H I PAV E 5 . 0
User Manual
MINCAD Systems Pty. Ltd.
P.O. Box 2114, 2114, Richmond South, South, Vic., 3121 Australia Australia Tel.:(03) 9427 1085 Intl. +613 9427 1085 Fax:(03) 9428 1197 Intl. +613 9428 1197 Email:
[email protected] [email protected] u Web: http://www.mincad.com.au http://www.mincad.com.au
April 2009 © MINCAD Systems Pty. Ltd.
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Contents Summary
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HIPAVE HIPAVE End User Licence Agreement
7
Introduction
9
Background Background .................................................................................................. ....................................................................................................................................9 ..................................9 Realistic Modelling with HIPAVE...................................................................................... HIPAVE..................................................................................................11 ............11 Material Modelling Modelling ........................................................................................ ..............................................................................................................12 ......................12 Modelling of Multiple Wheels and Axle Groups .................................................................14 Nature of Damage Pulses..................................................................................................14
Overview
15
How HIPAVE handles Traffic Distributions Distributions ..................................................................................1 ..................................................................................15 5 Cumulative Damage Concept ..................................................................................... ......................................................................................................16 .................16 Lateral Vehicle Wander......................................................................................................... Wander................................................................................................................18 .......18 Material Performance Performance........................................................................................ ...................................................................................................................18 ...........................18 Traffic and Loading............................................................................................... Loading.......................................................................................................................19 ........................19 How Vehicle characteristics are defined ......................................................................................1 ......................................................................................19 9 Standard Vehicle Library.......................................... Library....................................................................................................19 ..........................................................19 Unequal Axle Loads ...................................................................................... ...........................................................................................................20 .....................20 Equal Axle Loads ............................................................................................ ...............................................................................................................21 ...................21 Coordinate Coordinate System for Vehicles............................. Vehicles.........................................................................................22 ............................................................22 Methods for handling Damage Pulses Pulses .........................................................................................2 .........................................................................................24 4 Dynamic Load Factors Factors .............................................................................................. .................................................................................................................25 ...................25 Container Weight Distributions.....................................................................................................2 Distributions.....................................................................................................26 6 Automatic Thickness Design ............................................................................... ........................................................................................................26 .........................26 Cross-anisotropy Cross-anisotropy and Isotropy in Pavement Materials ................................................................27 Cost Calculation ............................................................................................ ...........................................................................................................................28 ...............................28 Automatic Parametric Parametric Analysis ...................................................................................... ....................................................................................................29 ..............29
Overview of User Interface
31
Introduction...................................................................................................................................31 Creating, Opening Opening and Saving Files ............................................................................................3 ............................................................................................32 2 Creating and Editing Input Data ........................................................................................... ...................................................................................................32 ........32 Database Approach Approach ................................................................................................. ...........................................................................................................33 ..........33 Running the Analysis and Plotting Results Results ..................................................................................3 ..................................................................................33 3 Run Analysis ................................................................................ ......................................................................................................................33 ......................................33 Plot Results .............................................................................................. ........................................................................................................................33 ..........................33 Options........................................................................................... Options .........................................................................................................................................34 ..............................................34
How to Start Using HIPAVE HIPAVE
35
Opening and Running an Existing Job.........................................................................................36
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Contents
Global Coordinate Coordinate System .................................................................................... ...........................................................................................................42 .......................42
Alternative Alternati ve Calculation Options Option s Overview ................................................................................................ ......................................................................................................................................45 ......................................45 Damage Calculation Details .................................................................................... .........................................................................................................45 .....................45 Thickness Design Capability .................................................................................................... ........................................................................................................47 ....47 Calculating Selected Selected Results at User-defined Z-values Z-values (depths) ................................................48
How to Use Advanced Advanc ed Features Features
51
Cost Calculation ............................................................................................ ...........................................................................................................................51 ...............................51 Calculation of Total Cost ............................................................................ ....................................................................................................51 ........................51 Material Costs .............................................................................. ....................................................................................................................52 ......................................52 Automatic Parametric Parametric Analysis ...................................................................................... ....................................................................................................53 ..............53 Example—Cost Example—Cost Optimization ........................................................................................ .......................................................................................................54 ...............54
How to Modify the Databases Databases
61
Introduction...................................................................................................................................61 Units .................................................................................................. ...................................................................................................................................61 .................................61 Sign Convention.............................................. Convention.................................................................................................................6 ...................................................................62 2 Overview of Database Approach Approach .......................................................................................6 .......................................................................................63 3 The "Layered System" and "Materials" Databases......................................................................64 Databases ......................................................................64 Overview of Layered System System and Material Proper Properties ties ......................................................64 Cross-anisotropy Cross-anisotropy and isotropy in road pavement pavement materials ..............................................65 Creating a new Layered System........................................................................................66 Defining the Layer properties.............................................................................................67 properties.............................................................................................67 Duplicating a Layered System ...........................................................................................6 ...........................................................................................68 8 Adding a new Elastic Material................................................................................... Material............................................................................................69 .........69 Adding a new Performance Performance Criterion.................................................................................71 Criterion .................................................................................71 Example: Asphalt Asphalt tensile strain relationship........................................................... relationship........................................................... 71 Example: Log-linear Log-linear performance performance relationship....................................................... relationship....................................................... 73 Adding a new Material Material Type ..............................................................................................7 ..............................................................................................75 5 The "Loads" and "Traffic Spectrum" Spectrum" Databases ..........................................................................76 Introduction Introduction ............................................................................................ ........................................................................................................................76 ............................76 Vehicle Specifications ............................................................................. ........................................................................................................76 ...........................76 Automatic Updates for for the Standard Vehicle Library Library ............................................. 77 Adding Custom Vehicle Specifications Specifications ................................................................... 77 Traffic Spectrums...............................................................................................................82 Spectrums...............................................................................................................82 Creating a new Traffic Spectrum Spectrum ............................................................................ 82 Characterizing Characterizing Payload Distributions............................................. Distributions...................................................................... ......................... 84 Using a Standard Standard Payload Payload Distribution................................................................... Distribution................................................................... 84 Defining a Custom Payload Distribution................................................................. Distribution................................................................. 85 Duplicating a Traffic Spectrum ............................................................................... 87 Standard Payload Distributions..........................................................................................8 Distributions..........................................................................................88 8 Introduction............................................................................................................. 88 Creating a new Standard Standard Payload Distribution....................................................... Distribution....................................................... 89 Dynamic Load Factors ................................................................................................. .......................................................................................................92 ......92 Wander Options ..................................................................................... .................................................................................................................93 ............................93 Coordinates Coordinates for Results................................................................................................................95 Results................................................................................................................95
Appendices References References .......................................................................... ...................................................................................................................................99 .........................................................99
Contents
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Coordinate System for Loads............................................................................................... Loads.................................................................................................... ..... 100
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Summary HIPAVE (Heavy Industrial PAVEment design) is for the mechanistic analysis and design of flexible pavements subjected to the extremely heavy wheel loads associated with freight handling vehicles in industrial facilities, in particular, intermodal container terminals. It is designed to conveniently model each combination of vehicle type and container load and to combine the damage using the Cumulative Damage Factor concept. HIPAVE is an outgrowth of CIRCLY and APSDS (Airport Pavement Structural Design System). CIRCLY was first released in 1977 and APSDS in 1995. HIPAVE has unique features to expedite pavement design projects—
a standard vehicle library - that can be automatically updated from our webserver;
ability to define and store container weight distributions; and
automatic calculation of axle loads from vehicle geometry and container weight.
HIPAVE can handle the variety of mobile equipment used in container facilities, such as forklifts, straddle carriers, gantry cranes and side loaders. HIPAVE takes account of vehicle wander at a more fundamental level than earlier methods. Vehicle wander is the statistical variation of the paths taken by successive vehicle movements relative to lane centrelines. Increased wander reduces pavement damage by different amounts that depend upon the pavement thickness. A Parametric Analysis feature can loop through a range of thicknesses for one or two layers, while simultaneously designing the thickness of another layer. This feature will optimise up to three layers. Combining this with a Cost Analysis feature, allows for fine-tuning of layer thicknesses to minimize construction and maintenance costs. HIPAVE has many other powerful features, including selection of–
cross-anisotropic and isotropic material properties;
fully continuous (rough) or fully frictionless (smooth) layer interfaces;
a comprehensive range of load types, including vertical, horizontal, torsional, etc.;
non-uniform surface contact stress distributions; and
automatic sub-layering of unbound granular materials.
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HIPAVE End User Licence Agreement HIPAVE © Mincad Systems Pty Ltd ABN 27 006 782 832. All rights Reserved Copyright This manual is copyright and may not be copied, photocopied, reproduced,
translated or reduced to any electronic medium or machine readable form, in whole or part, without the prior written consent of Mincad. This documentation is licensed and sold pursuant to the terms and conditions of the HIPAVE End User Licence Agreement, which appears under the HIPAVE "About" dialogue box which provides (in part). 20.Exclusio ns and Limitation of Liabilit y 20.1 To the maximum extent permitted by law all warranties whether express, implied,
statutory or otherwise, relating in any way to the subject matter of this Agreement or to this Agreement generally, are excluded. Where legislation implies in this Agreement any condition or warranty and that legislation avoids or prohibits provisions in a contract excluding or modifying the application of or the exercise of or liability under such term, such term shall be deemed to be included in this Agreement. However, the liability of Mincad for any breach of such term shall be limited, at the option of Mincad, to any one or more of the following: if the breach related to goods: the replacement of the goods or the supply of equivalent goods; the repair of such goods; the payment of the cost of replacing the goods or of acquiring equivalent goods; or the payment of the cost of having the goods repaired; and if the breach relates to services the supplying of the services again; or the payment of the cost of having the services supplied again. 20.2 To the maximum extent permitted by law and subject only subject only to the warranties
and remedies set out in Clause 12 and Sub-clause 21.1, Mincad shall not be under any liability (contractual, tortious or otherwise) to Customer in respect of any loss or damage (including, without limitation, consequential loss or damage) howsoever caused, which may be suffered or incurred or which may arise directly or indirectly in respect to the supply of goods or services pursuant to this Agreement or the act, failure or omission of Mincad. Customer warrants that it has not relied on any representation made by Mincad or upon any descriptions or illustrations or specifications contained in any document including any catalogues or publicity material produced by Mincad. 21. Acknowledgement 21.1Customer acknowledges and agrees that:
(a) pavement design and engineering is a complex area and the HIPAVE is not designed as a substitute in any way for professional advice; (b) HIPAVE is supplied with certain operating instructions and a failure to follow these instructions carefully could result in erroneous data being produced by HIPAVE;
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HIPAVE User Manual
(c) Whilst HIPAVE may be used by persons without a detailed knowledge of computers, HIPAVE is designed to be used by persons who have a detailed knowledge of, without limitation: (i) the applicable Pavement engineering standards; and (ii) All appropriate legislation and other relevant instruments, including, without limitation the relevant industry recognised engineering design guides; (d) They shall manually check all results provided by HIPAVE for any anomalies; and (e) They shall obtain professional advice in relation to all results provided by HIPAVE. 21.2 HIPAVE is licensed on the basis set out in this Agreement on the understanding that to
the extent permitted by law Mincad is not responsible for the results of any actions taken, either by Customer or a third party relying on figures supplied or not supplied by HIPAVE. 22. Indemnity
Customer warrants that any materials supplied to Mincad by Customer do not infringe Intellectual Property Right of any person. To the extent permitted by law, Customer shall fully indemnify and keep indemnified Mincad, its officers, employees and agents, against any loss, costs, expenses, demands, taxes or liability whether direct or indirect arising out of: (a) use of HIPAVE; (b) a breach of this agreement by Customer; or (c) any wilful, unlawful or negligent act or omission of Customer.
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C
HAPTER
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Introduction Background HIPAVE (Heavy Industrial PAVEment design) is an outgrowth of CIRCLY and APSDS (Airport Pavement Structural Design System). HIPAVE is targetted at structural design of flexible pavements subjected to the extremely heavy wheel loads associated with freight handling vehicles in industrial facilities, in particular, intermodal container terminals. It is designed to conveniently model each combination of vehicle type and container load and to combine the damage using the Cumulative Damage Factor concept. HIPAVE has unique features to expedite pavement design projects—
a standard vehicle library - that can be automatically updated from our webserver;
ability to define and store container weight distributions; and
automatic calculation of axle loads from vehicle geometry and container weight.
HIPAVE can handle the variety of mobile equipment used in container facilities, such as forklifts, straddle carriers, gantry cranes and side loaders. HIPAVE takes account of vehicle wander at a more fundamental level than earlier methods of treating wander. Vehicle wander is the statistical variation of the paths taken by successive vehicle movements relative to lane centrelines. Increased wander reduces pavement damage by different amounts that depend upon pavement thickness. Previous methods for structural design of container terminal pavements such as the British Ports Association guide (3rd edition, 1996) were developed prior to personal computers being commonplace. Therefore simplifying assumptions were necessary for manual calculation. For example the "equivalent thickness" concept was used to accommodate materials and properties not covered by the design charts. The variety of vehicle types and traffic levels were approximated by "Equivalent" wheel loads and "wheel proximity factors". These simplifying approximations are no longer justified now that personal computers are commonly available. HIPAVE has a user-friendly menu-driven interface that runs under Microsoft Windows. Databases are used for material properties and loadings, thus eliminating the need to constantly re-key information. Results can be obtained in tabular form or as report-quality plots on any printer or plotter supported by Microsoft Windows. Results can be easily exported to other application packages such as spreadsheets for further processing.
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HIPAVE User Manual
As well as the usual isotropic properties, cross-anisotropic material properties can also be considered. A cross-anisotropic material is assumed to have a vertical axis of symmetry. Anisotropies of this type have been observed in soil and rock deposits due to processes involved in their formation. The interfaces between the layers can be either fully continuous (rough) or fully frictionless (smooth), or a combination of both types. In practice, loads may be applied to soil or rock pavement layers in the form of vertical wheel loads, horizontal wheel loads due to traction and braking, torsional wheel loads due to cornering, and the "gripping" load developed by pneumatic tyres on pavements. The program allows all of these load types to be simulated for a circular loaded shape. HIPAVE can also model non-uniform contact stress distributions. HIPAVE is based on integral transform techniques and offers significant advantages over other linear elastic analysis techniques, such as the finite element method. Input data for the program is much simpler than that required for most finite element programs. For most problems the program uses less computer time than a finite element program. This Australian designed system has been developed by the Melbourne company, MINCAD Systems. The program on which it is based, CIRCLY, has been in regular use in Australia and worldwide for more than two decades, proving its worth in thousands of design applications. CIRCLY was first released in 1977 and handled polynomial type radial variations in contact stress and multiple loads which provide a much closer representation of the actual loading conditions (Wardle 1977). CIRCLY was commercialised in 1988 by MINCAD Systems. A limited release of the first Windows version (Version 2.4) was made in early 1996. CIRCLY 3.0 was released in late 1996 and included many improvements, including a major re-write of the integration algorithms and automatic sub-layer generation for granular materials. CIRCLY 4.0 was released in early 1999 and extended the software to include an automatic thickness design capability. CIRCLY 5.0 was released in early 2004. While CIRCLY and APSDS have been used very successfully for heavy duty industrial pavements, unwieldy data input makes it very difficult to model more than one or two payloads per vehicle. HIPAVE has been designed to conveniently handle comprehensive details of the freight handling vehicles and the characteristics of the payload distribution for each vehicle. The wander algorithm that is used in HIPAVE was first released in APSDS 3.0 in 1995 (Wardle and Rodway, 1998). HIPAVE incorporates all the features of CIRCLY 5.0. Commencing in 2004, MINCAD Systems has released a number of trial versions of HIPAVE. HIPAVE 5.0 was commercially released in September 2005. In 2007 Mincad Systems and Pioneer Road Services released the Heavy Duty Industrial Pavement Design Guide (Mincad Systems and Pioneer Road Services, 2007). The Guide has been developed to assist users of the HIPAVE software. The Guide is a collaborative effort currently involving Dr. Leigh Wardle of Mincad Systems, Ian Rickards (Pioneer Road Services Pty Ltd, Melbourne, Australia), John Lancaster (VicRoads, Australia) and Dr. Susan Tighe (Dept. Civil Engineering, University of Waterloo, Canada).
Chapter 1 Introducti on
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The Guide presents the author’s attempts to reflect best practice in the design of new construction and rehabilitation of industrial pavements. The Guide steers the designer through all necessary design considerations and suggests external sources for research updates. The Guide is a ‘living document’ that will be regularly updated to reflect advances in pavement technology and made freely available via the Internet at no charge. For further details see http://www.mincad.com.au/hdipdg/.
Realistic Modelling with HIPAVE You should be aware of a number of factors, including the accuracy of input material properties and the constraints of the layered elastic model, that will influence the reliability of design predictions made using HIPAVE, or for that matter, any alternative design software. The design values chosen for material properties are likely to be gross simplifications of the complex and variable properties of the pavement and subgrade materials. Although HIPAVE can produce what appear to be very accurate solutions to problems, the predictions cannot be any more reliable than indicated by the degree of scatter given by the back-analysis of the full-scale field tests against which HIPAVE has been 'calibrated'. Care must be taken to ensure that the sophistication of the analysis method is consistent with the quality of the input data. Otherwise so many assumptions must be made about the uncertain parameters that the model predictions will be meaningless. The following Sections summarize the "state of the art" with respect to modelling of heavy loads such as container handling equipment and the behaviour of pavement materials. Much of this knowledge has been derived from airport pavement research. More detailed advice is given in the Heavy Duty Industrial Pavement Design Guide (Mincad Systems and Pioneer Road Services, 2007). For further details see http://www.mincad.com.au/hdipdg/.
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Material Modelling HIPAVE is an open system that will accommodate material properties and transfer functions for any pavement design methodology. But research has shown that highway pavement design methods such as Austroads (1992, 2004) are not applicable to the higher loadings typically applied to heavy duty pavements used at ports and container terminals (Wardle et al., 2003). The process of establishing a performance relationship entails assigning moduli values to unbound basecourse and sub-base materials in accordance with a particular system of sublayering. Care should be taken to ensure that the sub-layering system used to establish the performance relationship is also used when analysing or designing pavement structures. Unless this is done, the empirical connection between the test data and the new design is broken. For example, using the Austroads design method for container handling equipment where the loads can be 20 tonnes per wheel has been shown to lead to grossly underdesigned pavements (Rodway and Wardle, 1998). Because each failure criterion is derived in the context of its own detailed design procedure, it will only produce sensible pavement designs when used as part of that same procedure. If a failure criterion is used in conjunction with a different design procedure, the vital empirical link between the design and the original performance data used to calibrate the criterion is broken. This issue is discussed in more detail by Wardle et al. (2003). The material performance characteristics recommended for use in HIPAVE are based on calibrations developed from airport pavement research. There are a number of differences to the Austroads pavement model:
Basecourse, sub-base and subgrade are assumed to be isotropic (Austroads assumes anisotropic);
A different methodology (Barker and Brabston, 1975) is used to sublayer the basecourse and sub-base.
A preferred subgrade performance relationship for heavy duty pavements was developed by Wardle et al. (2001). This performance relationship was established by calibrating pavement designs using APSDS against designs based on the US Army Corps of Engineers CBR method (Method S77-1, Pereira 1977). The relationship was developed using a range of different aircraft with masses varying from 40 tonnes to 397 tonnes and subgrade strengths varying from CBR = 3% to CBR = 15%. The subgrade strains are converted to damage using a performance relationship of the form: ⎡ k ⎤ N = ⎢ ⎥ ⎣ ε ⎦
b
Chapter 1 Introducti on
where N
is the predicted life (repetitions of ε) k
is a material constant
b
is the damage exponent of the material
ε is the load-induced strain (unitless strain)
The parameters k and b vary with subgrade modulus (E) in units of MPa as given by the following:
k = 1.64 10-09 E3 - 4.31 10-07 E2 + 2.18 10-05 E + 0.00289
b = -2.12 10-07 E3 +8.38 10-4 E2 -0.0274 E +9.57
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HIPAVE User Manual
Modelling of Multiple Wheels and Axle Groups HIPAVE lets you use the actual wheel layouts of the vehicles that operate on the pavement. Care needs to be taken to select which wheels to include in the model. Extensive research gives us guidance on choosing the "right" combination of wheels to include in the model. Using more wheels can lead to inaccurate model predictions. The recommended model for base/sub-base materials and subgrade performance relationship recommended for heavy duty loads was described above. This methodology was derived from full-scale aircraft pavement tests conducted by the US Army Corps of Engineers at their Waterways Experiment Station (WES). These 'WES' tests were essentially conducted using single gear assemblies. No tests were carried out to investigate the increased damage that might result due to interaction effects of adjacent gear assemblies. Considerable uncertainty exists with respect to prediction of damage for aircraft that have main gears in close proximity. APSDS has been used to study multiple gear interaction effects for a Boeing 747 and 777 aircraft using a range of alternative damage models (Rodway 1995a, Wardle and Rodway 1998, Rodway, Wardle and Wickham 1999). Results from these studies show that the successful calibration of simplified design models against the full-scale test data does not create a capability to confidently extrapolate beyond the limits of the test data. The studies showed that simple damage models give unrealistic predictions for the damage caused by all sixteen main wheels of the aircraft when compared to that computed for a single isolated 4wheel gear. Three different performance models, each of which gave a similar 'goodness of fit' to the full-scale test data, gave greatly different predictions of the damage caused by the interactions of the sixteen main wheels. The differences between the alternative predictions increased with increasing depth to subgrade. Given the above comments, as a general rule only groups of wheels that are within 2 metres of each other should be modelled as a single load case. For example, the most appropriate way of modelling a Fork Lift is described in Coordinate System for Vehicles (on page 22).
Nature of Damage Pulses The WES tests were performed on relatively thin pavements. In most of the test sections the elastic models predict a distinct strain pulse at subgrade level for each axle of a two-axled gear. For deep pavements (say 1.5 m or more) the models predict a single combined pulse resulting from the entire gear. In other words, a two-axled gear produces two strain pulses per pass for shallow subgrades and one strain pulse, of significantly different shape, for deep subgrades. HIPAVE uses strain repetitions as the basis for damage predictions, not passes or coverages. Pulse counts and pulse shapes both change with pavement thickness. There is significant uncertainty in the design of thick pavements because data must be extrapolated from thinner test pavements which have narrower pulses than those expected for the deeper subgrades. There is still no experimental data to show to what extent pavement damage depends on the transverse and longitudinal widths of the load pulse.
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HAPTER
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Overview HIPAVE has many features to facilitate pavement analysis and design.
How HIPAVE handles Traffic Distributions HIPAVE lets you define your vehicle loadings and traffic in detail. You define the anticipated repetitions over the design period for each vehicle model. You also define a payload distribution for each vehicle model. The following example illustrates the concepts. Here there are two vehicle models, A and B. Each vehicle model is assigned a payload distribution. Vehicle Model A
Vehicle Model A - Payload Distribution
8000 7000 6000 t 5000 n u 4000 o C
3000 2000 1000 0 2.5
4
6
8.5 12.5 17.5 22.5 27.5
Payload (tonnes)
Vehicle Model B
Vehicle Model B - Payload Distribution
8000 7000 6000 t 5000 n u 4000 o C
3000 2000 1000 0 2.5
4
6
8.5 12.5 17.5 22.5 27.5
Payload (tonnes)
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HIPAVE User Manual
Cumulative Damage Concept The system accumulates the contribution from each loading in the traffic spectrum at each analysis point by using Miner's hypothesis. The damage factor for any given loading is defined as the number of repetitions (n) of a given response parameter divided by the ‘allowable’ repetitions (N) of the response parameter that would cause failure:
CDF =
n N
The Cumulative Damage Factor (CDF) for the parameter is given by summing the damage factors over all the loadings in the traffic spectrum: M N k
CDF total =
∑ ∑ CDF kj
k =1 j =1
where:
k is summed over M vehicle models
Nk is the number of different payloads for vehicle model no. k
The system is presumed to have reached its design life when the cumulative damage reaches 1.0. If the cumulative damage is less than 1.0 the system has excess capacity and the cumulative damage represents the proportion of life consumed. If the cumulative damage is greater than 1.0 the system is predicted to ‘fail’ before all of the design traffic has been applied. The procedure takes account of—
the design repetitions of each vehicle model/payload combination; and
the material performance properties used in the design model.
This approach allows analyses to be conducted by directly using a mix of vehicle models. It is not necessary to approximate passes of different vehicles or axles to passes of an ‘equivalent’ standard load or "design vehicle".
Chapter 2 Overview
HIPAVE does a full spectral analysis of pavement damage by using the cumulative damage concept to sum the damage from multiple vehicle models and payload cases for one set of layered system material properties. The figure below is a sample cumulative damage plot produced by HIPAVE:
Note that there is a data point for each combination of vehicle model and payload. HIPAVE can also generate graphs that show the variation of the damage factor across the pavement, as shown below:
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HIPAVE User Manual
Lateral Vehicle Wander The analysis optionally includes the effect of the lateral distribution of successive vehicle passes along the pavement. You nominate a standard deviation of vehicle wander about the centreline that is appropriate to the particular vehicle and pavement. The sophisticated method of handling wander, bypasses the simplified concepts of “coverage” and “pass-tocoverage ratio” (PCR) that have been traditionally used for aircraft pavement design.
Material Performance Generally most performance models may be represented graphically by a plot of tolerable strain versus load repetitions (generally by a straight line of 'best fit' on a log-log plot). HIPAVE usually represents models in the form:
⎡ k ⎤ N = ⎢ ⎥ ⎣ ε ⎦ where N
b
is the predicted life (repetitions)
k
is a material constant
b
is the damage exponent of the material
ε
is the induced strain (dimensionless strain)
Log-log relationships can be readily converted to the above form. HIPAVE can also handle models of the form: log10 ( N ) = k − b ε This log-linear relationship is used by European designers for cement-treated materials. HIPAVE is supplied with a comprehensive range of published performance models. You can use your own performance equations by specifying values for ‘k’ and ‘b’ and the particular component to be used, for example vertical strain, vertical deflection, maximum tensile strain, etc.
Chapter 2 Overview
19
Traffic and Loading You define the anticipated repetitions over the design period for each vehicle or axle group and the payload mix — that is the repetitions for each payload that is modelled.
How Vehicle characteristics are defined Standard Vehicle Library In designing HIPAVE we have introduced the concept of a Standard Vehicle Library. The master version is maintained on our webserver. You can obtain updates (new vehicles) automatically by clicking the "Import" icon on the toolbar. We encourage all users to send us vehicle specifications for inclusion in the standard vehicle library. In designing HIPAVE account has been taken of a number of important issues relating to the definition of vehicle loading characteristics. Most importantly, a critical issue is choosing the optimum number of wheels to use in the model - a benefit of of the Standard Vehicle Library is that it takes the worry out of selecting which wheels to model. You will also save time by not having to seek vehicle specifications from manufacturers or facility operators. Of course, you can define your own vehicle models directly in HIPAVE. HIPAVE uses the following vehicle data—
wheel locations and numbers; and
axle mass characteristics.
Container handling equipment can be broadly sub-divided into two categories according to the load transfer characteristics:
unequal loads on each axle; and
equal loads on each axle.
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HIPAVE User Manual
Unequal Axle Loads Examples of these vehicles are Fork Lifts and Reach Stackers. In this case, the vehicle loading characteristics are specified in terms of two load cases that express the axle loads as a function of Container Weight. For example this could be the Unladen case together with one specific Container Weight. The graph below illustrates the concept. Axle loads for other container weights are obtained automatically by linear interpolation.
This screendump shows some sample data:
Chapter 2 Overview
21
If you now click on the Load Components and Locations tab, you will see more details for the currently selected Vehicle Model :
Equal Axle Loads Vehicles such as straddle carriers are assumed to have equal loads on each axle. In this case the vehicle loading characteristics are specified in terms of the unladen weight of the vehicle, the number of axle rows (i.e. the number of axles seen from one side of the vehicle), the total number of wheels on the vehicle and the tyre pressure. The screendump below shows some sample data:
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HIPAVE User Manual
If you now click on the Load Components and Locations tab, you will see more details for the currently selected Vehicle Model :
Coordinate System for Vehicles The X axis is taken as the direction transverse to the lane. To ensure consistency between results for different vehicle types it is recommended that X = 0 to the lane centreline. Usually all vehicles are assumed to have their centrelines at X=0.
Chapter 2 Overview
23
The Figure below illustrates the convention used to define the wheel locations. This example is for a Hyster Fork Lift -Model H40.00-16CH. HIPAVE will normally model the two axle loadings as separate components, with the front axle (assumed to be on Y=0) as component 1 and the rear axle as component 2. Modelling the two axles as separate components means that the two axles are modelled as two separate load cases, i.e. there is no interaction between axle loads.
Usually it is only necessary to model the wheels on one side (X ≥ 0) of the vehicle.
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HIPAVE User Manual
Methods for handling Damage Pulses The problems associated with damage pulses were introduced in the Overview section under Nature of damage pulses (on page 14). The damage that a given point in the pavement will experience during the passage of a multiple axle primarily depends on the depth below surface. The two extremes of behaviour are—
multiple distinct pulses resulting from each axle, for shallow depths; and
a single pulse that reflects the overall loading on the axle group, for large depths.
HIPAVE lets you specify the method to be used to calculate the damage. For shallow pavement depths compared to axle spacing one ‘pulse per axle’ is selected. HIPAVE then computes the damage beneath that axle due to the strain contributions for all wheels of the vehicle, then multiplies the computed damage by the number of axle rows (i.e. the number of axles seen from one side of the vehicle). HIPAVE relies on you specifying one set of axles at Y=0 [ see Convention used to define wheel locations (on page 23)]. However, for large depths relative to the axle spacing the maximum strain will generally occur under the centroid of the gear. In this case you specify 'combined pulse for gear' and HIPAVE will automatically shift the load coordinates so that the origin is at the centroid of t he gear as shown on Automatic shift of Y-coordinates for 'combined pulse for gear' case (on page 25). HIPAVE then computes the damage pulse beneath the centroid of the gear due to the strain contributions for all wheels of the vehicle, and ignores the number of axles in the group. Between these two extremes the pulses resulting from each axle overlap making the calculation of damage problematic. Recently the ‘reservoir’ method, as used in bridge design to handle complex loadings, was implemented in a prototype version of this software to overcome this problem and to ensure a smooth transition between the two extremes. But this method is not currently available.
Chapter 2 Overview
25
Figure 1: Automatic shift of Y-coordinates for ‘combined pulse for gear’ case
It is your decision whether the pavement is relatively deep or shallow compared the axle spacing. HIPAVE automatically shifts the position of the load coordinates if you specify 'combined pulse for gear'. Computation of damage at intermediate depths involves judgement based on knowledge of the strain pattern, whether HIPAVE or other analysis methods are used.
Dynamic Load Factors So-called Dynamic Load Factors are used in the British Ports Association Design Guide (British Ports Association, 1996) to account for the effects of dynamic loading induced by cornering, accelerating, braking and surface uneveness. These are simple multipliers that are applied to the design loads and can vary with each axle. HIPAVE lets you use your own values for the factors.
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Container Weight Distributions HIPAVE lets you specify detailed container weight distributions. For example, the British Ports Association Guide (1996) includes frequency data based on data provided by UK ports. The following graph shows the container weight distribution for 40 foot containers.
Container weight distribution for 40 foot containers based on data provided by UK ports (British Ports Association 1996).
The container weight distributions are categorized as being "Standard" or "Custom". The "Standard" distribution feature lets you re-use a particular distribution across a range of vehicle models and projects. HIPAVE includes the "Standard" distributions provided by British Ports Association (1996). The "Custom" distribution is used for just one traffic spectrum / vehicle model combination.
Automatic Thickness Design You can automatically determine the optimum thickness of a given layer. For further details see Thickness Design Capability.
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Cross-anisotropy and Isotropy in Pavement Materials The elastic material in each layer of the pavement structure is assumed to be homogeneous and of cross-anisotropic or isotropic symmetry. A cross-anisotropic material has an axis of symmetry of rotation, which is assumed to be vertical, i.e., the elastic properties are equivalent in all directions perpendicular to the axis of symmetry (in horizontal, radial directions). In general, these properties are different from those in the direction parallel to the axis, whereas isotropic materials have the same elastic properties in both the vertical and horizontal directions. In the Austroads pavement design method (1992 and 2004) cross-anisotropic properties are used for subgrade materials and unbound granular aggregates and isotropic properties are used for bound materials such as asphalt and cemented materials. The stress-strain relations for a cross-anisotropic material in a particular layer are: εxx =
(1/Eh) (σxx
- νh σyy - νhv σzz)
εyy =
(1/Eh) (- νh σxx + σyy - νhv σzz)
εzz =
(1/Ev) (- νvh σxx - νvh σyy + σzz)
εxy =
((1+ νh)/Eh) σxy
εxz =
(1/f) σxz
εyz =
(1/f) σyz
The moduli and Poisson's ratios are related by the following equation: νvh /Ev = νhv /Eh
The condition that the strain energy must be positive imposes restrictions on the values of the elastic constants: Eh > 0
Ev > 0
1 > νh > -1
f>0 1- νh-2 νhv νvh > 0
For isotropic materials the restrictions become: E>0
0.5 > ν > -1.0
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To be able to model a cross-anisotropic material you need to specify five constants: the vertical Elastic modulus (E v), the horizontal Elastic modulus (E h), the Poisson’s ratio ( νvh), the Poisson’s ratio ( νh) and the Shear modulus (f). Data values for all five constants are rarely available. The Austroads Pavement Design Guide uses the following simplifications to model subgrade and unbound granular materials: Eh = 0.5 Ev νvh = νh = ν
f = Ev /(1+ ν) In this case, the material is defined simply by the vertical Elastic modulus, E v, and a single Poisson's ratio, ν. For isotropic materials, only the Elastic modulus and Poisson’s ratio need to be entered, as they are assumed to be the same in all directions.
Cost Calculation The unit costs for the materials laid and constructed in the layers can be specified using a combination of both a volumetric (or weight) component and an areal component. The areal component lets you take account of costs that are primarily a function of area, such as surface treatments, subgrade stabilization and the like. The areal component can also be used in circumstances where the relationship between total layer cost and thickness has a non-zero component for zero thickness.
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Automatic Parametric Analysis Automatic Parametric Analysis lets you automatically loop through a range of thicknesses for one or two nominated layers. For example, you can have Layer 3 vary from 800 mm to 1000 mm in steps of 10 mm. Additionally, for each combination of those layer thicknesses, you can automatically design the thickness of another layer.
By combining Automatic Parametric Analysis with the Cost Analysis feature you can finetune layer thicknesses to optimise construction cost.
Automatically generated plot: Total Cost vs. Layer 3 Thickness
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Overview of User Interface Introduction HIPAVE has a standard format Microsoft Windows menu, but most commands can be accessed directly from the toolbar as shown below:
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Creating, Opening and Saving Files You supply a 'Jobname' to use as the basis for naming all of the files associated with a 'job' or analysis. If the job name is Jobname the following files are used– HIPAVE data file— this is used to save the details of your job.
Jobname.cls
All the other files are generated automatically by the system: Jobname.cli
HIPAVE32 input data file
Jobname.clo
HIPAVE32 'printable' results file
Jobname.prn
HIPAVE32 raw results file (i.e., strains, etc.)
Jobname.dam
HIPAVE32 cumulative damage results file (for plotting)
Jobname.dmx
HIPAVE32 results summary file (damage factors and critical strains)
All of these files are text files that can be opened by standard text editors. Three icons on the toolbar allow you to create, open and save job files. Icon
Description
Closes the current job, prompting you to save any changes; then creates a new job. Closes the current job, prompting you to save any changes; then opens an existing job. Updates the current job file. You can also save your job under a different name by clicking on the File Menu, then clicking Save As.
Creating and Editing Input Data The following eight icons allow you to create and modify your input data. Each icon corresponds to one of the main groups of data necessary to fully define a Job.
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Database Approach Some of the input data items are entered using very simple input forms. Most of the input data is handled using a relational database approach. This is designed to eliminate re-entry of data for design loads and material properties. You can tailor each of the databases to contain specific sets of regularly used data. The relational database approach gives maximum flexibility in data preparation. For example, the data for a commonly used material need only be entered into the system once. If this data is subsequently modified, all Layered systems that use that material and subsequently all Jobs that use those layered systems will automatically access the modified material properties.
Running the Analysis and Plotting Results Run Analysis This invokes the analysis. During a long analysis you can switch to another application (HIPAVE will continue to run at a lower priority using Microsoft Windows multi-tasking).
Plot Results Usually, this command will produce a graph of the damage contribution from each vehicle type and the overall total (damage contribution from all the traffic). This graph option shows the variation of the CDF as a function of X, the distance from the centreline of the pavement (i.e. X=0 corresponds the centrelines of the vehicles). Optionally you can graph the maximum CDF as a function of Payload. Alternatively, as an option you can produce a graph of a selected displacement, stress or strain component at your chosen Z-values (i.e., vertical distances/depths below the surface of the pavement) and results can be plotted for a selected displacement, stress or strain component.
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Options The Options screen allows specification of the following folder:
location for all data files (Defaults to the sub-folder, "data", in the folder in which HIPAVE has been installed.)
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How to Start Using HIPAVE The easiest way of trying HIPAVE out is to open one of the sample jobs, run the analysis and then graph the results.
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Opening and Running an Existing Job In the interests of providing instant hands-on experience, for this example you simply open an existing job, run the analsis and inspect the results. 1
Open the Job
Click on the
button.
Select the job "Example 1". 2
Run the Analysis
Click on the
button. This invokes the analysis.
When the analysis starts you will see a blue "progress bar" at the bottom left corner of the screen. When the analysis is complete the results for the damage factor (CDF) will be transferred to the top table on the screen, as shown below.
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3.
Plot the Results
Click on the
button. This will generate a graph of the results:
This graph option shows the variation of the CDF for the Subgrade as a function of X, the distance from the centreline of the pavement (i.e. X=0 corresponds the centrelines of the vehicles). Note that the results for the different payloads have been aggregated. Optionally you can graph the maximum CDF as a function of Payload. Click on the Plot Type combo box then click on CDF vs. Payload .
Chapter 4 How to Start Using HIPAVE
This graph option shows the maximum CDF for each Vehicle Model and Payload.
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As can be seen from the graph there is one result point for each combination of vehicle model and payload. The two graphs give results for the subgrade layer. You can switch to the CDF for the asphalt layer by clicking on the combo box in the top left-hand corner. You can print a copy of the chart by clicking on the Print icon
on the toolbar.
You can also copy the graph to the clipboard and then paste into another application such as Microsoft Word or Powerpoint . You do this via the context-sensitive graph menu that drops down when you right click with the mouse pointer anywhere on the graph as shown below:
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Then click on ' Export Dialog '. The 'Export Dialog ' lets you export to a variety of formats, but for most purposes select 'Metafile' to ensure that the graphics are scalable.
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Global Coordinate System A global coordinate system is used to define load locations, the layered system geometry and the points below the road surface at which results are required. The global coordinate system is also used to describe the resultant displacements and stress and strain tensors. The X-axis is usually taken as the direction transverse to the direction of vehicle travel. The Y-axis is then parallel to the direction of vehicle travel.
Figure 2: Global Coordinate System
The Z-axis is vertically downwards with Z = 0 on the pavement surface. Two alternative formats are available for specifying the points to be used for results calculation:
An array of equally spaced points along a line parallel to the X-axis ;
A grid of points with uniform spacing in both the X-direction and the Y-direction .
Chapter 4 How to Start Using HIPAVE
Y
Direction of Travel
X
0
Xmin
Xdel
Xmax Results points
Figure 3: Coordinates for results defined by a line of equally spaced points
Y
Ymax
Ydel
Ymin X
0
Xmin
Direction of Travel
Xdel
Xmax Results points
Figure 4: Coordinates for results defined by a uniform grid of points
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Alternative Calculation Options Overview HIPAVE offers a number of calculation options. Normally, you will calculate the damage factors (CDF) for your pavement. You can automatically determine the optimum thickness of a given layer. Alternatively, you can calculate results for any given displacement, stress or strain component at selected Z-values (depths below the pavement surface).
Damage Calculation Details Typically, between one layer (the subgrade) and three layers (asphalt surfacing, cementstabilised layer and subgrade) will have performance criteria associated with them. Click on the 1
2
3
button. This will bring up the following screen:
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Two alternative calculation options are available:
Calculate damage factors (CDF); or
Calculate selected results at user-defined Z-values (see Calculate Selected Results at User-defined Z-Values (see "Calculating Selected Results at User-defined Z-values (depths)" on page 48)).
When operating in 'calculate damage factors' mode, the key features on the screen (the numbers refer to the screenshot above) are:
2
This table is a summary of the layered system including material titles and current thicknesses. Also the current Cumulative Damage Factors (CDFs) will be shown if the problem has been run previously. The current thickness of any layer can be changed from this screen.
3
This table is a summary of the properties for those layers that have a performance criterion. Here the Traffic Multipliers are multipliers that are used in Equivalent Single Axle (ESA) calculations (as described in the Austroads Pavement Design Guide, 1992, Section 7.5). These multipliers are necessary to take account of the material type and the actual traffic mix. The multipliers are simply used to increase the ESA count (in the 'Movements' field) that is specified in the Traffic Spectrum screen. Traffic Multipliers are a consequence of the Equivalent Standard Axle approach and would not generally be used for heavy duty pavements.
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Thickness Design Capability You can automatically determine the optimum thickness of a given layer. This procedure is very fast, typically taking 4-5 times the usual analysis time.
1
The thickness design capability is invoked by clicking on the checkbox that is labelled 'Design thickness of layer highlighted below'.
2
You select the layer you wish to design by moving the mouse pointer to the appropriate layer and clicking the mouse button once. The layer selected will be highlighted in blue.
3
By default, the design will use the maximum damage factor (CDF max) from all the layers that have a performance criterion. The design involves bringing the maximum damage factor to 1.0 by varying the thickness of the highlighted layer. In some circumstances, it may be necessary to ignore one or more layers when calculating the maximum damage factor.
Here a tick ( ) denotes that the layer will be included in the maximum damage factor calculation. The tick-box can be toggled on and off by clicking on it.
1
2
3
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Minimum and maximum thicknesses can be specified for each layer, or these fields can be left blank, so that no constraints are applied. If a specified maximum or minimum thickness limit prevents attainment of a CDF of 1.0, the CDF for the thickness limit will be computed.
Calculating Selected Results at User-defined Z-values (depths) In some circumstances, you may need to calculate selected results (displacements, stresses and strains) at selected Z-values (depths). Specify first convenient Z-values and then plot results for a selected displacement, stress or strain component. When you use this option, damage factors are not calculated. Click on the
1
2 3 4 5
6
button. This will bring up the following screen:
Chapter 5 Al ternative Calculation Options
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49
This option is invoked by clicking the button that is labelled ' Calculate selected results at user-defined Z-values '.
2
You can choose the component that is to be plotted by first clicking on the 'Component type ' tab. You can then define the component type (e.g. displacement, strain etc.) by clicking on the down arrow on the right hand side of the ' component type ' combo box. This will invoke this drop down list:
Click on the component type that you wish to use.
3
The actual component (e.g., vertical, etc.) is specified by clicking on the down arrow on the right hand side of the ' Component ' combo box. A drop down list of alternatives will appear:
Click on the Component that you wish to use. 4
Now you can define the Z-values . Each Z-value is added by clicking the New button
6. You can delete any entry by clicking on it and then clicking the Delete button.
5
When a Z-value coincides with the interface between two layers, you can specify which side of the interface is to be used (i.e. above the interface, or below the interface).
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How to Use Advanced Features Cost Calculation Calculation of Total Cost HIPAVE can automatically calculate Total Cost for a pavement from the unit costs of materials in each layer. Click on the
button. This will bring up the following screen:
Total Cost
1
1 Click on the Calculate Cost checkbox
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Material Costs The unit costs for the layers can be specified using a combination of both a volumetric (or weight) component and an areal component. The areal component lets you take account of costs that are primarily a function of area such as surface treatments, subgrade stabilization, etc. The areal component can also be used in circumstances where the relationship between total layer cost and thickness has a non-zero component for zero thickness.
Unit Material Costs
The Total Cost for a given layer is calculated as follows: Total Cost (layer no. i) ($/m2) = Unit Volumetric Cost (layer no. i) ($/m3) x Thickness Unit Areal Cost (layer no. i) ($/m2)
The Unit Volumetric Cost can be defined in terms of: 1
Cost/Volume, or
2
Cost/Weight and the density of the material ( Weight/Volume ).
(layer no. i)
(mm) +
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Automatic Parametric Analysis Automatic Parametric Analysis lets you automatically loop through a range of thicknesses for one or two nominated layers. For example, you can have Layer 2 vary from 100 mm to 200 mm in steps of 10 mm. Additionally, for each combination of those layer thicknesses, you can automatically design the thickness of another layer. Combining this with the Cost Analysis feature lets you fine-tune layer thicknesses to optimize construction cost.
Click on the
button. This will bring up the following screen:
1
1 Click to switch on Parametric Analysis . This will bring up the following form:
1 This combo box lets you specify the number of Independent Variables (i.e. the number of Layers for which you are varying the thickness): 1. One Independent Variable, or 2. Two Independent Variables. 2 This section gives the details of the first Independent Variable. 3 This lets you choose which layer (thickness) is to be used as the first Independent Variable. 4 Here you specify the range of thicknesses to be used for that layer: The thickness will range from T 1minimum to T1maximum in steps of T1step.
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To use two Independent Variables , click the combo box ( 1 on the screenshot below).
2 This section gives the additional details for the second Independent Variable 3 Here you specify which layer (thickness) is to be used as the second Independent Variable 4 Here you specify the range of thicknesses to be used for that layer: The thickness will range from T 2minimum to T2maximum in steps of T2step.
Example—Cost Optimization In this example you will use the Automatic Parametric Analysis feature to automatically loop through a range of thicknesses for one layer (Layer 3) and to determine which thickness has the minimum Total Cost . For each Layer 3 thickness, you will get HIPAVE to automatically design the thickness of Layer 2.
Step 1. Open the sample file "Example for Cost Optimization".
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Step 2.
1 Make sure the Calculate Cost check-box is ticked. 2 Click the Parametric Analysis check-box. This will bring up the following form:
1 This combo box lets you specify the number of Independent Variables (i.e. the number of Layers for which you are varying the thickness). For this example you will use the default, One Independent Variable . 2 This section gives the details of the Independent Variable, the thickness of Layer 3. 3 This lets you choose which layer (thickness) is to be used as the first Independent Variable. For this example change this to "3". (as you are varying the thickness of Layer 3). 4 Here you specify the range of thicknesses to be used for Layer 3: For this example, you will let Layer 3 vary in thickness from 700 mm t o 1200 mm in steps of 100 mm.
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Enter the following values: Minimum: 700, Maximum: 1200, Step: 100.
Step 3. Now set the automatic thickness design feature to Layer 2. Click on the "Summary" tab (left of the "Variables" tab).
1 Click the check-box labelled ' Design thickness of layer highlighted below' . 2 Click anywhere on the Layer 2 row. Click in the "Minimum Thickness" cell on this row and enter 100 (mm).
Now click on
to run the analysis.
Step 4- Plot the Total Cost vs Layer 3 thickness.
When the analysis is finished, click on
to plot the results.
Chapter 6 How to Use Advanced Features
This plot shows the Minimum Total Cost condition for Layer 3 thickness is 220 mm (to a resolution of 100 mm).
Step 5- Plot the CDF (for Layer 4, Subgrade) vs. Layer 3 thickness. Click on the Parameter combo box.
Select CDF (Select Layer =>). Click on the Layer combo box.
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Select Subgrade - CBR=6 (This is Layer No. 4).
Step 6- Plot the CDF (for Layer 1, Asphalt) vs. Layer 3 thickness. Select CDF (Select Layer =>). Click on the Layer combo box. Select Asphalt- 3000 MPa, VB=11% (This is Layer No. 1).
Step 7- Plot the Layer 2 thickness (Design Layer) vs. Layer 3 thickness. Click on the Parameter combo box. Select Thickness (Layer used for Thickness Design).
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Further refinement.
So far we have used Layer 3 thicknesses that are multiples of 100 mm, at this resolution the minimum Total Cost is given by Layer 3 thickness = 900 mm. To refine this thickness we re-run the Parametric Analysis letting Layer 3 vary in thickness from 800 mm to 1000 mm in steps of 20 mm. As shown this Total Cost graph, the minimum Total Cost is given by Layer 3 thickness = 920 mm.
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How to Modify the Databases Introduction Units In order for HIPAVE to deliver coherent results, all data must use this system of units:
Quantity
Units
Length, Displacement
mm
Elastic modulus, Pressure
MPa
Weight
tonne
Force
N
Moment
N.mm
Strain
mm/mm
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Sign Convention Compressive direct stresses and strains are considered to be positive. Positive shear stresses are defined on the basis that both the stress and strain tensors obey the right hand rule. Displacements in negative coordinate directions are considered to be positive. Hence a load causing a positive stress acts in the positive coordinate direction. The sign conventions used in the rectangular coordinate system and cylindrical local coordinate system are illustrated below.
Figure 5: Sign Convention
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Overview of Database Approach The relational database approach is designed to eliminate re-entry of data for design loads and material properties. For example, the data for a commonly used material need only be entered into the system once. If this data is subsequently modified, all Layered Systems that use that material and subsequently all Jobs that use those Layered Systems will automatically access the modified material properties. The Figure below illustrates the relational database concept for the elastic material properties. Here, each of the components that make up a Layered System is linked to entries in the Elastic Material Properties database via an ID (index) field of up to 20 characters.
Figure 6: Relationships between elements in Layered System databases
A similar hierarchy applies for the Traffic database. Each load group referenced by the Traffic Spectrum is linked to a record in the Load Group data. A consequence of the relational database approach is that data should generally be prepared from the 'bottom up'. This means that:
Elastic Materials Properties data must be entered before the Layered System Components data;
Load Group data must be entered before the Traffic Spectrum Components data.
To create a new layered system, these steps must be followed: 1
Create any materials that are not already in the Elastic Materials database;
2
Create a new entry in the Layered Systems database;
3
Define each of the Materials and thicknesses for each of the Layers using the Layered System Components database.
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Worked examples in the following sections show how you can create new data.
The "Layered System" and " Materials" Databases Overview of Layered System and Material Properties HIPAVE models road pavements as a system of layers, each with differing elastic properties. The layered system consists of one or more layers. The layer interface planes are horizontal and each layer is assumed to be of infinite extent in all horizontal directions. The bottom layer may extend to a finite depth or to a semi-infinite depth (see the figure below). If the bottom layer is of finite depth, it is assumed to rest on a rigid base, and the contact can be either fully continuous (i.e., rough) or fully frictionless (i.e., smooth). Interfaces between the layers can be either fully continuous (rough) or fully frictionless (smooth), or a combination of both types.
Layer No. 1 Layer No. 2
Layer No. NL
∞ Rough rigid base
Smooth rigid base
Semi-infinite base
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Cross-anisotropy and isotropy in road pavement materials The elastic material in each layer of the pavement/road structure is assumed to be homogeneous and of cross-anisotropic or isotropic symmetry. A cross-anisotropic material has an axis of symmetry of rotation, which is assumed to be vertical, i.e., the elastic properties are equivalent in all directions perpendicular to the axis of symmetry (in horizontal, radial directions). In general, these properties are different from those in the direction parallel to the axis, whereas isotropic materials have the same elastic properties in both the vertical and horizontal directions. In the Austroads pavement design method (1992 and 2004) cross-anisotropic properties are used for subgrade materials and unbound granular aggregates and isotropic properties are used for bound materials such as asphalt and cemented materials. The stress-strain relations for a cross-anisotropic material in a particular layer are: εxx =
(1/Eh) (σxx
- νh σyy - νhv σzz)
εyy =
(1/Eh) (- νh σxx + σyy - νhv σzz)
εzz =
(1/Ev) (- νvh σxx - νvh σyy + σzz)
εxy =
((1+ νh)/Eh) σxy
εxz =
(1/f) σxz
εyz =
(1/f) σyz
The moduli and Poisson's ratios are related by the following equation: νvh /Ev = νhv /Eh
The condition that the strain energy must be positive imposes restrictions on the values of the elastic constants: Eh > 0
Ev > 0
1 > νh > -1
f>0 1- νh-2 νhv νvh > 0
For isotropic materials the restrictions become: E>0
0.5 > ν > -1.0
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To be able to model a cross-anisotropic material you need to specify five constants: the vertical Elastic modulus (E v), the horizontal Elastic modulus (E h), the Poisson’s ratio ( νvh), the Poisson’s ratio ( νh) and the Shear modulus (f). Data values for all five constants are rarely available. The Austroads Pavement Design Guide uses the following simplifications to model subgrade and unbound granular materials: Eh = 0.5 Ev νvh = νh = ν
f = Ev /(1+ ν) In this case, the material is defined simply by the vertical Elastic modulus, E v, and a single Poisson's ratio, ν. For isotropic materials, only the Elastic modulus and Poisson’s ratio need to be entered, as they are assumed to be the same in all directions.
Creating a new Layered System Click on the
button.
Click on the Layered System tab. Click on the New button. A dialog box will appear as shown below. You should now type in your ID (index) field of up to 20 characters and a descriptive title (up to 72 characters). For this example you can type in 'MyLayers' as the ID and 'Example of creating a new Layered System' as the Title . Click the OK button.
Now you can define the details of the layers in your layered system.
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Defining the Layer properties You add the layers working from the top of your pavement system, i.e., starting with typically asphalt or cemented material, and working downwards through the pavement. Click on the New button. A pop-up list will appear, as shown below. You will now choose the Material Type . To select the Material Type , click on the appropriate line then click the OK button.
A list of available materials will now appear. Select the required material by clicking on the appropriate line, then click on the OK button. A new record will be added at the bottom of the table and the cursor will be positioned in the Thickness column. Enter the layer thickness. You repeat this process to add as many layers as you require. The subgrade will extend to an infinite depth if you enter the thickness as 0.0 . As explained in Overview of Layered System and Material Properties, interfaces between the layers can be either fully continuous (rough) or fully frictionless (smooth), or a combination of both types. You can specify any interfaces as fully frictionless.
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1
By default, all interfaces are assumed to be rough . You can change the condition for the interface at the bottom of a given layer by clicking in the 'Interface Type' cell. You can then click on the down arrow at the right of the cell to select a 'Smooth' interface. Note that for a semi-infinite subgrade both 'Rough' and 'Smooth' are equivalent.
Duplicating a Layered System Sometimes you may want to create a Layered System that is similar to an existing one. The Duplicate function lets you duplicate an existing Layered System. Then you can change the settings that need to be different. Move the blue highlight to the Layered System that you want to duplicate:
Then click the Duplicate button. You will then see a form that will let you define the ID and Title of the newly duplicated Layered System:
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The ID and Title that are provided are based on the original Layered System - make sure that you modify the Title . After you click the OK button you will be taken to the Layered System Components table so that you can make your changes.
Adding a new Elastic Material Click on the
button.
Click on the Elastic Materials tab. You now choose the material type to be used. Click on the material type combo box as shown below to select from the available material types. Click on 'Subgrade (Austroads 2004)' for the Material Type . Click here to select Material Type
Click on the New button. A dialog box will appear, as shown below. You should now type in your ID (index) field of up to 20 characters. As you can see from the example below, the ID is used to sort the data. For this example, you can type in 'Sub_CBR2.5' . Type in 'Subgrade, CBR=2.5' for the Title . Click the OK button.
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You will now be given an opportunity to select a Performance Criterion . To select a Performance Criterion make sure the checkbox next to ‘Use performance criterion’ is checked, then click on the appropriate performance criterion. Click on the OK button.
A new record will be added to the table. Select 'Anisotropic' in the column headed 'Aniso?' . Then type in the moduli and Poisson's ratios as follows: Ev = 25.0 Eh = 12.5
(= 0.5 Ev)
νvh = νh = 0.45
f = 17.24
(= ν)
(= Ev /(1+ ν))
The new record should be as shown below:
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Adding a new Performance Criterion HIPAVE usually represents models in the form:
⎡ k ⎤ N = ⎢ ⎥ ⎣ ε ⎦ where N
b
(1) is the predicted life (repetitions)
k
is a material constant
b
is the damage exponent of the material
ε
is the induced strain (dimensionless strain)
HIPAVE can also handle log-linear models of the form: log10 ( N ) = k − b ε
(2)
Equation (1) is called a Standard Damage Relationship Type and Equation (2) is called a Log-Linear Damage Relationship Type. Before you add a new Performance Criterion you need to choose the appropriate Material Type. For each Material Type, all Performance Criteria use the same Damage Relationship Type.
Example: Asphalt tensile strain relationship For this example we consider the Shell asphalt fatigue criterion : ⎡ 6918(0.856 V + 1.08) ⎤ B ⎥ N = RF ⎢ ⎢ . ⎥ 0 36 Smix µ e ⎣ ⎦
5
where µε = maximum tensile strain (in units of microstrain ), VB = percentage by volume of bitumen in the asphalt, and
Smix= mix stiffness (Elastic modulus) in MPa.
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For this example, assume V B = 12.9 and Smix = 1600 MPa, so that the above equation simplifies to: N = [ 5889 / µε]5 To enter this data click on the
button.
Click on the Performance tab. You now choose the material type to be used. Click on the material type combo box (as shown on the first screenshot in Adding a new Elastic Material (on page 69)) to select from the available material types. For this example click on 'Asphalt' . Click on the New button. Now type in your ID (index) field of up to 10 characters and the Title (up to 72 characters). For this example type in 'Asph1600' for the ID. Type in 'Asphalt- 1600 MPa, Vb=12.9%' for the Title . Click the OK button.
A record will be added to the table and you can type in the relevant data as follows: The cursor will now be in the component field. Here you specify the particular displacement, stress or strain component to be used. You can select the component from a dropdown list by clicking on the button. If there are more entries than will fit in the listbox, there will be a slider bar on the right hand side. You can move down the list by clicking on the down arrow or by dragging the slider down. For this example select the ‘Max. Horizontal Tensile Strain’ (maximum horizontal tensile strain). The Location field defines the location (relative to a layer of this material) at which the criterion is to be applied. Click on the button to choose between ‘Top’ and ‘Bottom’ . For this example Location should be 'Bottom' . The entries for the remaining two parameters define the fatigue relationship N = [5889 / µε]5.
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Note carefully that strains in HIPAVE must be specified in dimensionless units (i.e., length/length, mm/mm). As HIPAVE assumes that the fatigue relationship is of the form N = [k / ε]b , the parameter µ (micro) must be replaced by 10 -6 giving: N = [k / ε]b So Constant (k) will be 0.005889 and Exponent (b) will be 5.0. The new record should be identical to the bottom row in the figure below:
Example: Log-linear performance relationship Click on the
button.
Click on the Performance tab. You now choose the material type to be used. Click on the material type combo box (as shown below) to select Cemented (Log-Linear) from the available material types.
Click on the New button. Now type in your ID (index) field of up to 20 characters and the Title (up to 72 characters). For this example type in 'CTB15000' for the ID. Type in ' CTB, E=15000MPa' for the Title . Click the OK button. A record will be added to the table and you can type in the relevant data as follows:
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For this example assume that equation (2) is used with: k = 10 b = 80000 The relevant strain component that is to be used is the maximum horizontal tensile strain at the base (bottom) of the layer. Note: Equation (2) expresses the strain component as a unitless (i.e. length/length, mm/mm)
quantity. If you are converting from an expression that uses microstrain, b must be adjusted appropriately. Move to the Component field by clicking on it or using the tab key. The screen should now look like this (the black highlight is on the new entry):
Here you specify the particular strain or stress component to be used (in this example it will be the maximum horizontal tensile strain. You select the component from the drop-down list by clicking on the button. If there are more entries than will fit in the list box there will be a slider bar on the right hand side. You can move down the list by clicking on the down arrow or by dragging the slider down. Select the entry Max. Horizont al Tensile Strain. The location field defines the location (relative to a layer of this material) at which the relationship is to be applied. Click on the
button to choose Bottom.
Now enter the values for k (= 10) and b (= 80000). The screen below shows the completed entries:
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Adding a new Material Type You can add new material types. To add a new material type, Click on the
button.
Click on the Material Types tab. Click New to create a new entry. A dialog box will now appear and you can enter the ID (index) field of up to 20 characters and Title field (up to 72 characters). Click the OK button. You will now choose the Generic Material Type for your new Material Type :
You will now be given an opportunity to select a Sub-Layering scheme . To select a Sub- Layering scheme , click the checkbox next to ‘use sub-layering’ , then click on the appropriate sub-layering scheme . Click on the OK button.
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The " Loads" and " Traffic Spectrum" Databases Introduction Seven inter-related databases are used for the Traffic data. The databases form a hierarchy:
Traffic Spectrum;
Traffic Spectrum Components;
Load Groups;
Load Group Components;
Load Locations;
Payload Distributions;
Payload Distribution Components.
Depending on whether or not the components you need already exist, the steps required are described in the following sub-sections.
Vehicle Specifications The HIPAVE vehicle library consists of so-called "Standard" vehicle specifications that are provided by Mincad Systems and "Custom" vehicles that you can define. You can browse the vehicle specifications as follows. Click on the
button.
Click on the Vehicle Models tab. You can browse by clicking on the Type and Manufacturer combo boxes. To see the specifications for any listed vehicle click on that row, then click on the Load Components and Locations tab.
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Automatic Updates for the Standard Vehicle Library Updates for the Standard Vehicle Library can be automatically imported from the Mincad Systems webserver. To do this, click on the
icon. You will then see a status screen like the one below.
The status screen shows the number of Vehicle records that have been imported/updated.
Adding Custom Vehicle Specifications You are encourage to send us vehicle specifications for inclusion in the Standard Vehicle Library. As soon as the Library is updated you will be able to update your Library by clicking the Import icon. But if required, here are details on how you define your own vehicle models directly: Click on the
button.
Make sure you make the correct choices for the Type and Manufacturer combo boxes, as shown below:
Contact Mincad Systems for a Library Update if the combination of Type and Manufacturer that you want to use is not available. The remaining details depend on the vehicle type, i.e. Fork Lift or Straddle Carrier.
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Vehicle with Unequal Axle Lo ads
Click on the New button. A dialog box will appear as shown below. You should now type in your ID (index) field of up to 20 characters and a descriptive title (up to 72 characters).
For this example you can type in 'HysterHxyz' as the ID and 'Hyster Hxyz' as the Title . Click the OK button. Now type 'Hyster Hxyz' as the Plot Label :
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Now click on the Load Components and Locations tab. This will bring up a form that lets you specify the axle load characteristics and wheel positions. The axle load versus payload characterstics are illustrated by the following graph:
Assuming the tyre pressure is 0.9 MPa for all tyres, after you enter the axle load characteristics the screen will look like this:
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Note that Component No. 1 is the Front axle. You can now add the Wheel Locations. Usually we only model one side of the vehicle. Click the New button to add each each wheel. After adding the 2 wheels wheels on the Front Front Axle (Component No. 1) and the one wheel on the Rear Axle (Component No. 2), the Wheel Locations table will look like this:
Vehicles Vehicles with Equal Axle Loads
Click on the New button. A dialog box will appear as shown below. You should now type in your ID (index) field of up to 20 characters and a descriptive title (up to 72 characters).
For this example you can type in 'KalmESCxyz' as the ID and 'Kalmar ESCxyz (fictitious)' as the Title . Click the OK button. Now type 'Kalmar ESCxyz' as the Plot Label :
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Now click on the Load Components and Locations tab. This will bring up a form that lets you specify the axle load characteristics and wheel positions. Vehicles such as straddle carriers carriers are assumed to have equal equal loads on each axle. In this case the vehicle loading characteristics are specified in terms of the unladen weight of the vehicle, the number of axle rows (i.e. the number of axles seen from one side of the vehicle), the total number of wheels on the vehicle and the tyre pressure. For this example, assume the following values: Number of Axle Rows (i.e. the number of axles seen from one side of the vehicle)
4
Total Number of Wheels
8
Tyre Pressure
0.56 MPa
Unladen Weight
62 tonne
After you enter these axle load characteristics the screen will look like this:
You can now add the Wheel Locations. Usually we only model one axle and only one side of the axle. Click the New button to add the wheel wheel details. After adding the one one wheel, the Wheel Wheel Loc ations table will look like this:
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Traffic Spect Spectrums rums HIPAVE is designed to let you conveniently specify a Traffic Spectrum in terms of a mix of different vehicle models. For each vehicle in the spectrum you specify the number of movements and the payload payload distribution. For each load case the wheel loads loads are automatically calculated from the vehicle characteristics and the payload. For an overview of the concepts see How HIPAVE handles Traffic Distributions (on page 15).
Creating Creating a new Traffic Traffic Spectru Spectru m Traffic Spectrum Spectrum screen is not already active, click on the If the Traffic
button.
Click on the Spectrum tab. Click on the New button. A dialog box will appear as shown below. You should now type in your ID (index) field of up to 20 characters and a descriptive descriptive title (up to 72 characters). For this example you can type in 'TrafficTry' as the ID and 'Example of creating a new Traffic Spectrum' as the Title . Click the OK button.
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The Spectrum Components form will now appear. Now define your Spectrum Components : Click New for each vehicle model you wish to include. This will activate a pop-up list of possible choices:
You can browse by clicking on the Type and Manufacturer combo boxes. You can move the highlight to the vehicle that you wish to use by positioning the mouse pointer on it and clicking once. If there are more entries than will fit in the listbox there will be a slider bar on the right. You can move down the list by clicking on the down arrow or by dragging the slider down. You finally select the vehicle by double clicking on it. For this example, choose the Hyster Forklift model H40.00E-16CH . A new record will be added at the bottom of the table and the cursor will be positioned in the Movements column.
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Enter the number of vehicle movements (or passages) over the desired design life. For this example, enter 100,000 movements. The Graph Label is an optional string of up to 20 characters that is appended to the Vehicle Model Plot Label used for the Legend when plotting the results. This is useful when you need to have more than one Spectrum Component that uses the same Vehicle Model, for example your spectrum may include the same model twice, once with unloaded containers and once with loaded containers.
Characterizing Payload Distributions As mentioned earlier, you can either use a "Standard" payload distribution (one that already exists in the database) or define a "Custom" distribution for the current load case.
Using a Standard Payload Distri buti on Click the Distribution Type combo and select Standard . A pop-up list will appear, as shown below. You will now choose the Standard Payload Distribution . To select the Standard Payload Distribution , click on the appropriate line then click the OK button.
The part of the screen that relates to the choice of Payload Distribution looks like this:
Chapter 7 How to Modify the Databases
Click the Select button if you want to choose another Standard Payload Distribution . See Standard Payload Distributions (on page 88) for details on how to create your own standard payload distributions and how to browse the details of existing ones.
Defining a Custom Payload Distribution Make sure Distribution Type is set to Custom . For this example, use the following payload distribution: Payload (tonnes)
Count
2.5 4 6 8.5 12.5 17.5 22.5 27.5
1000 200 300 200 100 1200 7500 1000
For each row in the table, click the New button and enter the Payload and Count . After you enter the last row of data, the screen should look like this:
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Values in the columns that are labelled Normalized Movements and Actual Movements are calculated from the values in the Count column. The Normalized Movements are given by normalizing the values of Count - so that the sum of the Normalized Movements values is 1.0. The Actual Movements values are scaled so that the total matches the total number of movements (100,000 in this example) defined for the current Spectrum Component . The absolute magnitude of the Count values is not important, as they are normalized (i.e. scaled so that they add up to 1.0) when you run a HIPAVE analysis. This gives you a lot of flexibility in how you define your Count values - for example they could be based on historical data or could be simply actual movements. The calculated columns are not updated while you type the data on a particular row - but are updated when you press the Enter key when in the Count cell. The following screendump shows the updated calculated columns after pressing the Enter key.
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Duplicating a Traffic Spectrum Sometimes you may want to create a Traffic Spectrum that is similar to an existing one. The Duplicate function lets you duplicate an existing Traffic Spectrum. Then you can change the settings that need to be different. Move the blue highlight to the Traffic Spectrum that you want to duplicate:
Then click the Duplicate button. You will then see a form that will let you define the ID and Title of the newly duplicated Traffic Spectrum:
The ID and Title that are provided are based on the original Traffic Spectrum - make sure that you modify the Title. After you click the OK button you will be taken to the Traffic Spectrum Components table so that you can make your changes.
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Standard Payload Distributions Introduction The "Standard" payload distribution feature is designed to conveniently facilitate re-use of particular distributions across a range of vehicle models and projects. Click on the
button.
Click on the Payload Distribution s tab.
To see the actual distribution for any entry in the list click on that row, then click on the Distribution Details tab.
Chapter 7 How to Modify the Databases
Creating a new Standard Payload Distribution If the Payload Distributi ons screen is not already active, click on the
button.
Click on the Payload Distribution s tab.
Click on the New button. A dialog box will appear as shown below. You should now type in your ID (index) field of up to 20 characters and a descriptive title (up to 72 characters). For this example you can type in 'TermXExport' as the ID and 'Terminal X - Loaded Export' as the Title . Click the OK button.
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The Distribution Details form will now appear. Now define your Distribution Components : For this example, use the following payload distribution: Payload (tonnes)
Count
8.0 10.0 12.0 15.0 18.0 24.0 30.0
200 400 600 800 1200 5500 1000
For each row in the table, click the New button and enter the Payload and Count . After you enter the last row of data, the screen should look like this:
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Values in the column that is labelled Normalized Movements are calculated from the values in the Count column. The Normalized Movements are given by normalizing the values of Count - so that the sum of the Normalized Movements values is 1.0. The absolute magnitude of the Count values is not important, as they are normalized (i.e. scaled so that they add up to 1.0) when you run a HIPAVE analysis. This gives you a lot of flexibility in how you define your Count values - for example they could be based on historical data or could be simply actual movements. The values in the Normalized Movements column are not updated while you type the data on a particular row - but are updated when you press the Enter key when in the Count cell. The following screendump shows the updated Normalized Movements column after pressing the Enter key.
You can now use your new Standard Payload Distribution in any Traffic Spectrum, see Creating a new Traffic Spectrum (on page 82).
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Dynamic Load Factors So-called Dynamic Load Factors are used in the British Ports Association Design Guide (British Ports Association, 1996) to account for the effects of dynamic loading induced by cornering, accelerating, braking and surface uneveness. These are simple multipliers that are applied to the design loads and can vary with each axle. If the Traffic Spectrum screen is not already active, click on the
button.
Click on the Load Factors tab. You should now see the Load Factors form:
To use Dynamic Load Factors, Click on the Use Dynamic Load Factors checkbox. You will now see the current Traffic Spectrum Components. For each Component, you can define Dynamic Load Factors for each axle, as shown below:
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Wander Options If the Traffic Spectrum screen is not already active, click on the
button.
Click on the Wander tab. You should now see the alternative Wander options:
Three alternative Wander options are available:
No Wander for any Vehicle Model in the Traffic Spectrum;
Same Wander for All Vehicle Models in the Traffic Spectrum;
Wander varies with Vehicle Model.
If the Wander varies with the Vehicle Model, you specify the Wander in the Spectrum Components table (accessed by clicking on the Spectrum Components tab):
The wander is assumed to follow the bell-shaped frequency distribution given by the Normal (or Gaussian) distribution. The degree of wander is given by the Standard Deviation. Some additional parameters define the numerical approximation used to model the effects of Wander. Normally the default values of these can be used.
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The parameter XWDEL is used to subdivide the wander distribution. For acceptable accuracy XWDEL must be no greater than 100 mm. The parameter X WMAX sets the limiting value used to approximate the Normal distribution. For acceptable numerical accuracy X WMAX needs to be 2.7 times the maximum Standard Deviation of wander, or greater. 4500
XWDEL (=100 mm)
4000
Total Movements = 100,000 3500
Standard Deviation = 1000 mm
t o3000 l S n i 2500 s t n e m2000 e v o 1500 M 1000
500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 6 4 2 0 1 8 1 6 1 4 0 8 6 - 4 - 2 3 1 2 1 - 2 - 2 - 2 - 2 - 2 -
0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 4 6 8 1 0 1 2 6 1 8 2 0 2 2 6 2 8 3 0 1 4 1 2 4 2
Lateral Position (mm)
XWMAX (=3000 mm)
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Coordinates for Results Click on the
button.
This screen has fields for specifying the locations for which results are to be computed and the method for treating damage pulses. Two alternative formats are available for specifying the points to be used for results calculation:
An array of equally spaced points along a line parallel to the x-axis ; or
A grid of points with uniform spacing in both the x-direction and the y-direction .
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Appendices
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References Austroads (1992). Pavement Design – A Guide to the Structural Design of Road Pavements. Austroads Publication No. AP-17/92. Austroads (2004). Pavement Design - A Guide to the Structural Design of Road Pavements , Report AP-G17/04. Barker, W. and Brabston, W. (1975). Development of a structural design procedure for flexible airport pavements . Report No. S-75-17. US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss. British Ports Association/Interpave (1996). The Structural Design of Heavy Duty Pavements for Ports and other Industries , 3rd ed., Interpave, Leicester. Mincad Systems and Pioneer Road Services (2007). Heavy Duty Industrial Pavement Design Guide . (Web: http://www.mincad.com.au/hdipdg/). Pereira, A. T. (1977). Procedures for development of CBR design curves . Instruction Report S-77-1, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss. Rodway, B. (1995a). Design Of Flexible Pavements For Large Multiwheeled Aircraft. Int. Conf. on Road & Pavement Technology , Singapore, 27-29 September, 1995. Rodway, B. and Wardle, L.J. (1998). Layered Elastic Design of Heavy Duty and Industrial Pavements. Proc. AAPA Pavements Industry Conf., Surfers Paradise, Australia. Rodway, B., Wardle, L.J. and Wickham, G. (1999). Interaction between wheels and wheel groups of new large aircraft. Airport Technology Transfer Conference , Atlantic City, U.S.A., April 1999, Federal Aviation Administration. Wardle, L.J. (1977). Program CIRCLY User’s Manual. CSIRO Australia. Division of Applied Geomechanics, Geomechanics Computer Program. No. 2. Wardle, L.J. (2004). Program CIRCLY Theory and Background Manual . Mincad Systems, Australia. Wardle, L.J. and Rodway, B. (1998). Recent Developments in Flexible Aircraft Pavement Design using the Layered Elastic Method. Third Int. Conf. on Road and Airfield Pavement Technology , Beijing, April 1998. Wardle, L.J., Rodway, B. and Rickards, I. (2001). Calibration of Advanced Flexible Aircraft Pavement Design Method to S77-1 Method. in Advancing Airfield Pavements, American Society of Civil Engineers, 2001 Airfield Pavement Specialty Conference , Chicago, Illinois, 58 August 2001 (Buttlar, W.G. and Naughton, J.E, eds.), pp. 192-201. Wardle, L.J., Youdale, G. and Rodway, B. (2003). Current Issues For Mechanistic Pavement Design. in 21st ARRB and 11th REAAA Conference , Cairns, Australia, 18 - 23 May, 2003, Session S32, ARRB Transport Research.
