Published in Airport Technology Transfer Conference, Atlantic City, U.S.A., April 1999, Federal Aviation Administration.
INTERACTION BETWEEN
WHEELS AND WHEEL GROUPS OF
NEW LARGE AIRCRAFT
Bruce Rodway
Pavement Consultant
Leigh J. Wardle
Director, MINCAD Systems Pty. Ltd.
Garry Wickham
Pavement Engineer, Sydney Airport
INTRODUCTION
The arrival of the Boeing B777, which has 6-wheeled landing gears, and proposals for new large aircraft (NLA) has focussed attention on the need for pavement design methods which can take account of interaction between wheels of large multiwheeled gears and also account for the interaction between all gears of the aircraft. Current methods cannot do this satisfactorily.
Permanent load-induced deformations develop at points within a flexible pavement structure and subgrade. The aggregate effect of these is to produce permanent surface deformations. Past and present design methods used in practice do not attempt to model this deformation process; deformations of individual soil elements are not computed and totalled to give predictions of surface deformations. Instead ‘damage indicators’ are computed, typically elastic deflections or strains at subgrade level. These are then correlated to the rate at which surface deformations have been observed to develop in full-scale trafficking tests. To date such tests have been essentially limited to single landing gears (or ‘struts’) containing up to six wheels, and to pavements that are thin relative to many currently in use at major aerodromes. Because of this simplified approach, and because the design methods are essentially empirical these correlations do not well represent situations that are significantly beyond those encompassed by the full-scale tests. In particular their use to predict interactions between gears is problematic.
Nevertheless deflection-based empirical CBR design curves catering for up to 24 main gear wheels have been used for many years to design pavement thicknesses for aircraft such as the B747, the C5 Galaxy and the A300 Airbus. These curves predict that, for very low strength subgrades, much greater pavement thicknesses are needed for the B777 and proposed NLAs. It is now widely believed, however, that the method overstates the pavement damage that will be caused by these aircraft. New data that is relevant to the new aircraft is required. FAA’s National Testing Machine has been designed to obtain this data.
‘Mechanistic’ methods based on layered elastic analysis have been recently introduced into regular design practice. The new methods are empirical to the same degree as the conventional empirical CBR method and are calibrated against the same limited full-scale tests. Consequently, as shown in this paper, they predict pavement thickness requirements for the B777 that are similar to the conventional method.
The new methods use subgrade vertical strain instead of deflection as a pavement damage indicator, primarily because this reduces predicted gear interactions. However, the use of vertical strain will often produce anomalous design results; methods predict that adding fully loaded wheels can increase rather than decrease pavement life. This effect is illustrated by some examples. Today’s layered elastic analysis methods are unlikely to be sophisticated enough to adequately interpret the results from the FAA National Testing Machine.
DEFLECTION and STRAIN as INDICATORS of PAVEMENT DAMAGE
The US Army Corps of Engineers’ empirical relationship between Aircraft Loads, CBR, and Required Flexible Pavement Thickness is detailed in the Corps’ Instruction Report S-77-1 (Pereira, 1977). The S-77-1 method is the basis of many of the world’s aircraft pavement design methods, including that used by the U.S. Federal Aviation Administration (FAA). It is also the basis of the International Civil Aviation Organization’s (ICAO’s) system for load rating of aircraft and for publishing aerodrome flexible pavement strength data (ICAO, 1983). The method adopts elastic vertical deflection at subgrade level as the indicator of the rate at which deformation develops at the pavement surface.
Corps of Engineers full-scale testing (Ahlvin et al, 1971) confirmed that their early deflection-based design curves overstated the pavement damage caused by multiwheeled gears. This led to the introduction of empirical pavement thickness reduction factors (alpha factors). The thickness reductions increased with wheel numbers and with load repetitions.
Computed elastic deflections attenuate more slowly than strains with distance from the load. Figure 1 illustrates this point. For the Boussinesq single layer, elastic vertical deflections and vertical strains at a depth to subgrade of 1,000mm are plotted for a single wheel load of tyre contact radius 215mm. For the single layer case the shapes of the strain and deflection curves do not depend on pavement modulus, E, and are insensitive to Poisson’s ratio. Because of this slower attenuation, deflection-based methods must predict higher degrees of wheel interaction than strain-based methods. This is largely why the newer ‘mechanistic’ methods usually use vertical strain rather than vertical deflection as the damage indicator.
Figure 1: Attenuation of subgrade strain and deflection with distance from the load
INCREASED PAVEMENT THICKNESSES FOR THE B777 AND NLA’S ?
The B747 will be used here as a reference aircraft for comparing pavement thickness requirements. The 397 tonne version of the B747-400 is compared to the 310 tonne version of the B777. According to the S-77-1 conventional design method, for a CBR 3 subgrade, 10,000 coverages of the B777 requires 235 mm more pavement depth than the 1680mm required by the B747, an increase of about 15% (see Table 1). This would constitute a significant problem to Boeing in their efforts to market the new aircraft. Yet, because of the different pass-to-coverage ratios of the two aircraft, these figures still understate the real magnitude of the problem. Ten thousand coverages correspond to 17,500 taxiway passes of the B747 but only 13,400 passes of the B777, and it is aircraft numbers, not coverages that reflect landing fee income. Furthermore, some wheel configurations being considered for future generation aircraft would, according to conventional empirical CBR design methods, require up to 65% more pavement thickness than the B747. These predictions are widely thought to be conservative and to result from inadequacies in the design methods.
LAYERED ELASTIC PAVEMENT DESIGN METHODS
The layered elastic method was introduced into regular airfield design practice in the mid-1990’s with the release of the computer program LEDFAA (Layered Elastic Design, Federal Aviation Administration) and also the Australian-developed APSDS (Airport Pavement Structural Design System), (Federal Aviation Administration, 1995) and (Rickards, 1994, Wardle and Rodway, 1995, 1998) respectively. The main distinction between the methods is that APSDS computes subgrade strains, or alternative indicators of pavement damage, for all points across the pavement in order to capture all damage contributions from the aircraft wheels in all their wandering positions. This contrasts with LEDFAA and previous methods which compute single maximum values of the damage indicators. It is this feature that eliminates the need for the pass-to-coverage concept and allows the designer to specify any degree of aircraft wander.
LEDFAA and APSDS use layered elastic programs, JULEA and CIRCLY respectively, to compute load-induced strains at subgrade level. These must then be related to observed test track pavement performance. This step in the design process is purely empirical. The new methods are empirical to the same degree as the conventional S-77-1 empirical CBR method and are calibrated against the same limited full-scale tests. Consequently they predict pavement thickness requirements for the B777 and NLA that are similar to the conventional method. As shown in Table 1, both APSDS and LEDFAA predict that, for a CBR 3 subgrade, the extra pavement thickness required by the B777 compared to the B747 is not significantly different from the 235 mm indicated by the standard ICAO Aircraft Classification System (ACN) which uses S-77-1. All the results in Table 1 are for single gear loadings.
A specialist ICAO Study Group has recommended a new interim alpha factor of 0.72 for 6-wheel gears, pending resolution of the B777 damage issue by future full-scale testing. As shown in the table, the effect of the 0.72 modification is to make the B777 pavement thickness similar to the B747’s at the 10,000 coverage level. Thus, with respect to the treatment of the B777, the Modified ICAO rating system is no longer consistent with the other pavement design methods.
|
Method |
Thickness |
Thickness |
Difference |
|
APSDS 3 |
2010 mm |
1735 mm |
275 mm |
|
LEDFAA 1.2 |
2045 mm |
1775 mm |
270 mm |
|
Standard ICAO ACN
Modified ICAO ACN |
1915 mm 1700 mm |
1680 mm 1680 mm |
235 mm 20 mm |
Table 1: Pavement thicknesses required over CBR 3 subgrade for 10,000 coverages
GEAR INTERACTION
The negative strain problem
The use of subgrade vertical strain as a pavement damage indicator often produces anomalous design results. This is because, unlike deflections, computed vertical subgrade strains become negative at a radial distance from the load that depends upon pavement thickness and the moduli of the pavement layers and the subgrade. The significance when calculating gear interactions is that, for some gear geometries, the zone of negative strain generated by one gear falls beneath other gears and consequently reduces the strain. In these cases adding fully loaded wheels increases rather than decreases pavement life. Although, as stated earlier, there is no empirical multiple gear data, this result seems to be counter-intuitive.
For a layered pavement structure, the horizontal distance from the load at which the computed subgrade strain becomes negative depends upon both the thicknesses and the stiffnesses of the pavement layers and subgrade. Figure 2 shows the subgrade strain caused by one wheel of a 310 tonne Boeing 777 gear for a typical ‘FAA-style’ pavement structure of thickness 2,000mm. In this example, the subgrade strains become negative at a horizontal distance of about 7,000mm from the load centre.
Figure 2: Subgrade strain due to B777 single wheel on 2,000mm ‘FAA’ pavement.
Details of the ‘FAA-style’ pavement used for figures 2 and 3 are given in Table 2. The same pavement (apart from changes to the subbase thickness) was also used for the LEDFAA and APSDS thickness requirements given in Table 1 and for the B747 example below. The unbound granular basecourse and subbase are sublayered with modulus values assigned to the sublayers by the method proposed by Barker and Brabson (1975). This method is used by both LEDFAA and APSDS.
The subgrade CBR is 3% (ICAO Subgrade ultra low strength category, Code D).
|
Material |
Thickness |
|
Asphaltic concrete: E = 1,400 MPa, Poisson’s ratio = 0.4 |
125 mm |
|
Basecourse (graded crushed rock, FAA’s P209): Poisson’s ratio =0.3 |
600 mm |
|
Subbase (uncrushed gravel,FAA’s P154): Poisson’s ratio = 0.3 |
1,275 mm |
|
Subgrade, CBR 3: |
Total 2,000 mm |
Table 2: Details of ‘FAA-style’ pavement structure.
B777 example
As stated above, there are gear geometries and pavement structures for which the negative zones of subgrade strain generated by one gear fall beneath another gear of the aircraft. Figure 3 shows the subgrade strain caused by one 6-wheeled gear of the 310 tonne Boeing 777. For an ‘FAA-style’ pavement of thickness 2,000mm, the centre of the zone of negative strain is a horizontal distance from the gear centre of approximately 10,000mm. The distance between the B777 gears is 10,970mm. The effect of including both gears rather than a single gear in the layered elastic computation is to reduce the maximum subgrade strain beneath the each gear by about 1% (0.0010903 reduces to 0.0010787). Therefore the pavement life calculated using methods such as LEDFAA and APSDS (both use subgrade strain as the indicator of pavement damage and normally use single gear loadings) will be greater if both gears are included in the computation. The magnitude of the effect of the reduced strain upon predicted pavement life depends upon the empirical performance relationship (relationship between repetitions and strain) used by the particular design method. For example, the pavement life predictions given by APSDS are 12,900 and 13,900 repetitions for the single gear and 2-gear cases respectively, a difference of approximately 8%.
Figure 3: Subgrade strain due to single B777 gear on 2000mm ‘FAA’pavement.
B747 example
The centre to centre spacing between the two rear 4-wheel gears of the B747 is 3,840mm. This relatively close spacing means that the negative strain effect will be most pronounced for a thinner pavement than the 2,000mm pavement used in the previous example for the B777. For an ‘FAA-style’ 1,000mm pavement over a CBR 10 subgrade, the centre of the zone of negative strain is a horizontal distance from the gear centre of approximately 4,000mm. The effect of including all four gears rather than a single gear in the layered elastic computation is to reduce the maximum subgrade strain beneath the rear gears by about 5% (0.0006697 reduces to 0.0006380). The increase in pavement life predicted by APSDS is approximately 40%.
LIMITATIONS of
LAYERED ELASTIC DESIGN METHODS to INTERPRET
NLA GEAR INTERACTION DATA.
The wheel configurations of future large aircraft such as Airbus’s A3XX have yet to be determined. Aircraft manufacturers have studied many arrangements. They include four 6-wheeled gears, six 4-wheeled gears, and two 6-wheeled with two 4-wheeled gears. Several wheel spacings within gears and several spacings between gears have been examined.
FAA’s National Pavement Testing Machine can accommodate twelve test wheels capable of being configured to represent two complete landing gears having from one to six wheels per gear and adjustable to vary the distance between the gears up to six metres forwards and sideways. Thus it has the capability to test gear interaction effects for a number of the configurations being considered for the NLAs.
The negative strain effects illustrated above for the B777 and B747 will affect attempts to use the layered elastic method to interpret the test results for many of the wheel configurations and pavement structures of interest.
The load response of unbound granular pavement materials such as P209 and P154 is elasto-plastic and stress-dependent. The layered elastic method cannot take account of plastic behaviour and cannot fully deal with stress dependence. An important limitation of the method is that elastic moduli must be constant within each horizontal layer. But stress diminishes with distance from the wheels so the modulus will also change with distance from the wheels. Consequently most of the modulus values used in the pavement model will be incorrect and therefore the strains and deflections calculated using the moduli must also be incorrect at most points.
The layered elastic method takes some account of stress-dependence by sublayering materials and assigning moduli to each sublayer to produce reasonable estimates of stesses or deflections measured at selected points in the pavement. For example, moduli can be chosen that produce reasonable estimates of measured stresses vertically beneath a load. More commonly layer moduli are estimated by ‘back calculating’ from measured surface deflection bowls produced by a Falling Weight Deflectometer. These localised ‘calibrations’ do not mean, however, that stresses, strains and deflections computed for other points in the pavement are reliable.
Thus the layered elastic method uses a much-simplified representation of the pavement that is known to assume incorrect modulus values throughout much of the pavement. Design methods based on surface rutting concentrate on the vertical compressive strain at subgrade level. Both LEDFAA and APSDS use single gear loadings so the critical strains occur in the region beneath the gear. The reliability of strains calculated for points that are at some horizontal distance from the load must be suspect. Yet it is these doubtful values that are used to predict gear interactions.
When the negative strains predicted by the layered elastic method fall beneath other wheels of an aircraft they can result in pavement life predictions that are counter-intuitive; it is hard to accept that extra loads on a pavement can increase pavement life. The negative strain problem is a reminder that the design method has serious limitations. The most serious is that material properties must be constant within horizontal layers. This means that, for stress-dependent materials, the extension of pavement design methods based on single aircraft gears to handle multiple gear loadings is problematic. Therefore their usefulness in interpreting the performance of the pavements tested in the National Pavement Testing Machine under multi-gear loadings is also questionable.
In addition to the limitations of the design methods discussed in this paper, the methods do not address the effect of the shape and extent of the pulses induced by aircraft loads. These load pulses, expressed for example as strain patterns at subgrade level, will be very different for the various wheel configurations and pavement structures of interest. The difficult and unresolved question of the effect of the shape of the load pulse upon pavement damage is beyond the scope of this paper but has been discussed elsewhere (Rodway, 1995). Because of the likely importance of the loading pulse shape, any design methods that are based simply on the value of a given strain component at a point are unlikely to be fully satisfactory to predict pavement behaviour.
SUMMARY OF CONCLUSIONS
Available pavement design methods use simplified representations of pavement structure and of the process of rut development. Because of this, and because the methods are essentially empirical they require empirical data that is relevant both to the aircraft and the pavement types; extrapolation from data obtained for significantly different loadings and materials is problematic. FAA’s National Testing Machine has been designed to produce the data needed for the B777, the NLAs and for typical pavement structures.
Conventional empirical CBR flexible pavement design methods predict that, for very low strength subgrades, much greater pavement thicknesses will be needed for the B777 and the NLAs. The new ‘mechanistic’ design methods based on layered elastic analysis predict similar increases to the conventional methods.
The use of vertical strain as an indicator of pavement damage often produces anomalous results; layered elastic models predict that adding fully loaded wheels can increase rather than decrease pavement life. This draws attention to limitations of the layered elastic method that may mean that it is not well suited to interpret the gear interaction data from the Testing Machine.
Because of the likely importance of the loading pulse shape, any design methods that are based simply on the value of a given strain component at a point are unlikely to be fully satisfactory to predict pavement behaviour.
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. 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.
Federal Aviation Administration (1995). Advisory Circular 150/5320-16. Airport pavement design for the Boeing 777 airplane. LEDFAA User’s Manual. U.S. Federal Aviation Administration
Federal Aviation Administration (1995). Advisory Circular 150/5320-6D. Airport pavement design and evaluation. U.S. Federal Aviation Administration.
ICAO, (1983). Aerodrome Design Manual, Document 9157-AN/901 Part 3, Pavements.
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.
Rickards, I. (1994). APSDS. A structural design system for airport and industrial pavements. Ninth AAPA International Asphalt Conference, Surfers Paradise, Australia.
Rodway, B. (1995). Design of flexible pavements for large multi-wheeled aircraft. Second International Conference on Road and Airfield Pavement Technology, Singapore.
Wardle, L.J. (1996). CIRCLY Users’ Manual, Version 3.0, MINCAD Systems Pty Ltd, Richmond, Australia.
Wardle, L.J. and Rodway, B. (1995). Development and application of an improved airport pavement design method. ASCE 1995 Transportation Congress, San Diego.
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.