Published in ASCE Transportation Congress, San Diego, 22-26 October, 1995.

Development and Application of an
Improved Airport Pavement Design Method

Leigh J. Wardle and Bruce Rodway

ABSTRACT: The paper provides an introduction to APSDS (Airport Pavement Structural Design System), a software package for the design of flexible airport and industrial pavements. APSDS is based on the layered elastic program CIRCLY. The use of the program is described briefly, and features that are considered to enhance the design of airport pavements are listed. The program’s ‘transparency’ and flexibility enables airport pavement designers to readily modify all input data, including aircraft mix, aircraft wander, numbers and mass, pavement layer thicknesses and material properties, and also the performance models. All main gear wheels can be included in the analyses to explore the interaction between wheels and wheel groups. The empirical data from the US Army Corps of Engineers full-scale tests are re- analysed to an unprecedented level of detail to develop pavement performance models. The re-interpreted results appear to give a better fit to the test data than alternative analysis methods. The design and reliability implications of this model are discussed.

A study of the interaction of multiple gears shows that although alternative performance models can give a similar ‘goodness of fit’ to the full-scale single gear test data, widely different damage predictions are obtained when they are used to extrapolate beyond the limits of the test data. Thus, further full-scale testing is required to quantify the pavement damage caused by large multiwheeled gears and by the interaction of aircraft gears.

INTRODUCTION

Most current procedures for flexible airport pavement design and analysis, in particular the Federal Aviation Administration (FAA) design method and the International Civil Aviation Authority (ICAO) system for aircraft load classification, have their origins in the empirical CBR thickness method originally developed for highways. The procedures involve simplifying assumptions that were necessary for manual calculation, but which are no longer justified given the availability of desk-top computers. The major simplifications are related to the use of single layer elastic theory, the pass-to-coverage ratio and the deflection-based Equivalent Single Wheel Load (ESWL) concept for multiwheel aircraft gear.

The empirical CBR method relates ESWL, pavement thickness and subgrade CBR. It does not address the makeup of pavement layers so it has no mechanism for crediting bound layers for their superior load spreading characteristics. Thick bound layers are increasingly used, however, and are required by airport authorities such as the FAA. Bound layers are typically accounted for within the empirical design by using layer equivalency factors based on elastic layer theory. The CBR method of pavement thickness design assumes a failure mode that consists of surface rutting caused by overstressing the subgrade. Pavement failure due to fatigue cracking of the bituminous surfacing or cracking of the other bound layers is not addressed by the method and must be separately considered by the designer. Although this paper primarily deals with the application of APSDS to the rutting mode, it is also applicable to the fatigue failure of bound layers.

A validated rational method of pavement analysis is needed primarily to cater for bound layers and to assess more rigorously the degree to which wheels and wheel groups interact to cause increased pavement damage. The need has become more urgent with the arrival of the B777 whose 6-wheel gear configuration differs from those used in full-scale pavement tests. The urgency is further increased by the proposed development of very large aircraft with more wheels on each strut and with some struts closely spaced near the centre of the aircraft.

Efforts by researchers have focussed on the layered elastic method as that most likely to provide an adequate solution within the short time frame that is available. Elastic models with isotropic (same property values along all axes) layers have been used to compute maximum values of chosen damage indicators, most commonly subgrade strain, which are then related to pavement life via interpretations of the full-scale test data. Generally the pavement life has been expressed in terms of ‘coverages’ (as defined later). The coverage concept is an unnecessary simplification that solely addresses the statistics of load distribution at the pavement surface and becomes increasingly inappropriate with increasing depth to subgrade. It incorrectly implies that the reduction in damage due to aircraft wander is the same for all pavement thicknesses.

APSDS (Airport Pavement Structural Design System) has been developed to help overcome some of the limitations of current design systems. It avoids the coverage concept by computing the strain distribution (not just a single maximum) at all points across the pavement for a given depth and relates this, rather than single maximums, to pavement life using the full-scale test data. As will be shown in a later section, this unique capability models the lateral distribution of traffic in more detail than alternative methods.

APSDS has a menu-driven interface that runs under Microsoft Windows 3.1 and is based on the layered elastic program CIRCLY (Wardle, 1977) that has been used on numerous pavement design projects over the last 20 years. CIRCLY is at the core of the Austroads Pavement Design Guide and is routinely used for highway design in Australia.

The US Army Corps of Engineers full-scale test data has been re-interpreted to an unprecedented level of detail using APSDS. Most importantly the re-interpreted results appear to give a better fit to the full-scale test data than alternative analysis methods.

A major focus during the development and application of APSDS has been to address the problems involved in extending current design methods to assess the gear layouts proposed for future generation ‘super-heavy’ aircraft. A number of the important unresolved difficulties are discussed.

METHODOLOGY

Cumulative Damage Concept

APSDS is based on a concept described by Monismith et al. (1987). The important new and unique feature is that subgrade strains, or alternative indicators of the rate at which surface rutting develops, are computed for all points across the pavement in order to capture all damage contributions from all the aircraft wheels in all their wandering positions. This contrasts with previous methods which computed single maximum values of the damage indicators. In the case of fatigue failure of bound layers, APSDS would typically compute the tensile strains at the undersides of the relevant layers.

The strains are converted to damage using a performance model of the form:

(1)

where N is the predicted life (repetitions of e )

k is a material constant

b is the damage exponent of the material

e is the load-induced strain (unitless strain)

More complex performance relationships could be accommodated by the program if required.

The Damage Factor for the i-th loading is defined as the number of repetitions (ni) of a given damage indicator divided by the ‘allowable’ repetitions (Ni) of the damage indicator that would cause failure. The Cumulative Damage Factor (CDF) is given by summing the damage factors over all the loadings in the traffic spectrum using Miner’s hypothesis.

Cumulative Damage Factor = (2)

The pavement is presumed to have reached its design life when the cumulative damage reaches 1.0. In the case of a rutting failure mode, parameters k and b must be established from full-scale aircraft trafficking tests to failure, using an iterative procedure. For the fatigue mode, k and b can potentially be obtained from laboratory testing. The extensive performance history of bound materials under highway conditions is expected to be adequate to calibrate laboratory-derived performance models for use in the airfield situation.

The method incorporates:

· the design repetitions of each aircraft at their various operating weights,

· the wander of the aircraft, and

· the material performance properties used in the design model

Figure 1 shows the general concepts for a single gear. The basic procedure is:

1. The strain distribution across the transverse section is determined.

2. The number of aircraft passes is determined for a series of equally spaced intervals that span the wander distribution.

3. The damage contributions due to each of the wander distribution intervals are summed at a series of points across the section.

Figure 2 is a typical cumulative damage ‘profile’ across the pavement generated by APSDS.

Aircraft Wander

The conventional pavement design and analysis systems relate the pavement life expressed in aircraft passes to the maximum value of a chosen damage indicator, typically subgrade vertical strain or deflection calculated from elastic models. In these systems the statistics of aircraft wander are accounted for in terms of a pass-to-coverage ratio (PCR). A point on the pavement is said to receive a ‘coverage’ when any part of a tyre’s contact area passes over it. The PCR is defined as the number of passes of a wandering aircraft that is statistically required for the most frequently covered point to receive one coverage. The PCR depends upon wheel configuration, tyre width and the degree of aircraft wander. The PCR concept solely addresses the statistics of load distribution at the pavement surface and, therefore, incorrectly

 

Figure 1 Schematic of effect of aircraft wander on cumulative damage

Figure 2 Sample cumulative damage plot

implies that the reduction in pavement damage due to aircraft wander is the same for all pavement thicknesses.

APSDS does not use the coverage concept. Instead the strain distribution (not just a single maximum strain) at all points across the pavement for a given depth is used to capture the damage contributions of all the aircraft wheels in all their wandering positions.

The user can specify the standard deviation of wander that is appropriate to the particular pavement. The standard deviation for a taxiway is typically taken as 773 mm and for a runway as 1546 mm (Ho Sang, 1975). These correspond to wander widths of 1778 mm (70 inches) and 3556 mm (140 inches) where wander is defined as the pavement width within which the centrelines of aircraft are contained 75% of the time. For a parking bay, a standard deviation of the order of 100 mm may be appropriate.

A simple example (Figure 3) illustrates how the coverage concept becomes increasingly inappropriate with increasing depth to subgrade. This shows the effect of aircraft wander upon damage for two depths, as calculated using APSDS. In the 500 mm case (Figure 3a), taxiway wander reduces damage by 80% of that caused in the channelised, no wander case. This contrasts with the 1500 mm case (Figure 3b) where taxiway wander reduces the channelised damage by only 30%.

RE-INTERPRETATION OF FULL-SCALE TESTS

Introduction

The empirical base for most airport pavement design systems in use world-wide are the full-scale pavement traffic tests conducted by the US Army Corps of Engineers over the past 50 years. Barker and Gonzalez (1994) summarise the test results and list citations to the original reports.

The most recent series of tests is the Multiple Wheel Heavy Gear Load Tests (MWHGLT) conducted at the Waterways Experiment Station, Vicksburg, Mississippi in the late 1960s and early 1970s (Ahlvin et al., 1971). Test pavements were constructed using unbound granular material. Total pavement thicknesses ranged from 380 mm to 1041 mm including 75 mm of asphalt surfacing. The pavements were trafficked to failure with single and multiwheel assemblies ballasted to full aircraft loadings.

The development of the conventional pavement design method from the full-scale test data is described by Pereira (1977). Multiwheel gear loads were accounted for by the concept of Equivalent Single Wheel Load. The ESWL was defined as the load on a single tyre that produced the same maximum vertical deflection at subgrade level as the multiwheel load. Thus maximum subgrade deflection was selected as the pavement damage indicator. The testing of multiwheel gears in the late 1960s and early 1970s showed that the deflection-based ESWL design method overstated the degree of interaction between wheels. This led to the introduction of pavement thickness reduction

 

(a) Depth = 500 mm

 

(b) Depth = 1500 mm

Figure 3 Effect of depth and wander on pavement damage

 

factors (a factors) which were a function of the total number of wheels used to compute the ESWL, and the level of traffic. They did not depend upon the wheel group configurations, the arrangement of wheels within a group, or pavement thickness.

This revised methodology has been used in practice for many years, but recently there has been a growing acknowledgement that the method has serious shortcomings, particularly for planes with more than four wheels on a strut. The method appears to give unrealistically high damage ratings to the new Boeing 777 that has six wheels on each of two main wheel struts.

Recent research efforts have used modern day numerical models such as layered elastic analysis to re-interpret the full-scale test data. Researchers have assessed a range of alternatives to deflection as a damage indicator. The ‘slope method’ of Preston (1991) was one of the first attempts. Subgrade vertical strain is currently the most commonly used damage indicator (Lane et al., 1993, FAA, 1994). Barker and Gonzalez (1992, 1994) explored the implications of alternative damage indicators including vertical strain, maximum shear strain, maximum horizontal shear strain and octahedral strain. They argued that the selection of a damage indicator for design appeared to be a matter of personal choice as the alternatives all had a similar ‘goodness of fit’ to the full-scale test data. However, as discussed in a later section, APSDS analyses indicate that alternative calibrated performance models have different attenuation characteristics that give quite different damage predictions for the same aircraft when gear interaction effects are included.

Method of Test Data Analysis

As APSDS does not use the coverage concept, existing damage models based on coverages could not be used. To derive appropriate damage models for APSDS, a detailed study of the original Corps of Engineers test data was undertaken. APSDS was able to model the lateral distribution of test traffic in more detail than previously attempted.

Attention was concentrated on tests involving wheel configurations that are most representative of modern large aircraft, i.e. the 4-wheeled twin tandem (B747, B36) and 6-wheeled delta twin tandem (C5A). The single wheel tests were specifically omitted because APSDS analyses showed that the spacing between wheel paths was too wide to produce a smooth distribution of strains at subgrade level. This unrealistically over-channelized traffic distribution would have damaged the test pavements to a much higher degree than the more uniform distribution expected in practice.

The following example illustrates the method: Test 3B-5 involved trafficking a twin tandem test rig (a single B747 gear) on a 1040 mm thick pavement over a CBR 4.0 subgrade. Figure 4 shows the material properties and layer thicknesses used in the re-analysis. A simple systematic sequence of sub-layering for the unbound basecourse and sub-base material was used to

 

Figure 4 Layer properties used for sample analysis

Figure 5 Re-analysis of full-scale test showing damage contributions from individual lanes and total
(B747 dual tandem on 1040 mm pavement)

represent stress dependency effects; the modulus of each 150 mm layer is double that of the underlying layer, up to a maximum of 600 MPa. Although the sub-layering is different in detail from the method used by the Corps of Engineers (see Barker and Brabston, 1975), the design implications are not sensitive to the layering method used. However it must be emphasised that, for consistency, the sub-layering system used to establish the performance model must also be used when analysing or designing pavement structures.

The test rig travelled along five equally spaced guidelines with the proportion of passes for each guideline calculated to approximate a prescribed aircraft wander distribution. The pavement was deemed to have failed after 454 passes. As shown on Figure 5 the APSDS sums the detailed contributions from the traffic on each guideline to give the total damage.

The particular parameters k (= 0.00423) and b (= 6.9) used in the damage model (see Equation 1) were determined so that the calculated maximum cumulative damage factor (CDF) for the two B747 tests (3B-5 and 3B-4) was 1.0. These parameters were then used for the other tests as shown on Figure 6a which plots the maximum CDF for each test against number of strain repetitions or pulses. The test numbers as used by Barker and Gonzalez (1994) are next to each data point. Values of k and b could, if required, be iteratively determined to give a least squares best fit to all the test data considered.

To provide a basis for comparison with the conventional method of analysis (i.e. maximum vertical strain vs. coverages) damage factors have been calculated using results reported by Barker and Gonzalez (1994). For consistency with the APSDS analysis, the values of parameters k and b used in a relationship between coverages and maximum subgrade strain (similar to Equation 1), were determined by assuming that the ‘best fit’ line (damage factor=1.0) passes through the two B747 test points (Figure 6b).

Re-interpretation of the test data with APSDS produces significantly less scatter than that given by the conventional method of analysis (ignoring the B36 test no. 28).

PAVEMENT DAMAGE DUE TO NEW LARGE AIRCRAFT

Attempts to assess the proposed gear configurations of future generation aircraft using APSDS have highlighted unresolved difficulties.

Methods for Handling Damage Pulses

The pattern of strains at subgrade level experienced during the passage of a multiple axle gear primarily depends on the pavement depth. This is illustrated in Figure 7. The two extremes are:

 

(a) APSDS method

 

 

(b) Coverages method (after Barker and Gonzalez, 1994)

 

Figure 6 Summary of predicted cumulative damage for full-scale tests.

The nature of subgrade strain pulses is a difficult and important issue for pavement analysis and design. It is expected that pavement rutting damage will depend upon pulse numbers, amplitudes and shapes. There is no empirical data that quantifies the extent to which the damage depends on the transverse and longitudinal dimensions of the pulse. However the elongated pulses of the B777 and especially the AN225 differ so markedly from those generated by the ‘well-conditioned’ gears used in the full-scale tests, that use of damage relationships derived from the tests must be problematic.

For most of the Corps of Engineers tests the elastic models predict a short distinct strain pulse at subgrade level for each axle. As illustrated in Figure 7, for deeper pavements (say 1.5 m or more) the models predict a single combined pulse corresponding to the entire gear for the B747 and B777 and an extremely long single pulse for the AN225. Note that the elastic model predicts significant zones of negative vertical strains. These negative zones have implications for the prediction of damage from multi-geared aircraft and will be discussed later.

With respect to pulse counts, methods of test interpretation in terms of coverages imply one subgrade pulse per axle regardless of pavement depth. This damage assumption becomes progressively more conservative with increasing pavement depths. Furthermore, the degree of conservatism is greater for aircraft having more axles per gear. For example the 3-axled B777 gear will be rated as increasingly more damaging relative to the 2-axled B747 gear as pavement thickness is increased. This conservatism may be offset to some degree if, as suspected, longer pulses are more damaging than shorter pulses of the same amplitude. There is, however, no test data to quantify these effects. APSDS allows the user to specify the number of subgrade pulses per aircraft pass to be used in damage calculations. This nomination is made having regard for the particular geometry of each case.

Multi-Gear Interaction

The recent arrival of the Boeing 777 and the necessity to evaluate gear configurations of new generation civil aircraft has focussed attention on the need to extend models to accommodate larger numbers of wheels in a gear and the interaction of all gears. Predictions of damage resulting from interaction between gears do not, however, have a high confidence level because there is no test data that addresses this issue. The full-scale tests essentially characterised loading by single gear assemblies. Although the C5A test rig consisted of two main gears, layered elastic analysis suggests they were too far apart to interact significantly at subgrade level. The FAA has proposed a 7-year research program, including extensive full-scale accelerated tests, to quantify the effects of more than four wheels on a strut and interaction effects between closely spaced struts (FAA, 1993).

The load response of most pavement construction materials is non-linear and stress-dependent. Load-induced deformations of material elements

 

(a) Depth = 1 m

 

(b) Depth = 2 m

 

Figure 7 Effect of depth on nature of vertical strain pulses

 

occur throughout the pavement structure, the aggregate effect of which is to produce surface ruts. Past and present methods of pavement analysis do not attempt to model this deformation process in a fundamental way that would confront its acknowledged complexity. Instead, single computable ‘damage indicators’ are chosen, typically vertical components of deflection, strain or stress at subgrade level. These are then correlated to the rate at which surface ruts develop in full-scale trafficking tests. The tests were essentially limited to single gears with no more than two axles, and pavements that were relatively thin. Because of this simplified approach, there appears to be no licence to use these correlations for situations beyond those encompassed by the tests.

It is clear that maximum subgrade vertical deflection, strain or stress will not indicate severity of surface rutting in the limiting case of extended uniform loading. A uniform pressure applied to a very large area of the pavement surface produces large vertical deflections, strains and stresses at subgrade level. But because they are uniform, the subgrade soil suffers no distortion, only uniform vertical compression, so no surface rutting develops.

Multiwheel landing gears proposed for some of the new generation aircraft will be likely to produce laterally extended, near-uniform loadings that will cause large maximum deflections, strains and stresses at subgrade level. Consequently the current design methods that use a single parameter such as maximum deflection, strain or stress as an indicator of surface rutting will predict very high damage, yet the high degree of uniformity may mean that relatively little rutting will actually occur.

APSDS has been used to study multiple gear interaction effects for a Boeing 747 using a range of alternative damage models. Results from this study 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. For each of three alternative damage models, single gear damage and the damage caused by all sixteen wheels is computed for two pavement depths, 1040 mm and 1710 mm. Damage beneath the rear and front gear as multiples of that computed for a single isolated 4-wheel gear is shown in Table 1.

The first method uses subgrade vertical strain as the damage indicator, and isotropic pavement layers and subgrade. As noted earlier, elastic theory predicts that vertical subgrade strains are negative in some locations (see Figure 7). The significance when calculating gear interaction effects is that, for some geometries, the negative zones generated by one gear fall beneath other gears and reduce the predicted damage. That is, the anomalous result is obtained that the addition of fully loaded wheels reduces rather than increases pavement damage. For the 1040 mm pavement, the damage beneath the rear and front B747 gears is reduced to 0.65 and 0.75 of the single gear value respectively when all gears are included. Reductions do not, however, occur for the deeper 1710 mm pavement. Here the damage beneath the rear and front gears increases to 2.50 and 1.25 times respectively.

The second method is identical to the first except that the subgrade has a 2:1 anisotropy. The third method retains the anisotropic subgrade but uses subgrade vertical stress rather than strain as the damage indicator. The merit of vertical stress is that, like vertical deflection, it produces no negative zones so anomalies of the kind that arise when using vertical strain cannot occur for any pavement and gear geometry.

Comparing the rows of the table, the three alternative methods, each of which was successfully calibrated against the full-scale test data, are seen to produce greatly different predictions of the damage caused by the interactions of the sixteen main wheels of the Boeing 747.

 

Table 1 B747 Multiple gear interaction

Relative damage, computed using three damage models

 


DAMAGE MODEL

1040mm PAVEMENT

1710mm PAVEMENT

REAR GEAR

FRONT GEAR

REAR GEAR

FRONT GEAR
 Vertical subgrade strain Isotropic subgrade

0.65

0.75

2.5

1.25
Vertical subgrade strain Anisotropic subgrade

1.1

0.97

4.8

2.1
Vertical subgrade stress Anisotropic subgrade

1.7

1.25

8.6

3.3

 

DESIGN RELIABILITY

Pavements designed with APSDS using the ‘best fit’ subgrade damage model parameters will have a 50% design reliability. That is, they are just as likely to fail before the design life as after the design life. This is because the parameters have been selected to give the best fit to the test points and because the pavement models use the best estimates of subgrade CBRs of the test sections, not lower, statistically derived values. The Corps of Engineers empirical CBR design curve was also drawn on this ‘best fit’ basis using the best estimates of subgrade CBR (Potter, 1985).

Failure of the test sections was defined as 25 mm rutting, or 25 mm heave outside the trafficked zone, or cracking judged to render the pavement surface permeable to water (the cracks extended through the full thickness of the asphalt). For design purposes a less severe pavement distress mode as an ‘end-of-life’ condition and/or a higher reliability than 50% may be specified. In these circumstances the APSDS damage relationship could be adjusted to give a higher percentage of the test points below the failure line (CDF=1.0). However, the resulting increase in reliability could not be estimated with confidence because of the small number of available test points.

In the context of modern aircraft pavement structures and traffic, the most serious reliability issues result from fundamental limitations of the test data. Design of major pavements now commonly entails substantial extrapolations beyond the data base in respect to:

The uncertainties inherent in these extrapolations cannot presently be quantified.

CONCLUSIONS

APSDS has unique features that will enhance and optimise the analysis and design of airport pavements:

The system’s transparency, speed and flexibility enables design specialists to readily change all problem inputs including aircraft wander, aircraft numbers and mass, layer thicknesses and material properties and also the performance models. This allows rapid assessment of the sensitivity to each component input and for all design assumptions.

The Corps of Engineers full-scale test data has been re-interpreted to an unprecedented level of detail by including the actual lateral traffic distribution. The APSDS model is shown to provide a better fit than previously reported. This suggests that the treatment of aircraft wander statistics is more realistic than the simplified ‘coverage’ concept used by other design systems, which only addresses the load distribution at the pavement surface. APSDS computes the effects of wander at subgrade level and so includes the influence of pavement thickness and properties upon the amount of damage reduction that results from aircraft wander.

Considerable difficulties remain in predicting the impact of new-generation large aircraft on the thickness requirements for flexible pavements. An APSDS study of the interaction of multiple gears shows that although alternative performance models can give a similar ‘goodness of fit’ to the full-scale single gear test data, widely different damage predictions are obtained when they are used to extrapolate beyond the limits of the test data.

The large wheel groups of the new and proposed large aircraft should cause less surface rutting than predicted by current methods and may not be significantly more damaging to flexible pavements than present generation aircraft. However, further full-scale testing, as planned by the US Federal Aviation Administration, is required to quantify damage caused by large multiwheeled gears and by interaction of aircraft gears.

ACKNOWLEDGEMENTS

The original system concept was developed by Ian Rickards, Technical Manager- Australia, Pioneer Road Services Pty. Ltd. Pioneer financed the initial development and have supported the promotion of APSDS to the international airport design community. The authors wish to acknowledge Ian Rickards for his enthusiastic support and active participation in our research. Permission of the Federal Airports Corporation to publish this paper is gratefully acknowledged.

All components of the APSDS (Airport Pavement Structural Design System) software are Copyright MINCAD Systems Pty. Ltd., 1970-95.

REFERENCES

Ahlvin, R. G. et al. (1971). Multiple-wheel heavy gear load pavement tests. Technical Report S-71-17, Vol. I, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.

Barker, W.R. and Brabston, W.N. (1975). Development of a structural design system for flexible aircraft pavements. Technical Report S-75-17, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.

Barker, W.R. and Gonzalez, C.R. (1992). Design considerations for multi-wheel aircraft. Proc. 22nd ASCE International Air Transportation Conf., Denver.

Barker, W.R. and Gonzalez, C.R. (1994). Super-Heavy Aircraft Study. Technical Report GL-94-12, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.

Federal Aviation Administration (1993). Airport pavements. Solutions for tomorrow’s aircraft. US Dept. of Transportation. FAA Technical Center, New Jersey.

Federal Aviation Administration (1994). LEDFAA User’s Manual. US Dept. of Transportation. FAA, Washington, D.C.

Ho Sang, V.A. (1975). Field survey and analysis of aircraft distribution on airport pavements. Report No. FAA-RD-74-36. U.S. Federal Aviation Administration.

Lane, R., Woodman, G. and Barenberg, E.J. (1993). Pavement design considerations for heavy aircraft loading at BAA airports. Proc. ASCE Conf., Airport Pavement Innovations: Theory to Practice, Vicksburg, Miss., (ed. J.W. Hall jr.)

Monismith, C.L., Finn, F.N., Ahlborn, G. and Markevich, N. (1987). A general analytically based approach to the design of asphalt concrete pavements. Proc. 6th. Int. Conf. on the Structural Design of Asphalt Pavements, Ann Arbor.

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.

Potter, J.C. (1985). Reliability of the flexible pavement design model. Misc. Paper GL-85-27, US Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss.

Preston, O.W. (1991). An improved method for determining aircraft flexible pavement requirements. Douglas Aircraft Company, McDonnell Douglas Corporation, Report No. MDC K5509.

Wardle, L.J. (1977). CIRCLY Users’ Manual, MINCAD Systems Pty Ltd, Richmond, Vic., Australia