75 11,429 91 60 B747 318 5,000 1.75 2,857 92 60 B747 318 5,000 1.75 2,857 93 60 B747 318 5,000 1.75 2,857 94 60 B747 318 10,000 1.75 5,714 95 60 B747 318 10,000 1.75 5,714 96 60 B747 318 10,000 1.75 5,714 97 60 B747 318 20,000 1.75 11,429 98 60 B747 318 20,000 1.75 11,429 99 60 B747 318 20,000 1.75 11,429

100 60 B747 238 5,000 1.75 2,857 101 60 B747 238 5,000 1.75 2,857 102 60 B747 238 5,000 1.75 2,857 103 60 B747 238 10,000 1.75 5,714 104 60 B747 238 10,000 1.75 5,714 105 60 B747 238 10,000 1.75 5,714 106 60 B747 238 20,000 1.75 11,429 107 60 B747 238 20,000 1.75 11,429 108 60 B747 238 20,000 1.75 11,429 109 60 B767 180 5,000 1.90 2,632





(MPa) Aircraft M

(t) P

(no.) PCR C




A4 - 27


(MPa) Aircraft M

(t) P

(no.) PCR C






(MPa) Aircraft M

(t) P

(no.) PCR C




A4 - 29


(MPa) Aircraft M

(t) P

(no.) PCR C






(MPa) Aircraft M

(t) P

(no.) PCR C




A4 - 31


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) 295 150 B767 108 20,000 1.90 10,526 296 150 B767 108 20,000 1.90 10,526 297 150 B767 108 20,000 1.90 10,526 298 150 B737 79 5,000 3.70 1,351 299 150 B737 79 5,000 3.70 1,351 300 150 B737 79 5,000 3.70 1,351 301 150 B737 79 10,000 3.70 2,703 302 150 B737 79 10,000 3.70 2,703 303 150 B737 79 10,000 3.70 2,703 304 150 B737 79 20,000 3.70 5,405 305 150 B737 79 20,000 3.70 5,405 306 150 B737 79 20,000 3.70 5,405 307 150 B737 63 5,000 3.70 1,351 308 150 B737 63 5,000 3.70 1,351 309 150 B737 63 5,000 3.70 1,351 310 150 B737 63 10,000 3.70 2,703 311 150 B737 63 10,000 3.70 2,703 312 150 B737 63 10,000 3.70 2,703 313 150 B737 63 20,000 3.70 5,405 314 150 B737 63 20,000 3.70 5,405 315 150 B737 63 20,000 3.70 5,405 316 150 B737 47 5,000 3.70 1,351 317 150 B737 47 5,000 3.70 1,351 318 150 B737 47 5,000 3.70 1,351 319 150 B737 47 10,000 3.70 2,703 320 150 B737 47 10,000 3.70 2,703 321 150 B737 47 10,000 3.70 2,703 322 150 B737 47 20,000 3.70 5,405 323 150 B737 47 20,000 3.70 5,405 324 150 B737 47 20,000 3.70 5,405




Appendix 5 Material Equivalence Results


A5 - 1

APPENDIX 5. MATERIAL EQUIVALENCE RESULTS

Practical Crushed Rock versus Uncrushed Gravel

Factor Levels Base Thickness Material Equivalence Run

SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 20 100 300 1.19 1.19 1.21 2 30 2600 60 80 5000 1000 40 100 500 1.17 1.22 1.18 3 30 2600 60 80 5000 1500 20 300 500 1.21 1.25 1.13 4 30 2600 60 80 5000 1500 100 100 300 1.22 1.16 1.28 5 30 2600 60 80 10000 1000 40 100 500 1.21 1.21 1.17 6 30 2600 60 80 10000 1000 100 300 500 1.26 1.30 1.24 7 30 2600 60 80 10000 2000 20 100 300 1.18 1.12 1.22 8 30 2600 60 80 10000 2000 40 100 500 1.22 1.23 1.19 9 30 2600 60 90 5000 1500 20 300 500 1.22 1.25 1.13

10 30 2600 60 90 5000 1500 100 100 300 1.22 1.23 1.28 11 30 2600 60 90 5000 2000 40 100 500 1.19 1.19 1.20 12 30 2600 60 90 5000 2000 100 300 500 1.31 1.23 1.14 13 30 2600 60 90 20000 1000 20 100 300 1.16 1.15 1.21 14 30 2600 60 90 20000 1000 40 100 500 1.20 1.22 1.24 15 30 2600 60 90 20000 1500 20 300 500 1.22 1.24 1.27 16 30 2600 60 90 20000 1500 100 100 300 1.20 1.25 1.20





SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 17 30 2600 80 80 10000 1000 40 100 500 1.21 1.17 1.20 18 30 2600 80 80 10000 1000 100 300 500 1.25 1.27 1.29 19 30 2600 80 80 10000 2000 20 100 300 1.15 1.19 1.21 20 30 2600 80 80 10000 2000 40 100 500 1.21 1.18 1.24 21 30 2600 80 80 20000 1500 20 300 500 1.22 1.22 1.28 22 30 2600 80 80 20000 1500 100 100 300 1.18 1.15 1.25 23 30 2600 80 80 20000 2000 40 100 500 1.18 1.21 1.21 24 30 2600 80 80 20000 2000 100 300 500 1.28 1.29 1.31 25 30 2600 80 100 5000 1000 20 100 300 1.23 1.15 1.16 26 30 2600 80 100 5000 1000 40 100 500 1.21 1.20 1.23 27 30 2600 80 100 5000 1500 20 300 500 1.22 1.23 1.26 28 30 2600 80 100 5000 1500 100 100 300 1.15 1.20 1.26 29 30 2600 80 100 10000 1000 40 100 500 1.21 1.17 1.20 30 30 2600 80 100 10000 1000 100 300 500 1.26 1.26 1.29 31 30 2600 80 100 10000 2000 20 100 300 1.16 1.19 1.22 32 30 2600 80 100 10000 2000 40 100 500 1.21 1.18 1.23 33 30 1000 60 90 5000 1500 20 300 500 1.25 1.25 1.26 34 30 1000 60 90 5000 1500 100 100 300 1.20 1.25 1.27 35 30 1000 60 90 5000 2000 40 100 500 1.18 1.24 1.19 36 30 1000 60 90 5000 2000 100 300 500 1.32 1.20 1.23 37 30 1000 60 90 20000 1000 20 100 300 1.21 1.21 1.21



A5 - 3










A5 - 5


SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 80 60 200 80 100 10000 2000 40 100 500 1.22 1.19 1.22 81 60 200 100 90 5000 1500 20 300 500 1.24 1.22 1.27 82 60 200 100 90 5000 1500 100 100 300 1.21 1.22 1.23 83 60 200 100 90 5000 2000 40 100 500 1.20 1.21 1.21 84 60 200 100 90 5000 2000 100 300 500 1.27 1.18 1.27 85 60 200 100 90 20000 1000 20 100 300 1.19 1.19 1.18 86 60 200 100 90 20000 1000 40 100 500 1.20 1.20 1.23 87 60 200 100 90 20000 1500 20 300 500 1.23 1.24 1.26 88 60 200 100 90 20000 1500 100 100 300 1.21 1.20 1.26 89 60 200 100 100 10000 1000 40 100 500 1.21 1.19 1.23 90 60 200 100 100 10000 1000 100 300 500 1.23 1.25 1.21 91 60 200 100 100 10000 2000 20 100 300 1.18 1.19 1.21 92 60 200 100 100 10000 2000 40 100 500 1.22 1.20 1.25 93 60 200 100 100 20000 1500 20 300 500 1.22 1.24 1.27 94 60 200 100 100 20000 1500 100 100 300 1.20 1.21 1.26 95 60 200 100 100 20000 2000 40 100 500 1.22 1.19 1.25 96 60 200 100 100 20000 2000 100 300 500 1.26 1.28 1.21 97 60 1800 60 80 5000 1000 20 100 300 1.21 1.21 1.16 98 60 1800 60 80 5000 1000 40 100 500 1.14 NA NA 99 60 1800 60 80 5000 1500 20 300 500 1.12 NA NA

100 60 1800 60 80 5000 1500 100 100 300 1.22 1.22 1.19





SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 101 60 1800 60 80 10000 1000 40 100 500 1.17 NA NA 102 60 1800 60 80 10000 1000 100 300 100 1.18 1.22 1.19 103 60 1800 60 80 10000 2000 20 100 300 1.22 1.22 1.16 104 60 1800 60 80 10000 2000 40 100 500 1.17 NA NA 105 60 1800 60 90 5000 1500 20 300 500 1.12 NA NA 106 60 1800 60 90 5000 1500 100 100 300 1.22 1.21 1.19 107 60 1800 60 90 5000 2000 40 100 500 1.14 NA NA 108 60 1800 60 90 5000 2000 100 300 100 1.22 1.20 1.19 109 60 1800 60 90 20000 1000 20 100 300 1.20 1.21 1.20 110 60 1800 60 90 20000 1000 40 100 500 1.18 1.15 NA 111 60 1800 60 90 20000 1500 20 300 500 1.17 1.13 1.05 112 60 1800 60 90 20000 1500 100 100 300 1.23 1.21 1.22 113 60 1800 80 80 10000 1000 40 100 500 1.18 1.19 1.20 114 60 1800 80 80 10000 1000 100 300 500 1.20 1.10 NA 115 60 1800 80 80 10000 2000 20 100 300 1.20 1.20 1.20 116 60 1800 80 80 10000 2000 40 100 500 1.19 1.20 1.20 117 60 1800 80 80 20000 1500 20 300 500 1.23 1.19 1.21 118 60 1800 80 80 20000 1500 100 100 300 1.20 1.24 1.25 119 60 1800 80 80 20000 2000 40 100 500 1.22 1.23 1.21 120 60 1800 80 80 20000 2000 100 300 500 1.21 1.13 NA 121 60 1800 80 100 5000 1000 20 100 300 1.20 1.20 1.20



A5 - 7


SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 122 60 1800 80 100 5000 1000 40 100 500 1.18 1.19 1.18 123 60 1800 80 100 5000 1500 20 300 500 1.15 1.18 1.18 124 60 1800 80 100 5000 1500 100 100 300 1.24 1.23 1.20 125 60 1800 80 100 10000 1000 40 100 500 1.18 1.19 1.20 126 60 1800 80 100 10000 1000 100 300 500 1.19 1.14 NA 127 60 1800 80 100 10000 2000 20 100 300 1.20 1.18 1.20 128 60 1800 80 100 10000 2000 40 100 500 1.19 1.20 1.20 129 100 2600 60 90 5000 1500 20 300 100 1.20 1.19 1.17 130 100 2600 60 90 5000 1500 100 100 300 1.14 NA NA 131 100 2600 60 90 5000 2000 40 100 300 1.20 1.19 1.16 132 100 2600 60 90 5000 2000 20 300 100 1.19 1.19 1.17 133 100 2600 60 90 20000 1000 20 100 300 1.18 1.18 1.17 134 100 2600 60 90 20000 1000 40 100 300 1.19 1.19 1.17 135 100 2600 60 90 20000 1500 20 300 100 1.20 1.19 1.18 136 100 2600 60 90 20000 1500 100 100 300 1.16 1.12 NA 137 100 2600 60 100 10000 1000 40 100 300 1.19 1.19 1.17 138 100 2600 60 100 10000 1000 100 300 100 1.16 1.13 NA 139 100 2600 60 100 10000 2000 20 100 300 1.19 1.19 1.18 140 100 2600 60 100 10000 2000 40 100 300 1.19 1.19 1.17 141 100 2600 60 100 20000 1500 20 300 100 1.18 1.19 1.17 142 100 2600 60 100 20000 1500 100 100 300 1.16 1.12 NA





SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 143 100 2600 60 100 20000 2000 40 100 300 1.20 1.20 1.18 144 100 2600 60 100 20000 2000 100 300 100 1.16 NA NA 145 100 2600 100 80 5000 1000 20 100 300 1.20 1.20 1.19 146 100 2600 100 80 5000 1000 40 100 500 1.17 NA NA 147 100 2600 100 80 5000 1500 20 300 500 1.16 NA NA 148 100 2600 100 80 5000 1500 100 100 300 1.19 1.20 1.20 149 100 2600 100 80 10000 1000 40 100 500 1.18 NA NA 150 100 2600 100 80 10000 1000 100 300 100 1.21 1.20 1.19 151 100 2600 100 80 10000 2000 20 100 300 1.21 1.21 1.20 152 100 2600 100 80 10000 2000 40 100 500 1.18 NA NA 153 100 2600 100 90 5000 1500 20 300 500 1.15 1.11 NA 154 100 2600 100 90 5000 1500 100 100 300 1.19 1.20 1.19 155 100 2600 100 90 5000 2000 40 100 500 1.17 NA NA 156 100 2600 100 90 5000 2000 100 300 100 1.20 1.20 1.20 157 100 2600 100 90 20000 1000 20 100 300 1.20 1.20 1.19 158 100 2600 100 90 20000 1000 40 100 500 1.18 1.17 1.15 159 100 2600 100 90 20000 1500 20 300 500 1.16 1.14 1.15 160 100 2600 100 90 20000 1500 100 100 300 1.22 1.19 1.20 161 100 1000 80 80 10000 1000 40 100 300 1.20 1.18 1.19 162 100 1000 80 80 10000 1000 100 300 100 1.20 1.19 1.18 163 100 1000 80 80 10000 2000 20 100 300 1.21 1.19 1.18



A5 - 9


SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 164 100 1000 80 80 10000 2000 40 100 300 1.22 1.20 1.20 165 100 1000 80 80 20000 1500 20 300 500 1.12 1.04 NA 166 100 1000 80 80 20000 1500 100 100 300 1.19 1.19 1.19 167 100 1000 80 80 20000 2000 40 100 300 1.22 1.20 1.20 168 100 1000 80 80 20000 2000 100 300 100 1.20 1.19 1.18 169 100 1000 80 100 5000 1000 20 100 300 1.21 1.20 1.17 170 100 1000 80 100 5000 1000 40 100 300 1.19 1.18 1.18 171 100 1000 80 100 5000 1500 20 300 100 1.20 1.18 1.18 172 100 1000 80 100 5000 1500 100 100 300 1.19 1.18 1.16 173 100 1000 80 100 10000 1000 40 100 300 1.20 1.18 1.19 174 100 1000 80 100 10000 1000 100 300 100 1.19 1.19 1.18 175 100 1000 80 100 10000 2000 20 100 300 1.21 1.21 1.17 176 100 1000 80 100 10000 2000 40 100 300 1.22 1.19 1.20 177 100 1000 100 90 5000 1500 20 300 500 1.16 1.13 1.12 178 100 1000 100 90 5000 1500 100 100 300 1.20 1.20 1.20 179 100 1000 100 90 5000 2000 40 100 500 1.18 NA NA 180 100 1000 100 90 5000 2000 100 300 100 1.20 1.20 1.20 181 100 1000 100 90 20000 1000 20 100 300 1.18 1.20 1.19 182 100 1000 100 90 20000 1000 40 100 500 1.18 1.17 1.18 183 100 1000 100 90 20000 1500 20 300 500 1.16 1.16 1.18 184 100 1000 100 90 20000 1500 100 100 300 1.22 1.19 1.20





SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 185 100 1000 100 100 10000 1000 40 100 500 1.18 1.17 1.16 186 100 1000 100 100 10000 1000 100 300 500 1.10 NA NA 187 100 1000 100 100 10000 2000 20 100 300 1.20 1.21 1.20 188 100 1000 100 100 10000 2000 40 100 300 1.22 1.22 1.21 189 100 1000 100 100 20000 1500 20 300 500 1.16 1.16 1.17 190 100 1000 100 100 20000 1500 100 100 300 1.22 1.20 1.19 191 100 1000 100 100 20000 2000 40 100 500 1.19 1.18 1.17 192 100 1000 100 100 20000 2000 100 300 100 1.22 1.19 1.20 193 150 200 60 80 5000 1000 20 100 300 1.17 1.16 1.14 194 150 200 60 80 5000 1000 40 100 300 1.16 1.14 NA 195 150 200 60 80 5000 1500 20 300 100 1.17 1.16 NA 196 150 200 60 80 10000 1000 40 100 300 1.16 1.15 NA 197 150 200 60 80 10000 2000 20 100 300 1.17 1.16 1.14 198 150 200 60 80 10000 2000 40 100 300 1.16 NA NA 199 150 200 60 90 5000 1500 20 300 100 1.16 1.16 1.14 200 150 200 60 90 5000 2000 40 100 300 1.16 1.14 NA 201 150 200 60 90 20000 1000 20 100 300 1.17 1.17 1.15 202 150 200 60 90 20000 1000 40 100 300 1.16 1.16 1.13 203 150 200 60 90 20000 1500 20 300 100 1.17 1.16 1.15 204 150 200 80 80 10000 1000 40 100 300 1.20 1.18 1.16 205 150 200 80 80 10000 1000 100 300 100 1.15 NA NA



A5 - 11


SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 206 150 200 80 80 10000 2000 20 100 300 1.18 1.18 1.17 207 150 200 80 80 10000 2000 40 100 300 1.19 1.19 1.16 208 150 200 80 80 20000 1500 20 300 100 1.18 1.18 1.17 209 150 200 80 80 20000 1500 100 100 300 1.15 NA NA 210 150 200 80 80 20000 2000 40 100 300 1.19 1.19 1.17 211 150 200 80 80 20000 2000 100 300 100 1.14 NA NA 212 150 200 80 100 5000 1000 20 100 300 1.17 1.18 1.16 213 150 200 80 100 5000 1000 40 100 300 1.17 1.17 1.15 214 150 200 80 100 5000 1500 20 300 100 1.18 1.18 1.16 215 150 200 80 100 5000 1500 100 100 300 1.14 NA NA 216 150 200 80 100 10000 1000 40 100 300 1.17 1.17 1.16 217 150 200 80 100 10000 1000 100 300 100 1.15 1.13 NA 218 150 200 80 100 10000 2000 20 100 300 1.18 1.18 1.16 219 150 200 80 100 10000 2000 40 100 300 1.18 1.18 1.16 220 150 1800 60 90 5000 1500 20 300 100 1.16 1.15 NA 221 150 1800 60 90 5000 2000 40 100 300 1.15 NA NA 222 150 1800 60 90 20000 1000 20 100 300 1.16 1.16 1.14 223 150 1800 60 90 20000 1000 40 100 300 1.16 1.18 NA 224 150 1800 60 90 20000 1500 20 300 100 1.17 1.16 1.13 225 150 1800 60 100 10000 1000 40 100 300 1.16 1.14 NA 226 150 1800 60 100 10000 2000 20 100 300 1.17 1.15 1.13





SM W M TP P AM AT BT 1 BT 2 B747 B767 B737 227 150 1800 60 100 10000 2000 40 100 300 1.16 NA NA 228 150 1800 60 100 20000 1500 20 300 100 1.17 1.16 1.14 229 150 1800 60 100 20000 2000 40 100 300 1.16 1.14 NA 230 150 1800 100 80 5000 1000 20 100 300 1.18 1.19 1.17 231 150 1800 100 80 5000 1000 40 100 300 1.19 1.18 1.17 232 150 1800 100 80 5000 1500 20 300 100 1.19 1.19 1.18 233 150 1800 100 80 5000 1500 100 100 300 1.17 1.14 NA 234 150 1800 100 80 10000 1000 40 100 300 1.19 1.19 1.17 235 150 1800 100 80 10000 1000 100 300 100 1.17 1.16 1.14 236 150 1800 100 80 10000 2000 20 100 300 1.19 1.19 1.18 237 150 1800 100 80 10000 2000 40 100 300 1.20 1.20 1.18 238 150 1800 100 90 5000 1500 20 300 100 1.18 1.19 1.17 239 150 1800 100 90 5000 1500 100 100 300 1.16 1.15 NA 240 150 1800 100 90 5000 2000 40 100 300 1.20 1.19 1.18 241 150 1800 100 90 5000 2000 100 300 100 1.16 1.13 NA 242 150 1800 100 90 20000 1000 20 100 300 1.19 1.19 1.17 243 150 1800 100 90 20000 1000 40 100 300 1.18 1.19 1.17 244 150 1800 100 90 20000 1500 20 300 100 1.18 1.19 1.18 245 150 1800 100 90 20000 1500 100 100 300 1.17 1.16 1.14



A5 - 13

Practical Asphalt versus Uncrushed Gravel

Factor Levels Asphalt Thickness Material Equivalence Run

SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 100 20 40 1.90 1.85 1.85 2 30 2600 60 80 5000 1500 300 20 100 1.64 1.54 1.61 3 30 2600 60 80 10000 1000 500 40 100 1.40 1.73 1.72 4 30 2600 60 80 10000 2000 100 20 40 2.30 1.55 2.05 5 30 2600 60 90 5000 1500 300 20 100 1.63 1.58 1.61 6 30 2600 60 90 5000 2000 500 40 100 1.90 1.67 1.42 7 30 2600 60 90 20000 1000 100 20 40 1.65 1.40 1.90 8 30 2600 60 90 20000 1500 300 20 100 1.81 1.80 1.60 9 30 2600 80 80 10000 1000 500 40 100 1.72 1.77 1.75

10 30 2600 80 80 10000 2000 100 20 40 2.25 2.50 1.90 11 30 2600 80 80 20000 1500 300 20 100 1.78 1.70 1.69 12 30 2600 80 80 20000 2000 500 40 100 2.07 1.75 1.92 13 30 2600 80 100 5000 1000 100 20 40 2.15 1.60 1.45 14 30 2600 80 100 5000 1500 300 20 100 1.70 1.84 1.85 15 30 2600 80 100 10000 1000 500 40 100 1.72 1.77 1.77 16 30 2600 80 100 10000 2000 100 20 40 2.30 2.50 2.10 17 30 1000 60 90 5000 1500 300 20 100 1.61 1.78 1.60 18 30 1000 60 90 5000 2000 500 40 100 1.97 1.35 1.73 19 30 1000 60 90 20000 1000 100 20 40 2.00 2.00 1.95





SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 20 30 1000 60 90 20000 1500 300 20 100 1.70 1.65 1.84 21 30 1000 60 100 10000 1000 500 40 100 1.40 1.57 1.23 22 30 1000 60 100 10000 2000 100 20 40 2.40 2.25 2.15 23 30 1000 60 100 20000 1500 300 20 100 1.70 1.66 1.83 24 30 1000 60 100 20000 2000 500 40 100 1.98 1.58 1.33 25 30 1000 100 80 5000 1000 100 20 40 2.25 2.20 1.60 26 30 1000 100 80 5000 1500 300 20 100 1.99 1.79 1.88 27 30 1000 100 80 10000 1000 500 40 100 1.48 1.70 1.77 28 30 1000 100 90 5000 1500 300 20 100 1.99 1.79 1.88 29 30 1000 100 90 5000 2000 500 40 100 1.83 2.10 1.57 30 30 1000 100 90 20000 1000 100 20 40 1.95 2.35 2.05 31 30 1000 100 90 20000 1500 300 20 100 2.05 1.88 1.75 32 60 200 80 80 10000 1000 500 40 100 1.30 1.48 1.40 33 60 200 80 80 10000 2000 100 20 40 1.80 1.70 1.60 34 60 200 80 80 20000 1500 300 20 100 1.68 1.54 1.63 35 60 200 80 80 20000 2000 500 40 100 1.43 1.63 1.55 36 60 200 80 100 5000 1000 100 20 40 1.70 1.60 1.50 37 60 200 80 100 5000 1500 300 20 100 1.55 1.54 1.66 38 60 200 80 100 10000 1000 500 40 100 1.30 1.48 1.42 39 60 200 80 100 10000 2000 100 20 40 1.80 1.75 1.65 40 60 200 100 90 5000 1500 300 20 100 1.64 1.65 1.64



A5 - 15


SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 41 60 200 100 90 5000 2000 500 40 100 1.73 1.43 1.73 42 60 200 100 90 20000 1000 100 20 40 1.75 1.90 1.60 43 60 200 100 90 20000 1500 300 20 100 1.78 1.65 1.76 44 60 200 100 100 10000 1000 500 40 100 1.48 1.58 1.37 45 60 200 100 100 10000 2000 100 20 40 2.20 2.00 2.05 46 60 200 100 100 20000 1500 300 20 100 1.76 1.65 1.78 47 60 200 100 100 20000 2000 500 40 100 1.70 1.78 1.48 48 60 1800 60 80 5000 1000 100 20 40 1.60 1.50 1.25 49 60 1800 60 80 5000 1500 300 20 100 1.48 1.51 1.55 50 60 1800 60 80 10000 1000 100 40 100 1.40 1.32 1.37 51 60 1800 60 80 10000 2000 100 20 40 1.60 1.60 1.35 52 60 1800 60 90 5000 1500 300 20 100 1.46 1.48 1.56 53 60 1800 60 90 5000 2000 100 40 100 1.52 1.57 1.65 54 60 1800 60 90 20000 1000 100 20 40 1.60 1.55 1.60 55 60 1800 60 90 20000 1500 300 20 100 1.59 1.48 1.50 56 60 1800 80 80 10000 1000 500 40 100 1.50 1.18 NA 57 60 1800 80 80 10000 2000 100 20 40 1.70 1.65 1.75 58 60 1800 80 80 20000 1500 300 20 100 1.56 1.61 1.66 59 60 1800 80 80 20000 2000 500 40 100 1.43 1.20 NA 60 60 1800 80 100 5000 1000 100 20 40 1.60 1.55 1.65 61 60 1800 80 100 5000 1500 300 20 100 1.55 1.59 1.53





SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 62 60 1800 80 100 10000 1000 500 40 100 1.47 1.32 NA 63 60 1800 80 100 10000 2000 100 20 40 1.75 1.45 1.75 64 100 2600 60 90 5000 1500 100 20 100 1.56 1.55 1.53 65 100 2600 60 90 5000 1500 300 20 100 1.40 NA NA 66 100 2600 60 90 5000 2000 100 40 20 1.50 1.50 1.50 67 100 2600 60 90 5000 2000 300 40 20 1.60 1.50 1.40 68 100 2600 60 90 20000 1000 100 20 40 1.35 1.45 1.45 69 100 2600 60 90 20000 1000 300 20 40 1.50 1.50 1.45 70 100 2600 60 90 20000 1500 100 20 100 1.53 1.54 1.55 71 100 2600 60 90 20000 1500 300 20 100 1.44 1.36 NA 72 100 2600 60 100 10000 1000 100 40 100 1.42 1.42 1.42 73 100 2600 60 100 10000 1000 300 40 100 1.33 1.22 NA 74 100 2600 60 100 10000 2000 100 20 40 1.55 1.55 1.55 75 100 2600 60 100 10000 2000 300 20 40 1.55 1.55 1.45 76 100 2600 60 100 20000 1500 100 20 100 1.49 1.55 1.54 77 100 2600 60 100 20000 1500 300 20 100 1.45 1.38 NA 78 100 2600 60 100 20000 2000 100 40 100 1.65 1.68 1.68 79 100 2600 60 100 20000 2000 300 40 100 1.50 NA NA 80 100 2600 100 80 5000 1000 100 20 40 1.55 1.50 1.50 81 100 2600 100 80 5000 1500 300 20 100 1.46 1.44 1.48 82 100 2600 100 80 10000 1000 100 40 100 1.37 1.33 1.32



A5 - 17


SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 83 100 2600 100 80 10000 2000 100 20 40 1.60 1.60 1.60 84 100 2600 100 90 5000 1500 300 20 100 1.45 1.45 1.46 85 100 2600 100 90 5000 2000 100 40 100 1.53 1.52 1.52 86 100 2600 100 90 20000 1000 100 20 40 1.55 1.50 1.50 87 100 2600 100 90 20000 1500 300 20 100 1.51 1.45 1.49 88 100 1000 80 80 10000 1000 100 40 100 1.33 1.33 1.37 89 100 1000 80 80 10000 1000 300 40 100 1.32 1.37 1.35 90 100 1000 80 80 10000 2000 100 20 40 1.55 1.55 1.45 91 100 1000 80 80 10000 2000 300 20 40 1.65 1.65 1.65 92 100 1000 80 80 20000 1500 300 20 100 1.44 1.43 1.49 93 100 1000 80 80 20000 2000 100 40 100 1.52 1.55 1.57 94 100 1000 80 100 5000 1000 100 20 40 1.60 1.55 1.40 95 100 1000 80 100 5000 1000 300 20 40 1.45 1.30 1.55 96 100 1000 80 100 5000 1500 100 20 100 1.46 1.49 1.50 97 100 1000 80 100 5000 1500 300 20 100 1.43 1.49 1.46 98 100 1000 80 100 10000 1000 100 40 100 1.32 1.33 1.38 99 100 1000 80 100 10000 1000 300 40 100 1.30 1.37 1.35

100 100 1000 80 100 10000 2000 100 20 40 1.60 1.60 1.45 101 100 1000 80 100 10000 2000 300 20 40 1.65 1.40 1.70 102 100 1000 100 90 5000 2000 100 40 100 1.52 1.52 1.52 103 100 1000 100 90 20000 1000 100 20 40 1.40 1.50 1.60





SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 104 100 1000 100 90 20000 1500 300 20 100 1.53 1.46 1.50 105 100 1000 100 100 10000 1000 500 40 100 1.18 NA NA 106 100 1000 100 100 10000 2000 100 20 40 1.60 1.55 1.65 107 100 1000 100 100 10000 2000 300 20 40 1.75 1.70 1.80 108 100 1000 100 100 20000 1500 300 20 100 1.53 1.50 1.49 109 100 1000 100 100 20000 2000 100 40 100 1.50 1.53 1.50 110 150 200 60 80 5000 1000 100 20 40 1.45 1.45 1.40 111 150 200 60 80 5000 1000 300 20 40 1.35 1.20 NA 112 150 200 60 80 5000 1500 100 20 100 1.49 1.50 1.51 113 150 200 60 80 10000 1000 100 40 100 1.33 1.35 1.37 114 150 200 60 80 10000 1000 300 40 20 1.35 1.30 NA 115 150 200 60 80 10000 2000 100 20 40 1.50 1.50 1.45 116 150 200 60 80 10000 2000 300 20 40 1.40 NA NA 117 150 200 60 90 5000 1500 100 100 40 1.52 1.52 1.53 118 150 200 60 90 5000 2000 100 40 100 1.63 1.68 1.70 119 150 200 60 90 5000 2000 300 40 20 1.40 1.25 NA 120 150 200 60 90 20000 1000 100 20 40 1.45 1.45 1.35 121 150 200 60 90 20000 1000 300 20 40 1.40 1.35 1.15 122 150 200 60 90 20000 1500 100 20 100 1.49 1.49 1.51 123 150 200 80 80 10000 1000 100 40 100 1.45 1.37 1.35 124 150 200 80 80 10000 1000 300 40 100 1.28 NA NA



A5 - 19


SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 125 150 200 80 80 10000 2000 100 20 40 1.50 1.50 1.50 126 150 200 80 80 10000 2000 300 20 40 1.55 1.55 1.45 127 150 200 80 80 20000 1500 100 20 100 1.48 1.49 1.50 128 150 200 80 80 20000 1500 300 20 100 1.40 NA NA 129 150 200 80 80 20000 2000 100 40 100 1.60 1.62 1.62 130 150 200 80 80 20000 2000 300 40 100 1.42 NA NA 131 150 200 80 100 5000 1000 100 20 40 1.45 1.50 1.45 132 150 200 80 100 5000 1000 300 20 40 1.45 1.45 1.40 133 150 200 80 100 5000 1500 100 20 100 1.49 1.50 1.49 134 150 200 80 100 5000 1500 300 20 100 1.38 NA NA 135 150 200 80 100 10000 1000 100 40 100 1.37 1.38 1.38 136 150 200 80 100 10000 1000 300 40 100 1.30 1.25 NA 137 150 200 80 100 10000 2000 100 20 40 1.50 1.50 1.50 138 150 200 80 100 10000 2000 300 20 40 1.55 1.55 1.50 139 150 1800 60 90 5000 1500 100 100 40 1.52 1.53 1.57 140 150 1800 60 90 5000 2000 100 100 20 1.61 1.64 1.66 141 150 1800 60 90 20000 1000 100 20 40 1.40 1.45 1.40 142 150 1800 60 90 20000 1000 300 20 40 1.40 1.65 NA 143 150 1800 60 90 20000 1500 100 20 100 1.50 1.50 1.51 144 150 1800 60 100 10000 1000 100 40 100 1.33 1.35 1.35 145 150 1800 60 100 10000 2000 100 20 40 1.50 1.45 1.50





SM W M TP P AM BT AT 1 AT 2 B747 B767 B737 146 150 1800 60 100 10000 2000 300 20 40 1.40 NA NA 147 150 1800 60 100 20000 1500 100 20 100 1.49 1.50 1.51 148 150 1800 60 100 20000 2000 100 40 100 1.63 1.67 1.72 149 150 1800 100 80 5000 1000 100 20 40 1.45 1.50 1.50 150 150 1800 100 80 5000 1000 300 20 40 1.50 1.45 1.50 151 150 1800 100 80 5000 1500 100 20 100 1.48 1.49 1.48 152 150 1800 100 80 5000 1500 300 20 100 1.41 1.36 NA 153 150 1800 100 80 10000 1000 100 40 100 1.35 1.37 1.37 154 150 1800 100 80 10000 1000 300 40 100 1.30 1.28 1.25 155 150 1800 100 80 10000 2000 100 20 40 1.50 1.50 1.55 156 150 1800 100 80 10000 2000 300 20 40 1.55 1.55 1.55 157 150 1800 100 90 5000 1500 100 20 100 1.46 1.49 1.49 158 150 1800 100 90 5000 1500 300 20 100 1.43 1.39 NA 159 150 1800 100 90 5000 2000 100 40 100 1.58 1.60 1.62 160 150 1800 100 90 5000 2000 300 40 100 1.45 1.38 NA 161 150 1800 100 90 20000 1000 100 20 40 1.50 1.50 1.45 162 150 1800 100 90 20000 1000 300 20 40 1.40 1.50 1.45 163 150 1800 100 90 20000 1500 100 20 100 1.46 1.49 1.49 164 150 1800 100 90 20000 1500 300 20 100 1.44 1.40 1.39



A5 - 21

Practical Asphalt versus Crushed Rock


SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 1 30 2600 60 80 5000 1000 200 20 40 1.50 1.50 1.50 2 30 2600 60 80 5000 1500 400 40 100 1.30 1.25 1.20 3 30 2600 60 80 10000 1000 200 20 100 1.34 1.30 1.19 4 30 2600 60 80 10000 2000 800 20 40 1.90 1.75 NA 5 30 2600 60 90 5000 1500 400 40 100 1.30 1.23 1.20 6 30 2600 60 90 5000 2000 800 20 100 1.39 NA NA 7 30 2600 60 90 20000 1000 200 20 40 1.30 1.50 1.50 8 30 2600 60 90 20000 2000 400 40 100 1.32 1.30 1.25 9 30 2600 80 80 10000 1500 200 20 100 1.56 1.20 1.46

10 30 2600 80 80 10000 2000 800 20 40 2.05 1.90 1.80 11 30 2600 80 80 20000 1000 400 40 100 1.23 1.28 1.27 12 30 2600 80 80 20000 1500 800 20 100 1.50 1.46 1.39 13 30 2600 80 100 5000 1500 200 20 40 1.80 1.20 1.75 14 30 2600 80 100 5000 2000 400 40 100 1.48 1.35 1.30 15 30 2600 80 100 10000 1000 200 20 100 1.35 1.20 1.34 16 30 2600 80 100 10000 1500 800 20 40 1.80 1.75 1.75 17 30 1000 60 80 5000 1000 400 40 100 1.18 1.23 1.20 18 30 1000 60 80 5000 2000 800 20 100 1.43 1.36 NA 19 30 1000 60 80 20000 1000 200 20 40 1.45 1.50 1.45





SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 20 30 1000 60 80 20000 1500 400 40 100 1.37 1.28 1.30 21 30 1000 60 90 10000 1000 200 20 100 1.29 1.30 1.18 22 30 1000 60 90 10000 2000 800 20 40 1.85 1.75 NA 23 30 1000 60 90 20000 1500 400 40 100 1.37 1.32 1.28 24 30 1000 60 90 20000 2000 800 20 100 1.50 1.40 NA 25 30 1000 100 80 5000 1000 200 20 40 1.50 0.95 0.90 26 30 1000 100 80 5000 2000 400 40 100 1.62 1.52 1.32 27 30 1000 100 80 10000 1500 200 20 100 1.66 1.51 1.36 28 30 1000 100 80 10000 2000 800 20 40 2.10 2.10 1.90 29 30 1000 100 100 5000 1000 400 40 100 1.32 1.28 1.27 30 30 1000 100 100 5000 1500 800 20 100 1.54 1.50 1.41 31 30 1000 100 100 20000 1500 200 20 40 1.90 1.95 1.80 32 30 1000 100 100 20000 2000 400 40 100 1.63 1.65 1.45 33 60 200 60 80 10000 1000 200 20 100 1.24 1.24 1.24 34 60 200 60 80 10000 1500 400 20 40 1.35 1.35 1.40 35 60 200 60 80 20000 1000 400 40 100 1.13 1.17 1.17 36 60 200 60 80 20000 2000 400 20 100 1.28 1.30 1.31 37 60 200 60 90 5000 1000 200 20 40 1.40 1.40 1.35 38 60 200 60 90 5000 1500 400 40 100 1.23 1.25 1.25 39 60 200 60 90 10000 1000 200 20 100 1.24 1.25 1.24 40 60 200 60 90 10000 2000 400 20 40 1.40 1.40 1.45



A5 - 23


SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 41 60 200 80 80 5000 1500 400 40 100 1.22 1.20 1.22 42 60 200 80 80 5000 2000 200 20 100 1.29 1.35 1.36 43 60 200 80 80 20000 1000 200 20 40 1.40 1.35 1.50 44 60 200 80 80 20000 2000 400 40 100 1.27 1.25 1.22 45 60 200 80 100 10000 1500 200 20 100 1.26 1.24 1.34 46 60 200 80 100 10000 2000 400 20 40 1.60 1.50 1.60 47 60 200 80 100 20000 1000 400 40 100 1.22 1.18 1.18 48 60 200 80 100 20000 1500 200 20 100 1.31 1.25 1.38 49 60 1800 60 80 5000 1500 200 20 40 1.40 1.35 1.40 50 60 1800 60 80 5000 2000 400 40 100 1.30 1.32 NA 51 60 1800 60 80 10000 1000 200 20 100 1.24 1.16 1.18 52 60 1800 60 80 10000 1500 400 20 40 1.40 1.30 NA 53 60 1800 60 90 5000 1000 400 40 100 1.17 1.17 1.17 54 60 1800 60 90 5000 2000 200 20 100 1.31 1.29 1.31 55 60 1800 60 90 20000 1000 200 20 40 1.40 1.35 1.40 56 60 1800 60 90 20000 1500 400 40 100 1.22 1.23 1.23 57 60 1800 100 80 10000 1000 200 20 100 1.26 1.16 1.20 58 60 1800 100 80 10000 2000 800 20 40 1.75 1.55 NA 59 60 1800 100 80 20000 1500 400 40 100 1.27 1.25 1.23 60 60 1800 100 80 20000 2000 800 20 100 1.39 NA NA 61 60 1800 100 100 5000 1000 200 20 40 1.40 1.35 1.40





SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 62 60 1800 100 100 5000 2000 400 40 100 1.28 1.23 1.22 63 60 1800 100 100 10000 1500 200 20 100 1.39 1.28 1.29 64 60 1800 100 100 10000 2000 800 20 40 1.70 1.60 NA 65 100 2600 60 80 5000 1000 200 40 100 1.18 1.18 1.22 66 100 2600 60 80 5000 1500 200 20 100 1.28 1.30 1.33 67 100 2600 60 80 20000 1500 200 20 40 1.25 1.30 1.30 68 100 2600 60 80 20000 2000 200 40 100 1.38 1.38 1.43 69 100 2600 60 90 10000 1000 200 20 100 1.18 1.20 1.20 70 100 2600 60 90 10000 1500 200 20 40 1.20 1.25 1.30 71 100 2600 60 90 20000 1000 200 40 100 1.13 1.17 1.18 72 100 2600 60 90 20000 2000 200 20 100 1.33 1.36 1.39 73 100 2600 80 80 5000 1000 200 20 40 1.30 1.25 1.20 74 100 2600 80 80 5000 1500 400 40 100 1.22 NA NA 75 100 2600 80 80 10000 1000 200 20 100 1.14 1.15 1.16 76 100 2600 80 80 10000 2000 200 20 40 1.25 1.25 1.30 77 100 2600 80 100 5000 1500 400 40 100 1.22 NA NA 78 100 2600 80 100 5000 2000 200 20 100 1.25 1.29 1.31 79 100 2600 80 100 20000 1000 200 20 40 1.30 1.30 1.30 80 100 2600 80 100 20000 2000 400 40 100 1.28 1.30 NA 81 100 1000 60 80 10000 1500 200 20 100 1.25 1.29 1.30 82 100 1000 60 80 10000 2000 200 20 40 1.15 1.25 1.35



A5 - 25


SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 83 100 1000 60 80 20000 1000 400 40 100 1.13 NA NA 84 100 1000 60 80 20000 1500 200 20 100 1.25 1.28 1.30 85 100 1000 60 90 5000 1500 200 20 40 1.20 1.30 1.30 86 100 1000 60 90 5000 2000 200 40 100 1.40 1.40 1.47 87 100 1000 60 90 10000 1000 200 20 100 1.18 1.20 1.21 88 100 1000 60 90 10000 1500 200 20 40 1.20 1.30 1.30 89 100 1000 100 80 5000 1000 400 40 100 1.17 1.13 1.15 90 100 1000 100 80 5000 2000 200 20 100 1.31 1.23 1.28 91 100 1000 100 80 20000 1000 200 20 40 1.40 1.30 1.35 92 100 1000 100 80 20000 1500 400 40 100 1.20 1.20 1.22 93 100 1000 100 100 10000 1000 200 20 100 1.21 1.20 1.20 94 100 1000 100 100 10000 2000 400 20 40 1.35 1.35 1.45 95 100 1000 100 100 20000 1500 400 40 100 1.20 1.20 1.20 96 100 1000 100 100 20000 2000 200 20 100 1.33 1.33 1.33 97 150 200 60 80 5000 1000 200 20 40 1.25 1.20 1.20 98 150 200 60 80 5000 2000 200 40 100 1.42 1.45 NA 99 150 200 60 80 10000 1500 200 20 100 1.28 1.29 1.33

100 150 200 60 80 10000 2000 200 20 40 1.30 1.25 1.25 101 150 200 60 90 5000 1000 200 40 100 1.15 1.18 1.20 102 150 200 60 90 5000 1500 200 20 100 1.28 1.30 1.33 103 150 200 60 90 20000 1500 200 20 40 1.25 1.25 1.25





SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 104 150 200 60 90 20000 2000 200 40 100 1.40 1.43 1.52 105 150 200 80 80 10000 1000 200 20 100 1.19 1.16 1.18 106 150 200 80 80 10000 1500 200 20 40 1.30 1.25 1.30 107 150 200 80 80 20000 1000 200 40 100 1.13 1.13 1.15 108 150 200 80 80 20000 2000 200 20 100 1.31 1.33 1.36 109 150 200 80 100 5000 1000 200 20 40 1.25 1.30 1.25 110 150 200 80 100 5000 1500 200 40 100 1.25 1.27 1.30 111 150 200 80 100 10000 1000 200 20 100 1.18 1.18 1.19 112 150 200 80 100 10000 2000 200 20 40 1.25 1.30 1.30 113 150 1800 60 80 5000 1500 200 40 100 1.30 1.33 NA 114 150 1800 60 80 5000 2000 200 20 100 1.40 1.41 NA 115 150 1800 60 80 20000 1000 200 20 40 1.25 1.20 1.15 116 150 1800 60 80 20000 2000 200 40 100 1.43 1.45 NA 117 150 1800 60 90 10000 1500 200 20 100 1.29 1.30 1.34 118 150 1800 60 90 10000 2000 200 20 40 1.30 1.30 1.25 119 150 1800 60 90 20000 1000 200 40 100 1.15 1.17 1.20 120 150 1800 60 90 20000 1500 200 20 100 1.28 1.30 1.34 121 150 1800 100 80 5000 1500 200 20 40 1.25 1.30 1.30 122 150 1800 100 80 5000 2000 200 40 100 1.28 1.30 1.37 123 150 1800 100 80 10000 1000 200 20 100 1.15 1.15 1.18 124 150 1800 100 80 10000 1500 400 20 40 1.25 1.20 1.20



A5 - 27


SM W M TP P AM ST AT 1 AT 2 B747 B767 B737 125 150 1800 100 100 5000 1000 200 40 100 1.12 1.15 1.15 126 150 1800 100 100 5000 2000 200 20 100 1.29 1.33 1.34 127 150 1800 100 100 20000 1000 200 20 40 1.30 1.25 1.25 128 150 1800 100 100 20000 1500 800 40 100 1.22 NA NA

Notes

Bold denotes changed parameters to return a positive SB thickness for B747 aircraft.

NA denotes a combination of parameters for which no SB thickness was required to achieve a CDF of less than 1.0.






A5 - 29

Isolated Material Equivalence


(MPa) RL RM

(MPs) RT

(mm) E MR TR

1 30 Full 50 Full 0.50 0.1 NA 2 30 Full 100 Full 0.59 0.2 NA 3 30 Full 250 Full 0.78 0.5 NA 4 30 Full 750 Full 1.16 1.5 NA 5 30 Full 1000 Full 1.30 2.0 NA 6 30 Full 2000 Full 1.72 4.0 NA 7 30 Full 4000 Full 2.28 8.0 NA 8 60 Full 50 Full 0.57 0.1 NA 9 60 Full 100 Full 0.64 0.2 NA

10 60 Full 250 Full 0.80 0.5 NA 11 60 Full 750 Full 1.15 1.5 NA 12 60 Full 1000 Full 1.28 2.0 NA 13 60 Full 2000 Full 1.69 4.0 NA 14 60 Full 4000 Full 2.23 8.0 NA 15 100 Full 50 Full 0.63 0.1 NA 16 100 Full 100 Full 0.68 0.2 NA 17 100 Full 250 Full 0.82 0.5 NA 18 100 Full 750 Full 1.14 1.5 NA 19 100 Full 1000 Full 1.26 2.0 NA 20 100 Full 2000 Full 1.64 4.0 NA 21 100 Full 4000 Full 2.17 8.0 NA 22 150 Full 50 Full 0.68 0.1 NA 23 150 Full 100 Full 0.73 0.2 NA 24 150 Full 250 Full 0.84 0.5 NA 25 150 Full 750 Full 1.13 1.5 NA 26 150 Full 1000 Full 1.24 2.0 NA 27 150 Full 2000 Full 1.59 4.0 NA 28 150 Full 4000 Full 2.10 8.0 NA 29 30 Top 50 100 0.66 0.1 0.11 30 30 Top 50 200 0.65 0.1 0.23 31 30 Top 50 400 0.59 0.1 0.52 32 30 Top 100 100 0.71 0.2 0.11 33 30 Top 100 200 0.70 0.2 0.23 34 30 Top 100 400 0.66 0.2 0.54 35 30 Top 250 100 0.83 0.5 0.11





(MPa) RL RM

(MPs) RT

(mm) E MR TR

36 30 Top 250 200 0.84 0.5 0.24 37 30 Top 250 400 0.82 0.5 0.60 38 30 Top 750 100 1.12 1.5 0.11 39 30 Top 750 200 1.12 1.5 0.26 40 30 Top 750 400 1.13 1.5 0.73 41 30 Top 1000 100 1.22 2.0 0.11 42 30 Top 1000 200 1.21 2.0 0.26 43 30 Top 1000 400 1.23 2.0 0.79 44 30 Top 2000 100 1.49 4.0 0.12 45 30 Top 2000 200 1.45 4.0 0.28 46 30 Top 2000 400 1.52 4.0 1.02 47 30 Top 4000 100 1.78 8.0 0.12 48 30 Top 4000 200 1.76 8.0 0.31 49 30 Top 4000 400 1.99 8.0 1.96 50 30 Bottom 50 100 0.43 0.1 0.10 51 30 Bottom 50 200 0.49 0.1 0.22 52 30 Bottom 50 400 0.51 0.1 0.50 53 30 Bottom 100 100 0.31 0.2 0.10 54 30 Bottom 100 200 0.44 0.2 0.22 55 30 Bottom 100 400 0.52 0.2 0.51 56 30 Bottom 250 100 0.53 0.5 0.11 57 30 Bottom 250 200 0.64 0.5 0.23 58 30 Bottom 250 400 0.72 0.5 0.56 59 30 Bottom 750 100 1.41 1.5 0.12 60 30 Bottom 750 200 1.28 1.5 0.27 61 30 Bottom 750 400 1.20 1.5 0.77 62 30 Bottom 1000 100 1.75 2.0 0.12 63 30 Bottom 1000 200 1.49 2.0 0.28 64 30 Bottom 1000 400 1.35 2.0 0.87 65 30 Bottom 2000 100 2.64 4.0 0.14 66 30 Bottom 2000 200 2.02 4.0 0.34 67 30 Bottom 2000 400 1.75 4.0 1.32 68 30 Bottom 4000 100 3.50 8.0 0.15 69 30 Bottom 4000 200 2.54 8.0 0.41 70 30 Bottom 4000 400 2.26 8.0 4.17 71 60 Top 50 100 0.74 0.1 0.11 72 60 Top 50 200 0.72 0.1 0.23



A5 - 31


(MPa) RL RM

(MPs) RT

(mm) E MR TR

73 60 Top 50 400 0.65 0.1 0.54 74 60 Top 100 100 0.78 0.2 0.11 75 60 Top 100 200 0.76 0.2 0.24 76 60 Top 100 400 0.71 0.2 0.56 77 60 Top 250 100 0.87 0.5 0.11 78 60 Top 250 200 0.87 0.5 0.24 79 60 Top 250 400 0.84 0.5 0.60 80 60 Top 750 100 1.09 1.5 0.11 81 60 Top 750 200 1.09 1.5 0.26 82 60 Top 750 400 1.12 1.5 0.72 83 60 Top 1000 100 1.17 2.0 0.11 84 60 Top 1000 200 1.17 2.0 0.26 85 60 Top 1000 400 1.22 2.0 0.78 86 60 Top 2000 100 1.38 4.0 0.12 87 60 Top 2000 200 1.40 4.0 0.28 88 60 Top 2000 400 1.52 4.0 1.02 89 60 Top 4000 100 1.62 8.0 0.12 90 60 Top 4000 200 1.70 8.0 0.30 91 60 Top 4000 400 1.98 8.0 1.92 92 60 Bottom 50 100 0.89 0.1 0.11 93 60 Bottom 50 200 0.81 0.1 0.24 94 60 Bottom 50 400 0.71 0.1 0.56 95 60 Bottom 100 100 0.57 0.2 0.11 96 60 Bottom 100 200 0.63 0.2 0.23 97 60 Bottom 100 400 0.65 0.2 0.54 98 60 Bottom 250 100 0.61 0.5 0.11 99 60 Bottom 250 200 0.71 0.5 0.23

100 60 Bottom 250 400 0.77 0.5 0.58 101 60 Bottom 750 100 1.37 1.5 0.12 102 60 Bottom 750 200 1.25 1.5 0.27 103 60 Bottom 750 400 1.18 1.5 0.76 104 60 Bottom 1000 100 1.68 2.0 0.12 105 60 Bottom 1000 200 1.45 2.0 0.28 106 60 Bottom 1000 400 1.33 2.0 0.85 107 60 Bottom 2000 100 2.53 4.0 0.13 108 60 Bottom 2000 200 1.96 4.0 0.33 109 60 Bottom 2000 400 1.72 4.0 1.28





(MPa) RL RM

(MPs) RT

(mm) E MR TR

110 60 Bottom 4000 100 3.36 8.0 0.15 111 60 Bottom 4000 200 2.49 8.0 0.40 112 60 Bottom 4000 400 2.23 8.0 3.67 113 100 Top 50 100 0.80 0.1 0.11 114 100 Top 50 200 0.77 0.1 0.24 115 100 Top 50 400 0.69 0.1 0.55 116 100 Top 100 100 0.82 0.2 0.11 117 100 Top 100 200 0.80 0.2 0.24 118 100 Top 100 400 0.74 0.2 0.57 119 100 Top 250 100 0.89 0.5 0.11 120 100 Top 250 200 0.89 0.5 0.24 121 100 Top 250 400 0.86 0.5 0.61 122 100 Top 750 100 1.06 1.5 0.11 123 100 Top 750 200 1.08 1.5 0.25 124 100 Top 750 400 1.11 1.5 0.72 125 100 Top 1000 100 1.12 2.0 0.11 126 100 Top 1000 200 1.15 2.0 0.26 127 100 Top 1000 400 1.21 2.0 0.77 128 100 Top 2000 100 1.29 4.0 0.11 129 100 Top 2000 200 1.36 4.0 0.27 130 100 Top 2000 400 1.50 4.0 1.00 131 100 Top 4000 100 1.50 8.0 0.12 132 100 Top 4000 200 1.65 8.0 0.30 133 100 Top 4000 400 1.95 8.0 1.83 134 100 Bottom 50 100 1.35 0.1 0.12 135 100 Bottom 50 200 1.10 0.1 0.26 136 100 Bottom 50 400 0.88 0.1 0.62 137 100 Bottom 100 100 0.85 0.2 0.11 138 100 Bottom 100 200 0.82 0.2 0.24 139 100 Bottom 100 400 0.77 0.2 0.58 140 100 Bottom 250 100 0.70 0.5 0.11 141 100 Bottom 250 200 0.78 0.5 0.24 142 100 Bottom 250 400 0.81 0.5 0.59 143 100 Bottom 750 100 1.32 1.5 0.12 144 100 Bottom 750 200 1.22 1.5 0.26 145 100 Bottom 750 400 1.17 1.5 0.75 146 100 Bottom 1000 100 1.60 2.0 0.12



A5 - 33


(MPa) RL RM

(MPs) RT

(mm) E MR TR

147 100 Bottom 1000 200 1.40 2.0 0.28 148 100 Bottom 1000 400 1.30 2.0 0.83 149 100 Bottom 2000 100 2.41 4.0 0.13 150 100 Bottom 2000 200 1.88 4.0 0.32 151 100 Bottom 2000 400 1.68 4.0 1.22 152 100 Bottom 4000 100 3.22 8.0 0.15 153 100 Bottom 4000 200 2.41 8.0 0.39 154 100 Bottom 4000 400 2.18 8.0 3.08 155 150 Top 50 100 0.84 0.1 0.11 156 150 Top 50 200 0.82 0.1 0.24 157 150 Top 50 400 0.73 0.1 0.56 158 150 Top 100 100 0.87 0.2 0.11 159 150 Top 100 200 0.84 0.2 0.24 160 150 Top 100 400 0.77 0.2 0.58 161 150 Top 250 100 0.92 0.5 0.11 162 150 Top 250 200 0.91 0.5 0.24 163 150 Top 250 400 0.87 0.5 0.61 164 150 Top 750 100 1.05 1.5 0.11 165 150 Top 750 200 1.07 1.5 0.25 166 150 Top 750 400 1.11 1.5 0.72 167 150 Top 1000 100 1.10 2.0 0.11 168 150 Top 1000 200 1.13 2.0 0.26 169 150 Top 1000 400 1.20 2.0 0.77 170 150 Top 2000 100 1.24 4.0 0.11 171 150 Top 2000 200 1.33 4.0 0.27 172 150 Top 2000 400 1.49 4.0 0.99 173 150 Top 4000 100 1.42 8.0 0.12 174 150 Top 4000 200 1.62 8.0 0.30 175 150 Top 4000 400 1.93 8.0 1.74 176 150 Bottom 50 100 1.78 0.1 0.12 177 150 Bottom 50 200 1.35 0.1 0.27 178 150 Bottom 50 400 1.02 0.1 0.68 179 150 Bottom 100 100 1.13 0.2 0.11 180 150 Bottom 100 200 0.99 0.2 0.25 181 150 Bottom 100 400 0.87 0.2 0.61 182 150 Bottom 250 100 0.81 0.5 0.11 183 150 Bottom 250 200 0.85 0.5 0.24





(MPa) RL RM

(MPs) RT

(mm) E MR TR

184 150 Bottom 250 400 0.85 0.5 0.61 185 150 Bottom 750 100 1.28 1.5 0.11 186 150 Bottom 750 200 1.19 1.5 0.26 187 150 Bottom 750 400 1.15 1.5 0.74 188 150 Bottom 1000 100 1.54 2.0 0.12 189 150 Bottom 1000 200 1.35 2.0 0.27 190 150 Bottom 1000 400 1.27 2.0 0.81 191 150 Bottom 2000 100 2.29 4.0 0.13 192 150 Bottom 2000 200 1.81 4.0 0.31 193 150 Bottom 2000 400 1.64 4.0 1.16 194 150 Bottom 4000 100 3.08 8.0 0.14 195 150 Bottom 4000 200 2.32 8.0 0.37 196 150 Bottom 4000 400 2.12 8.0 2.61



A5 - 35

Equivalence Examples

Factor Levels APSDS Thickness Equivalent Thickness Run SM

(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)

1 30 B747 397 5,000 1.75 2,857 75 150 1305 1530 1545 1530 1530 2 30 B747 397 5,000 1.75 2,857 50 400 1050 1500 1545 1600 1535 3 30 B747 397 5,000 1.75 2,857 150 300 1016 1466 1545 1616 1541 4 30 B747 397 10,000 1.75 5,714 75 150 1397 1622 1635 1622 1622 5 30 B747 397 10,000 1.75 5,714 40 200 1407 1647 1635 1637 1636 6 30 B747 397 10,000 1.75 5,714 100 400 1048 1548 1635 1698 1613 7 30 B747 397 20,000 1.75 11,429 75 150 1481 1706 1720 1706 1706 8 30 B747 397 20,000 1.75 11,429 50 350 1290 1690 1720 1765 1715 9 30 B747 397 20,000 1.75 11,429 300 100 1220 1620 1720 1820 1745

10 30 B747 318 5,000 1.75 2,857 75 150 1061 1286 1327 1286 1286 11 30 B747 318 5,000 1.75 2,857 50 400 814 1264 1327 1364 1299 12 30 B747 318 5,000 1.75 2,857 150 300 783 1233 1327 1383 1308 13 30 B747 318 10,000 1.75 5,714 75 150 1142 1367 1409 1367 1367 14 30 B747 318 10,000 1.75 5,714 40 200 1148 1388 1409 1378 1377 15 30 B747 318 10,000 1.75 5,714 150 300 849 1299 1409 1449 1374 16 30 B747 318 20,000 1.75 11,429 75 150 1219 1444 1487 1444 1444 17 30 B747 318 20,000 1.75 11,429 50 400 972 1422 1487 1522 1457 18 30 B747 318 20,000 1.75 11,429 100 350 946 1396 1487 1521 1451 19 30 B747 238 5,000 1.75 2,857 75 150 796 1021 1070 1021 1021





(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)

20 30 B747 238 5,000 1.75 2,857 40 100 904 1044 1070 984 1013 21 30 B747 238 5,000 1.75 2,857 100 300 581 981 1070 1081 1026 22 30 B747 238 10,000 1.75 5,714 75 150 853 1078 1142 1078 1078 23 30 B747 238 10,000 1.75 5,714 60 400 587 1047 1142 1157 1088 24 30 B747 238 10,000 1.75 5,714 50 600 343 993 1142 1193 1068 25 30 B747 238 20,000 1.75 11,429 75 150 924 1149 1212 1149 1149 26 30 B747 238 20,000 1.75 11,429 150 300 634 1084 1212 1234 1159 27 30 B747 238 20,000 1.75 11,429 100 550 399 1049 1212 1274 1144 28 30 B767 180 5,000 1.90 2,632 75 150 1207 1432 1445 1432 1432 29 30 B767 180 5,000 1.90 2,632 50 400 954 1404 1445 1504 1439 30 30 B767 180 5,000 1.90 2,632 150 300 914 1364 1445 1514 1439 31 30 B767 180 10,000 1.90 5,263 75 150 1284 1509 1532 1509 1509 32 30 B767 180 10,000 1.90 5,263 40 200 1293 1533 1532 1523 1522 33 30 B767 180 10,000 1.90 5,263 150 400 868 1418 1532 1618 1513 34 30 B767 180 20,000 1.90 10,526 75 150 1374 1599 1616 1599 1599 35 30 B767 180 20,000 1.90 10,526 200 500 756 1456 1616 1756 1601 36 30 B767 180 20,000 1.90 10,526 100 200 1270 1570 1616 1620 1595 37 30 B767 144 5,000 1.90 2,632 75 150 974 1199 1235 1199 1199 38 30 B767 144 5,000 1.90 2,632 150 400 563 1113 1235 1313 1208 39 30 B767 144 5,000 1.90 2,632 40 100 1087 1227 1235 1167 1196 40 30 B767 144 10,000 1.90 5,263 75 150 1040 1265 1315 1265 1265



A5 - 37


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 39


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)

83 60 B747 397 5,000 1.75 2,857 50 100 806 956 931 906 931 84 60 B747 397 5,000 1.75 2,857 100 400 369 869 931 1019 934 85 60 B747 397 10,000 1.75 5,714 75 150 769 994 994 994 994 86 60 B747 397 10,000 1.75 5,714 50 250 687 987 994 1012 992 87 60 B747 397 10,000 1.75 5,714 100 400 423 923 994 1073 988 88 60 B747 397 20,000 1.75 11,429 75 140 828 1043 1054 1038 1041 89 60 B747 397 20,000 1.75 11,429 60 300 673 1033 1054 1093 1054 90 60 B747 397 20,000 1.75 11,429 150 250 609 1009 1054 1134 1074 91 60 B747 318 5,000 1.75 2,857 75 150 540 765 784 765 765 92 60 B747 318 5,000 1.75 2,857 40 200 532 772 784 762 761 93 60 B747 318 5,000 1.75 2,857 200 300 173 673 784 873 778 94 60 B747 318 10,000 1.75 5,714 75 150 586 811 835 811 811 95 60 B747 318 10,000 1.75 5,714 60 250 486 796 835 831 807 96 60 B747 318 10,000 1.75 5,714 100 400 240 740 835 890 805 97 60 B747 318 20,000 1.75 11,429 75 150 632 857 887 857 857 98 60 B747 318 20,000 1.75 11,429 100 300 412 812 887 912 857 99 60 B747 318 20,000 1.75 11,429 150 350 279 779 887 954 864

100 60 B747 238 5,000 1.75 2,857 75 150 392 617 634 617 617 101 60 B747 238 5,000 1.75 2,857 50 250 305 605 634 630 610 102 60 B747 238 5,000 1.75 2,857 100 300 173 573 634 673 618 103 60 B747 238 10,000 1.75 5,714 75 150 416 641 672 641 641





(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 41


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 43


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 45


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 47


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)




A5 - 49


(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)






(MPa) Aircraft M

(t) P

(no.) PCR C

(no.) AT

(mm) BT

(mm) ST

(mm) TT

(mm) S77-1(mm)

FAA (mm)

Revised (mm)

314 150 B737 63 20,000 3.70 5,405 50 100 285 435 366 385 410 315 150 B737 63 20,000 3.70 5,405 100 250 44 394 366 469 429 316 150 B737 47 5,000 3.70 1,351 75 150 108 333 265 333 333 317 150 B737 47 5,000 3.70 1,351 40 100 217 357 265 297 326 318 150 B737 47 5,000 3.70 1,351 60 200 75 335 265 345 336 319 150 B737 47 10,000 3.70 2,703 75 150 116 341 280 341 341 320 150 B737 47 10,000 3.70 2,703 40 100 224 364 280 304 333 321 150 B737 47 10,000 3.70 2,703 80 200 54 334 280 364 347 322 150 B737 47 20,000 3.70 5,405 75 150 123 348 295 348 348 323 150 B737 47 20,000 3.70 5,405 60 100 204 364 295 324 345 324 150 B737 47 20,000 3.70 5,405 100 200 32 332 295 382 357

Appendix 6 Damage Indicators with Depth


A6 - 1

APPENDIX 6. DAMAGE INDICATORS WITH DEPTH

B737 at mass of 78.5 t and tyre pressure of 1.39 MPa

B&B Base on CBR 6 Subgrade

Under Wheel Centre of Gear Depth

(m) Strain (uE)

Stress (MPa)

Deflection(mm)

Strain (uE)

Stress (MPa)

Deflection(mm)

0.00 836 1.360 2.320 -186 0.000 1.906 0.05 1197 1.339 2.269 -202 0.002 1.916 0.10 1350 1.237 2.220 -185 0.017 1.925 0.15 1293 1.064 2.137 -129 0.046 1.933 0.20 1134 0.871 2.076 -54 0.078 1.938 0.25 755 0.568 2.000 75 0.140 1.947 0.30 714 0.469 1.962 149 0.150 1.941 0.35 616 0.384 1.928 193 0.152 1.932 0.40 537 0.314 1.900 227 0.149 1.922 0.45 478 0.255 1.874 253 0.142 1.910 0.50 444 0.210 1.852 274 0.133 1.897 0.55 495 0.174 1.825 351 0.122 1.879 0.60 445 0.144 1.802 352 0.110 1.862 0.65 411 0.120 1.780 356 0.099 1.844 0.70 392 0.100 1.760 363 0.089 1.826 0.75 392 0.086 1.741 375 0.081 1.808 0.80 525 0.075 1.714 521 0.074 1.781 0.85 494 0.067 1.689 506 0.067 1.755 0.90 475 0.060 1.664 497 0.061 1.730 0.95 467 0.054 1.641 497 0.057 1.706 1.00 473 0.050 1.617 505 0.053 1.681 1.05 778 0.047 1.577 837 0.051 1.638 1.10 734 0.045 1.539 794 0.048 1.597 1.15 695 0.042 1.504 754 0.046 1.558 1.20 661 0.040 1.470 717 0.043 1.521 1.25 629 0.039 1.437 683 0.041 1.486 1.30 600 0.037 1.407 652 0.040 1.453 1.35 573 0.035 1.377 622 0.038 1.421 1.40 549 0.034 1.349 595 0.036 1.391 1.45 526 0.032 1.322 520 0.035 1.362 1.50 505 0.031 1.297 546 0.033 1.334





B&B Base on CBR 15 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection (μm)

0.00 942 1.360 1.398 -90 0.000 0.959 0.05 1281 1.341 1.342 -123 0.003 0.964 0.10 1418 1.244 1.273 -123 0.018 0.970 0.15 1349 1.078 1.203 -84 0.048 0.976 0.20 1178 0.893 1.140 -20 0.083 0.978 0.25 780 0.594 1.062 10 0.148 0.986 0.30 681 0.498 1.025 146 0.162 0.979 0.35 587 0.416 0.993 180 0.168 0.971 0.40 507 0.348 0.966 204 0.168 0.962 0.45 442 0.292 0.943 219 0.164 0.951 0.50 393 0.246 0.922 229 0.156 0.940 0.55 386 0.208 0.901 260 0.147 0.927 0.60 343 0.177 0.883 259 0.136 0.914 0.65 311 0.151 0.867 257 0.126 0.901 0.70 288 0.130 0.852 256 0.116 0.888 0.75 276 0.114 0.838 257 0.106 0.875 0.80 335 0.101 0.820 327 0.098 0.859 0.85 312 0.090 0.804 316 0.090 0.843 0.90 296 0.081 0.789 308 0.083 0.827 0.95 288 0.074 0.774 305 0.077 0.812 1.00 287 0.068 0.760 306 0.073 0.796 1.05 412 0.064 0.739 444 0.069 0.774 1.10 388 0.060 0.719 421 0.065 0.752 1.15 366 0.057 0.700 400 0.062 0.732 1.20 347 0.054 0.682 380 0.058 0.712 1.25 329 0.051 0.665 361 0.055 0.694 1.30 313 0.049 0.650 344 0.053 0.676 1.35 298 0.046 0.634 327 0.050 0.659 1.40 285 0.044 0.619 312 0.048 0.643 1.45 272 0.042 0.605 298 0.046 0.628 1.50 260 0.040 0.592 285 0.044 0.613



A6 - 3


B&B Sub-base on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection(μm)

0.00 2397 1.360 3.665 -241 0.000 2.518 0.05 3292 1.340 3.521 -324 0.003 2.532 0.10 3656 1.241 3.345 -317 0.019 2.549 0.15 3488 1.072 3.164 -207 0.049 2.562 0.20 2309 0.696 2.906 117 0.127 2.597 0.25 2114 0.585 2.793 293 0.149 2.586 0.30 1830 0.489 2.694 417 0.163 2.569 0.35 1585 0.408 2.609 509 0.169 2.545 0.40 1387 0.341 2.535 571 0.169 2.518 0.45 1308 0.287 2.465 670 0.164 2.486 0.50 1143 0.242 2.404 691 0.157 2.452 0.55 1017 0.205 2.350 701 0.148 2.417 0.60 929 0.175 2.301 707 0.138 2.382 0.65 972 0.151 2.250 811 0.128 2.340 0.70 886 0.131 2.204 793 0.118 2.300 0.75 825 0.115 2.161 780 0.108 2.261 0.80 790 0.102 2.121 774 0.100 2.222 0.85 943 0.092 2.072 957 0.093 2.174 0.90 889 0.083 2.026 925 0.086 2.127 0.95 853 0.076 1.982 903 0.080 2.081 1.00 835 0.071 1.940 893 0.076 2.036 1.05 1071 0.066 1.885 1157 0.071 1.977 1.10 1008 0.062 1.833 1096 0.068 1.920 1.15 952 0.059 1.784 1040 0.064 1.867 1.20 901 0.056 1.738 988 0.061 1.816 1.25 854 0.053 1.694 939 0.058 1.768 1.30 812 0.050 1.652 893 0.055 1.722 1.35 773 0.048 1.613 850 0.052 1.679 1.40 738 0.046 1.575 810 0.050 1.637 1.45 704 0.043 1.539 773 0.047 1.598 1.50 674 0.042 1.504 738 0.045 1.560





B&B Sub-base on CBR 15 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection (μm)

0.00 2503 1.360 2.482 -73 0.000 1.331 0.05 3342 1.342 2.335 -181 0.003 1.337 0.10 3672 1.246 2.157 -199 0.020 1.347 0.15 3490 1.082 1.976 -112 0.052 1.355 0.20 2322 0.710 1.720 188 0.131 1.385 0.25 2062 0.603 1.610 328 0.156 1.372 0.30 1789 0.510 1.514 434 0.173 1.353 0.35 1546 0.432 1.431 510 0.182 1.329 0.40 1340 0.368 1.359 559 0.185 1.303 0.45 1190 0.315 1.295 604 0.183 1.273 0.50 1038 0.271 1.239 616 0.178 1.242 0.55 915 0.234 1.190 616 0.171 1.212 0.60 816 0.205 1.147 608 0.162 1.181 0.65 770 0.180 1.107 627 0.153 1.149 0.70 695 0.160 1.070 607 0.144 1.118 0.75 635 0.143 1.037 587 0.135 1.089 0.80 590 0.128 1.006 569 0.126 1.060 0.85 609 0.117 0.975 610 0.118 1.028 0.90 568 0.107 0.945 585 0.110 0.999 0.95 537 0.098 0.918 564 0.104 0.970 1.00 514 0.091 0.891 547 0.098 0.942 1.05 535 0.085 0.864 576 0.092 0.913 1.10 503 0.080 0.838 548 0.087 0.885 1.15 474 0.075 0.813 520 0.082 0.858 1.20 448 0.071 0.790 494 0.078 0.833 1.25 425 0.069 0.769 470 0.074 0.808 1.30 403 0.064 0.748 447 0.070 0.786 1.35 383 0.060 0.728 425 0.066 0.764 1.40 365 0.057 0.709 405 0.063 0.743 1.45 348 0.054 0.692 385 0.060 0.723 1.50 332 0.052 0.675 367 0.057 0.704



A6 - 5


B737 Pavement with 50 mm of 1500 MPa Asphalt

on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection(μm)

0.00 -728 1.360 -332 0.000 -728 1.360 0.05 -331 1.270 -297 0.040 -331 1.270 0.10 2232 1.117 -96 0.047 2232 1.117 0.15 2004 0.894 15 0.075 2004 0.894 0.20 1737 0.682 145 0.108 1737 0.682 0.25 1606 0.522 247 0.130 1606 0.522 0.30 2007 0.414 512 0.139 2007 0.414 0.35 1659 0.330 651 0.142 1659 0.330 0.40 1411 0.265 705 0.141 1411 0.265 0.45 1435 0.218 862 0.135 1435 0.218 0.50 1244 0.181 870 0.128 1244 0.181 0.55 1108 0.153 872 0.120 1108 0.153 0.60 1023 0.131 874 0.112 1023 0.131 0.65 1201 0.114 1097 0.105 1201 0.114 0.70 1106 0.101 1066 0.098 1106 0.101 0.75 1042 0.090 1043 0.096 1042 0.090 0.80 1010 0.083 1032 0.086 1010 0.083 0.85 1269 0.077 1322 0.081 1269 0.077 0.90 1182 0.072 1252 0.077 1182 0.072 0.95 1106 0.068 1186 0.072 1106 0.068 1.00 1038 0.064 1123 0.068 1038 0.064 1.05 978 0.060 1065 0.065 978 0.060 1.10 924 0.057 1011 0.061 924 0.057 1.15 876 0.054 960 0.058 876 0.054 1.20 831 0.051 912 0.055 831 0.051 1.25 790 0.048 868 0.053 790 0.048 1.30 753 0.046 827 0.050 753 0.046 1.35 719 0.044 788 0.048 719 0.044 1.40 687 0.042 752 0.045 687 0.042 1.45 657 0.040 718 0.043 657 0.040 1.50 629 0.038 687 0.041 629 0.038






on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection (μm)

0.00 -732 1.360 -167 0.000 -732 1.360 0.05 441 1.260 -197 0.027 441 1.260 0.10 2249 1.057 -21 0.045 2249 1.057 0.15 1949 0.828 96 0.078 1949 0.828 0.20 1667 0.626 217 0.109 1667 0.626 0.25 1530 0.478 308 0.128 1530 0.478 0.30 1887 0.378 609 0.135 1887 0.378 0.35 1564 0.302 671 0.136 1564 0.302 0.40 1333 0.243 710 0.133 1333 0.243 0.45 1352 0.200 849 0.127 1352 0.200 0.50 1174 0.166 847 0.120 1174 0.166 0.55 1047 0.140 843 0.112 1047 0.140 0.60 967 0.120 840 0.104 967 0.120 0.65 1129 0.105 1042 0.097 1129 0.105 0.70 1040 0.093 1009 0.090 1040 0.093 0.75 980 0.084 985 0.084 980 0.084 0.80 948 0.077 971 0.079 948 0.077 0.85 1194 0.071 1246 0.075 1194 0.071 0.90 1111 0.066 1178 0.071 1111 0.066 0.95 1038 0.063 1113 0.066 1038 0.063 1.00 975 0.060 1052 0.063 975 0.060 1.05 918 0.056 996 0.060 918 0.056 1.10 867 0.054 946 0.056 867 0.054 1.15 820 0.051 897 0.054 820 0.051 1.20 778 0.048 852 0.051 778 0.048 1.25 740 0.046 810 0.048 740 0.046 1.30 704 0.044 771 0.046 704 0.044 1.35 672 0.042 735 0.044 672 0.042 1.40 642 0.040 701 0.042 642 0.040 1.45 614 0.038 669 0.040 614 0.038 1.50 588 0.035 640 0.038 588 0.035



A6 - 7



on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection(μm)

0.00 -417 1.360 -324 0.000 -417 1.360 0.05 82 1.280 -251 0.014 82 1.280 0.10 387 1.055 -146 0.054 387 1.055 0.15 598 0.765 -29 0.102 598 0.765 0.20 918 0.579 60 0.124 918 0.579 0.25 1298 0.442 356 0.135 1298 0.442 0.30 1074 0.338 434 0.140 1074 0.338 0.35 935 0.261 495 0.139 935 0.261 0.40 886 0.208 541 0.136 886 0.208 0.45 1163 0.174 833 0.126 1163 0.174 0.50 1026 0.146 830 0.117 1026 0.146 0.55 932 0.125 814 0.108 932 0.125 0.60 877 0.109 809 0.101 877 0.109 0.65 1022 0.097 993 0.094 1022 0.097 0.70 951 0.087 960 0.087 951 0.087 0.75 904 0.079 937 0.081 904 0.079 0.80 881 0.073 924 0.076 881 0.073 0.85 1126 0.068 1199 0.072 1126 0.068 0.90 1054 0.064 1134 0.068 1054 0.064 0.95 990 0.060 1074 0.065 990 0.060 1.00 934 0.056 1017 0.061 934 0.056 1.05 883 0.053 965 0.058 883 0.053 1.10 836 0.051 916 0.055 836 0.051 1.15 794 0.048 871 0.052 794 0.048 1.20 756 0.046 828 0.050 756 0.046 1.25 720 0.044 789 0.047 720 0.044 1.30 688 0.042 752 0.045 688 0.042 1.35 657 0.040 718 0.043 657 0.040 1.40 629 0.038 686 0.041 629 0.038 1.45 603 0.036 656 0.039 603 0.036 1.50 578 0.035 628 0.037 578 0.035






on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Deflection(μm)

Strain (με)

Stress (MPa)

Deflection (μm)

0.00 -371 1.360 -255 0.000 -371 1.360 0.05 -76 1.239 -160 0.020 -76 1.239 0.10 -13 0.929 -52 0.069 -13 0.929 0.15 304 0.564 59 0.124 304 0.564 0.20 560 0.371 153 0.142 560 0.371 0.25 887 0.292 414 0.140 887 0.292 0.30 765 0.231 452 0.135 765 0.231 0.35 691 0.185 484 0.128 691 0.185 0.40 668 0.153 512 0.119 668 0.153 0.45 895 0.131 752 0.111 895 0.131 0.50 811 0.113 738 0.102 811 0.113 0.55 753 0.099 723 0.094 753 0.099 0.60 719 0.088 715 0.087 719 0.088 0.65 850 0.079 871 0.081 850 0.079 0.70 802 0.072 841 0.075 802 0.072 0.75 769 0.066 819 0.070 769 0.066 0.80 753 0.062 808 0.066 753 0.062 0.85 971 0.058 1050 0.063 971 0.058 0.90 914 0.055 995 0.059 914 0.055 0.95 864 0.052 943 0.056 864 0.052 1.00 819 0.049 896 0.053 819 0.049 1.05 778 0.047 851 0.051 778 0.047 1.10 740 0.045 810 0.048 740 0.045 1.15 705 0.042 771 0.046 705 0.042 1.20 673 0.041 735 0.044 673 0.041 1.25 643 0.039 702 0.042 643 0.039 1.30 616 0.037 671 0.040 616 0.037 1.35 591 0.035 642 0.038 591 0.035 1.40 567 0.034 614 0.037 567 0.034 1.45 544 0.033 589 0.035 544 0.033 1.50 523 0.031 565 0.033 523 0.031



A6 - 9

50 t Macro at mass of 15 t and tyre pressure of 0.4 MPa

1000 mm of B&B Base on CBR 6 Subgrade


(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 260 0.400 -36 0.000 0.05 377 0.390 -36 0.000 0.10 403 0.346 -34 0.001 0.15 357 0.281 -28 0.004 0.20 292 0.217 -20 0.007 0.25 187 0.138 -26 0.001 0.30 171 0.111 -8 0.008 0.35 143 0.089 7 0.013 0.40 122 0.071 19 0.016 0.45 106 0.057 28 0.018 0.50 97 0.046 36 0.019 0.55 107 0.038 52 0.019 0.60 96 0.032 56 0.018 0.65 88 0.026 60 0.017 0.70 84 0.022 64 0.017 0.75 84 0.019 68 0.016 0.80 112 0.017 100 0.015 0.85 110 0.016 100 0.014 0.90 106 0.014 100 0.013 0.95 105 0.013 102 0.013 1.00 107 0.013 104 0.012 1.05 180 0.011 178 0.012 1.10 172 0.011 172 0.011 1.15 165 0.010 167 0.011 1.20 159 0.010 161 0.011 1.25 153 0.010 156 0.010 1.30 148 0.009 152 0.010 1.35 144 0.009 147 0.010 1.40 139 0.009 143 0.009 1.45 135 0.009 139 0.009 1.50 131 0.009 135 0.009







(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 324 0.500 -46 0.000 0.05 470 0.488 -46 0.000 0.10 503 0.434 -43 0.002 0.15 448 0.352 -36 0.005 0.20 366 0.273 -25 0.009 0.25 235 0.173 -34 0.010 0.30 215 0.140 -11 0.001 0.35 180 0.112 8 0.016 0.40 153 0.090 24 0.021 0.45 134 0.072 36 0.023 0.50 122 0.059 45 0.024 0.55 135 0.048 66 0.024 0.60 121 0.040 72 0.023 0.65 111 0.034 77 0.022 0.70 106 0.028 81 0.021 0.75 106 0.025 86 0.020 0.80 146 0.022 127 0.019 0.85 139 0.020 126 0.018 0.90 135 0.018 127 0.017 0.95 133 0.017 129 0.016 1.00 135 0.016 132 0.015 1.05 227 0.015 225 0.015 1.10 218 0.014 218 0.014 1.15 209 0.014 211 0.014 1.20 201 0.013 204 0.013 1.25 194 0.013 198 0.013 1.30 188 0.012 192 0.013 1.35 182 0.012 186 0.012 1.40 176 0.012 181 0.012 1.45 171 0.011 176 0.011 1.50 166 0.011 171 0.011



A6 - 11




(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 391 0.600 -53 0.000 0.05 568 0.585 -53 0.000 0.10 604 0.517 -50 0.002 0.15 533 0.418 -42 0.006 0.20 433 0.322 -29 0.011 0.25 280 0.205 -38 0.002 0.30 254 0.165 -12 0.012 0.35 212 0.132 10 0.019 0.40 180 0.105 28 0.024 0.45 156 0.084 42 0.027 0.50 143 0.068 52 0.028 0.55 158 0.056 76 0.027 0.60 141 0.047 83 0.027 0.65 129 0.039 89 0.026 0.70 123 0.033 94 0.025 0.75 123 0.029 100 0.023 0.80 170 0.025 147 0.022 0.85 161 0.023 146 0.021 0.90 156 0.021 147 0.020 0.95 154 0.019 149 0.019 1.00 156 0.018 153 0.018 1.05 263 0.017 261 0.017 1.10 252 0.017 252 0.017 1.15 242 0.016 244 0.016 1.20 233 0.015 237 0.016 1.25 225 0.015 229 0.015 1.30 218 0.014 222 0.015 1.35 211 0.014 216 0.014 1.40 204 0.013 209 0.014 1.45 198 0.013 203 0.013 1.50 193 0.013 198 0.013







(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 455 0.700 -63 0.000 0.05 661 0.683 -63 0.000 0.10 705 0.605 -59 0.002 0.15 624 0.489 -49 0.007 0.20 508 0.379 -35 0.013 0.25 327 0.240 -45 0.002 0.30 298 0.193 -14 0.014 0.35 249 0.155 12 0.023 0.40 211 0.124 33 0.028 0.45 184 0.099 49 0.031 0.50 168 0.081 62 0.033 0.55 186 0.067 90 0.032 0.60 166 0.055 98 0.031 0.65 153 0.046 105 0.030 0.70 146 0.039 111 0.029 0.75 146 0.034 118 0.027 0.80 200 0.030 173 0.026 0.85 190 0.027 173 0.024 0.90 184 0.025 174 0.023 0.95 182 0.023 176 0.022 1.00 185 0.021 180 0.021 1.05 311 0.020 308 0.020 1.10 280 0.019 298 0.020 1.15 286 0.018 289 0.019 1.20 276 0.017 279 0.018 1.25 266 0.017 271 0.018 1.30 257 0.016 263 0.017 1.35 249 0.016 255 0.017 1.40 241 0.015 247 0.016 1.45 234 0.015 240 0.016 1.50 228 0.015 234 0.015



A6 - 13




(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 519 0.800 -72 0.000 0.05 754 0.781 -72 0.000 0.10 806 0.692 -68 0.003 0.15 714 0.561 -57 0.008 0.20 583 0.434 -40 0.015 0.25 375 0.276 -53 0.018 0.30 342 0.221 -17 0.002 0.35 287 0.178 13 0.026 0.40 243 0.143 38 0.033 0.45 212 0.114 57 0.038 0.50 194 0.093 71 0.037 0.55 214 0.077 104 0.036 0.60 191 0.063 113 0.035 0.65 176 0.053 121 0.033 0.70 168 0.045 129 0.031 0.75 168 0.039 136 0.030 0.80 231 0.035 200 0.028 0.85 219 0.031 200 0.027 0.90 212 0.028 201 0.025 0.95 210 0.026 203 0.024 1.00 213 0.025 208 0.024 1.05 359 0.024 356 0.023 1.10 343 0.023 344 0.022 1.15 330 0.022 333 0.022 1.20 318 0.021 322 0.021 1.25 307 0.020 312 0.019 1.30 297 0.019 303 0.090 1.35 287 0.019 294 0.018 1.40 278 0.018 285 0.018 1.45 270 0.018 277 0.017 1.50 263 0.017 270 0.017







(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 586 0.900 -79 0.000 0.05 852 0.878 -80 0.000 0.10 906 0.776 -75 0.003 0.15 800 0.626 -62 0.008 0.20 650 0.484 -44 0.016 0.25 419 0.308 -57 0.029 0.30 382 0.247 -18 0.002 0.35 319 0.198 15 0.029 0.40 269 0.158 42 0.036 0.45 234 0.127 63 0.040 0.50 214 0.103 79 0.042 0.55 237 0.085 114 0.041 0.60 211 0.070 124 0.040 0.65 194 0.058 133 0.038 0.70 185 0.049 141 0.037 0.75 185 0.043 150 0.035 0.80 255 0.038 220 0.033 0.85 241 0.034 220 0.031 0.90 234 0.031 221 0.029 0.95 231 0.029 224 0.028 1.00 235 0.027 229 0.027 1.05 395 0.026 391 0.026 1.10 378 0.025 379 0.025 1.15 363 0.024 366 0.024 1.20 350 0.023 355 0.023 1.25 337 0.022 344 0.023 1.30 326 0.021 333 0.022 1.35 316 0.021 323 0.022 1.40 306 0.020 314 0.021 1.45 297 0.019 305 0.020 1.50 289 0.019 297 0.019



A6 - 15




(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 653 1.000 -86 0.000 0.05 949 0.975 -87 0.000 0.10 1007 0.859 -81 0.003 0.15 885 0.692 -68 0.009 0.20 717 0.532 -48 0.017 0.25 464 0.339 -61 0.004 0.30 421 0.272 -18 0.020 0.35 350 0.218 17 0.032 0.40 296 0.174 46 0.039 0.45 257 0.139 68 0.044 0.50 234 0.112 86 0.045 0.55 259 0.093 125 0.045 0.60 231 0.077 136 0.044 0.65 212 0.064 145 0.042 0.70 202 0.054 154 0.040 0.75 202 0.047 163 0.038 0.80 278 0.042 240 0.036 0.85 264 0.037 240 0.034 0.90 255 0.034 241 0.032 0.95 253 0.031 244 0.031 1.00 256 0.030 250 0.030 1.05 431 0.028 427 0.029 1.10 413 0.027 413 0.028 1.15 396 0.026 400 0.027 1.20 382 0.025 387 0.026 1.25 368 0.024 375 0.026 1.30 356 0.023 364 0.025 1.35 345 0.023 353 0.024 1.40 334 0.022 343 0.023 1.45 324 0.022 333 0.022 1.50 315 0.021 324 0.022







(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 717 1.100 -96 0.000 0.05 1042 1.073 -96 0.001 0.10 1108 0.947 -91 0.004 0.15 975 0.764 -76 0.010 0.20 792 0.589 -53 0.019 0.25 511 0.375 -68 0.004 0.30 465 0.301 -21 0.022 0.35 398 0.241 18 0.035 0.40 328 0.192 50 0.044 0.45 285 0.154 76 0.049 0.50 260 0.125 95 0.050 0.55 287 0.103 139 0.050 0.60 256 0.085 151 0.049 0.65 235 0.071 161 0.047 0.70 225 0.060 171 0.044 0.75 224 0.052 181 0.042 0.80 309 0.046 267 0.040 0.85 293 0.042 266 0.038 0.90 283 0.038 268 0.036 0.95 281 0.035 271 0.034 1.00 285 0.033 277 0.033 1.05 479 0.031 474 0.031 1.10 459 0.030 459 0.030 1.15 440 0.029 444 0.029 1.20 424 0.028 430 0.028 1.25 409 0.027 417 0.027 1.30 396 0.026 404 0.027 1.35 383 0.025 392 0.026 1.40 371 0.024 381 0.025 1.45 360 0.023 370 0.024 1.50 350 0.022 360 0.023



A6 - 17




(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 784 1.200 -103 0.000 0.05 1140 1.170 -104 0.001 0.10 1209 1.030 -97 0.004 0.15 1061 0.829 -81 0.011 0.20 858 0.637 -58 0.021 0.25 556 0.406 -22 0.005 0.30 504 0.326 -22 0.024 0.35 420 0.260 20 0.038 0.40 354 0.208 55 0.047 0.45 307 0.166 82 0.052 0.50 280 0.134 103 0.054 0.55 309 0.111 149 0.054 0.60 276 0.092 162 0.054 0.65 253 0.076 173 0.052 0.70 242 0.064 184 0.050 0.75 241 0.056 195 0.048 0.80 332 0.050 287 0.042 0.85 315 0.045 287 0.040 0.90 305 0.041 288 0.039 0.95 302 0.038 292 0.036 1.00 306 0.035 298 0.035 1.05 515 0.034 510 0.034 1.10 493 0.032 493 0.033 1.15 473 0.031 477 0.032 1.20 456 0.030 462 0.030 1.25 440 0.029 448 0.029 1.30 425 0.028 434 0.029 1.35 412 0.027 421 0.028 1.40 399 0.026 409 0.027 1.45 387 0.025 398 0.026 1.50 376 0.024 387 0.025







(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 848 1.300 -113 0.000 0.05 1233 1.267 -113 0.001 0.10 1309 1.118 -106 0.004 0.15 1151 0.901 -89 0.012 0.20 933 0.693 -63 0.022 0.25 603 0.442 -50 0.005 0.30 548 0.355 -24 0.026 0.35 457 0.284 22 0.041 0.40 386 0.226 59 0.051 0.45 335 0.181 89 0.057 0.50 306 0.147 112 0.059 0.55 338 0.121 163 0.059 0.60 301 0.100 177 0.057 0.65 277 0.083 190 0.055 0.70 264 0.070 201 0.052 0.75 264 0.061 213 0.049 0.80 363 0.054 313 0.047 0.85 334 0.049 313 0.044 0.90 333 0.044 314 0.042 0.95 330 0.041 319 0.040 1.00 334 0.039 326 0.038 1.05 563 0.037 557 0.037 1.10 539 0.035 539 0.036 1.15 517 0.034 522 0.034 1.20 498 0.033 505 0.033 1.25 481 0.032 490 0.032 1.30 465 0.031 475 0.031 1.35 450 0.030 461 0.030 1.40 436 0.029 447 0.029 1.45 423 0.028 435 0.028 1.50 411 0.027 423 0.027



A6 - 19




(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 915 1.400 -120 0.000 0.05 1331 1.364 -120 0.001 0.10 1420 1.201 -113 0.004 0.15 1236 0.966 -95 0.013 0.20 1000 0.742 -67 0.024 0.25 648 0.474 -83 0.006 0.30 587 0.380 -25 0.028 0.35 489 0.303 24 0.044 0.40 412 0.242 63 0.055 0.45 358 0.193 95 0.061 0.50 326 0.156 119 0.063 0.55 360 0.129 173 0.062 0.60 321 0.106 188 0.061 0.65 295 0.089 201 0.058 0.70 281 0.075 214 0.055 0.75 280 0.065 227 0.052 0.80 386 0.058 333 0.050 0.85 366 0.052 333 0.047 0.90 354 0.047 335 0.045 0.95 351 0.044 339 0.042 1.00 356 0.041 347 0.041 1.05 590 0.039 593 0.039 1.10 573 0.038 574 0.038 1.15 551 0.036 555 0.037 1.20 530 0.035 538 0.035 1.25 511 0.034 521 0.034 1.30 494 0.032 505 0.033 1.35 474 0.031 490 0.032 1.40 464 0.030 476 0.031 1.45 451 0.029 462 0.030 1.50 438 0.028 450 0.029




50 t Test Rig at mass of 50 t and tyre pressure of 1.65 MPa



(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 1027 1.650 -170 0.000 0.05 1451 1.628 -162 0.001 0.10 1649 1.516 -150 0.003 0.15 1606 1.322 -130 0.009 0.20 1433 1.099 -100 0.017 0.25 910 0.686 -179 0.004 0.30 874 0.574 -115 0.002 0.35 763 0.475 -45 0.014 0.40 609 0.390 14 0.033 0.45 598 0.319 65 0.047 0.50 553 0.262 105 0.056 0.55 612 0.216 178 0.062 0.60 545 0.178 213 0.065 0.65 497 0.147 244 0.066 0.70 469 0.122 271 0.066 0.75 465 0.104 294 0.065 0.80 619 0.090 440 0.063 0.85 575 0.079 451 0.061 0.90 547 0.070 461 0.059 0.95 535 0.063 473 0.057 1.00 540 0.058 485 0.055 1.05 887 0.055 832 0.053 1.10 836 0.052 808 0.052 1.15 791 0.049 783 0.050 1.20 750 0.047 759 0.048 1.25 714 0.045 735 0.046 1.30 682 0.043 711 0.045 1.35 653 0.041 689 0.043 1.40 626 0.039 666 0.042 1.45 601 0.037 645 0.040 1.50 579 0.036 624 0.039



A6 - 21

200 t Supercompactor at mass of 200 t and

tyre pressure of 1.65 MPa



(m) Strain (με)

Stress (MPa)

Strain (με)

Stress (MPa)

0.00 279 1.000 -414 0.000 0.05 491 0.994 -421 0.003 0.10 660 0.969 -385 0.024 0.15 776 0.924 -300 0.061 0.20 842 0.860 -189 0.103 0.25 1029 0.822 -28 0.171 0.30 1054 0.764 92 0.191 0.35 974 0.658 182 0.204 0.40 908 0.564 262 0.211 0.45 862 0.483 333 0.214 0.50 843 0.416 395 0.212 0.55 1000 0.361 564 0.206 0.60 948 0.314 609 0.200 0.65 916 0.274 653 0.192 0.70 909 0.242 697 0.184 0.75 928 0.218 741 0.177 0.80 1316 0.199 1114 0.169 0.85 1277 0.183 1126 0.163 0.90 1256 0.170 1142 0.156 0.95 1258 0.159 1164 0.151 1.00 1279 0.151 1193 0.146 1.05 2178 0.146 2070 0.142 1.10 2100 0.140 2021 0.138 1.15 2028 0.135 1972 0.134 1.20 1962 0.130 1925 0.130 1.25 1902 0.127 1879 0.127 1.30 1845 0.123 1834 0.123 1.35 1792 0.119 1790 0.120 1.40 1743 0.115 1748 0.117 1.45 1696 0.112 1707 0.113 1.50 1651 0.109 1668 0.110




Appendix 7 Proof Rolling Regimes


A7 - 1

APPENDIX 7. PROOF ROLLING REGIMES


Depth (m)

Pavement structure

Aircraft Stress (MPa)

Roller Stress (MPa)

Roller configuration

0.00 Asphalt 1.360 0.05 1.339 1.400 0.10 1.237 1.364 0.15 1.064 1.201 0.20 0.871 0.966 0.25

Base

0.568 0.742

50 t at 1.4 MPa

0.25 0.568 1.000 0.30 0.469 0.975 0.35 0.384 0.859 0.40 0.314 0.692 0.45 0.255 0.532 0.50 0.210 0.339 0.55 0.174 0.272 0.60 0.144 0.218 0.65 0.120 0.174 0.70 0.100 0.139 0.75 0.086 0.112 0.80

Sub-base

0.075 0.093

36 t at 1.0 MPa

0.80 0.075 0.600 0.85 0.067 0.585 0.90 0.060 0.517 0.95 0.054 0.418 1.00 0.050 0.322 1.05 0.047 0.205 1.10 0.045 0.165 1.15 0.042 0.132 1.20 0.040 0.105 1.25 0.039 0.084 1.30 0.037 0.068 1.35 0.035 0.056 1.40 0.034 0.047 1.45 0.032 0.039 1.50

Subgrade

0.031 0.033

22 t at 0.6 MPa




B767 at mass of 180 t and tyre pressure of 1.24 MPa

Depth (m)

Pavement structure


Roller Stress (MPa)


0.00 Asphalt 1.240 0.05 1.225 1.400 0.10 1.153 1.364 0.15 1.021 1.201 0.20 0.864 0.966 0.25

Base 1

0.573 0.742

50 t at 1.4 MPa

0.25 0.573 0.600 0.30 0.482 0.585 0.35 0.402 0.517 0.40 0.333 0.418 0.45

Base 2

0.276 0.322

22 t at 0.6 MPa

0.45 0.276 0.700 0.50 0.230 0.683 0.55 0.193 0.605 0.60 0.162 0.489 0.65 0.137 0.379 0.70 0.117 0.240 0.75 0.103 0.193 0.80 0.092 0.155 0.85 0.083 0.124 0.90 0.076 0.099 0.95

Sub-base

0.070 0.081

26 t at 0.7 MPa

0.95 0.070 0.500 1.00 0.066 0.488 1.05 0.064 0.434 1.10 0.061 0.352 1.15 0.059 0.273 1.20 0.057 0.173 1.25 0.055 0.140 1.30 0.053 0.112 1.35 0.051 0.090 1.40 0.049 0.072 1.45 0.048 0.059 1.50

Subgrade

0.047 0.048

19 t at 0.5 MPa



A7 - 3

B747 at mass of 397 t and tyre pressure of 1.38 MPa

Depth (m)

Pavement structure


Roller Stress (MPa)


0.00 Asphalt 1.380 0.05 1.364 1.400 0.10 1.282 1.364 0.15 1.134 1.201 0.20 0.958 0.966 0.25

Base 1

0.638 0.742

50 t at 1.4 MPa

0.25 0.638 0.700 0.30 0.536 0.683 0.35 0.446 0.605 0.40 0.369 0.489 0.45

Base 2

0.305 0.379

26 t at 0.7 MPa

0.45 0.305 0.600 0.50 0.254 0.585 0.55 0.213 0.517 0.60 0.179 0.418 0.65 0.151 0.322 0.70 0.129 0.205 0.75 0.113 0.165 0.80 0.101 0.132 0.85

Sub-base

0.091 0.105

22 t at 0.6 MPa

0.85 0.091 0.800 0.90 0.083 0.781 0.95 0.077 0.692 1.00 0.073 0.561 1.05 0.070 0.434 1.10 0.067 0.276 1.15 0.064 0.221 1.20 0.062 0.178 1.25 0.060 0.143 1.30 0.058 0.114 1.35 0.056 0.093 1.40 0.054 0.077 1.45 0.053 0.063 1.50

Subgrade

0.052 0.053

30 t at 0.8 MPa




F111 at mass of 50.8 t and tyre pressure of 1.48 MPa

Depth (m)

Pavement structure


Roller Stress (MPa)


0.00 Asphalt 1.480 0.05 1.461 1.400 0.10 1.368 1.364 0.15 1.203 1.201 0.20 1.009 0.966 0.25

Base

0.653 0.742

50 t at 1.4 MPa

0.25 0.653 0.800 0.30 0.545 0.781 0.35 0.450 0.692 0.40 0.368 0.561 0.45 0.299 0.434 0.50 0.244 0.276 0.55 0.200 0.221 0.60 0.162 0.178 0.65 0.131 0.143 0.70 0.107 0.114 0.75 0.089 0.093 0.80

Sub-base

0.076 0.077

30 t at 0.8 MPa

0.80 0.076 0.500 0.85 0.065 0.488 0.90 0.056 0.434 0.95 0.049 0.352 1.00 0.044 0.273 1.05 0.041 0.173 1.10 0.038 0.140 1.15 0.036 0.112 1.20 0.033 0.090 1.25 0.031 0.072 1.30 0.030 0.059 1.35 0.028 0.048 1.40 0.027 0.040 1.45 0.025 0.034 1.50

Subgrade

0.024 0.028

19 t at 0.5 MPa

Bibliography


B - 1

BIBLIOGRAPHY

Ahlvin, R. G., et al. (1971). Multiple-wheel heavy gear load pavement tests. Technical Report S71-17. Volume 1. US Army Corps of Engineers. Waterways Experiment Station. Vicksburg, USA.

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