ESWL

[pilotho]

I have read upon ESWL - Equivalent single wheel loading

It gives me a bunch of ratio e.g. a 4 wheels unit has a ESWL ratio of 2.25.

What does this actually mean? Is it suppose a unit has 4 wheels a single wheel would exert a loading of 2.25 x the weight? Not really sure....

[john_tullamarine]

Rather than get it half right myself, I'll bang a note off to our resident airports engineering boffin .... hopefully he is able to give you the precise answer you are after ...

[OverRun]

ESWL - Equivalent single wheel loading.
The old airport pavement design method which was adapted from the highway California Bearing Ratio (CBR) design method, and extrapolated to cater for higher single wheel aircraft loads using Boussinesq's single layer elastic theory.

The B-29 bomber appeared in 1943-44 and, at a mass of 64 tonnes, was double the weight of previous World War II aircraft, and was supported on the first dual-wheel gears. The mass doubled again to 148 tonnes with the post-war B-36, which had dual-tandem gears. To accommodate these multi-wheeled gears the CBR method was extended using the concept of equivalent single wheel load (ESWL), which is intended to be the single wheel load which will cause pavement damage equal to that caused by a multi-wheel gear.

In practice the ESWL is defined as the load on a single tyre which will produce the same maximum deflection at subgrade level as the multiwheel load. The ESWL is also a function of pavement depth. So a 4 wheels unit off a Boeing 747, with say 20 t per wheel, is 80 tonnes on the leg. This is equivalent to a loading by 2.25 * 20 = 45 tonnes on a single wheel on the leg (at a subgrade depth of 750mm or 30 inches).

It varies with depth. Simplistically, at a very shallow depth of 1cm, where only the effect of the tyre immediately above can be felt by the soil particles, the ESWL is equivalent to a single wheel load of 20 tonnes. Down at 2 metres (or 6 feet) where the loads from all the tyres can be felt by the soil particles, the ESWL is 4 * 20 = 80 tonnes. At depths in between the two extremes, it varies.

A major consideration at the time the concept was developed was that the ESWL methodology should produce safe designs for the new multiwheel loadings, and testing of gears in the late 1960s and early 1970s confirmed that the deflection-based ESWL design method overstated the damaging effect of multi-wheel gears. This led to the introduction of pavement thickness reduction factors, or 'load repetition factors' called alpha factors. The design thickness of the pavement is reduced by multiplying the 'standard' thickness, T, by alpha (giving typically a 10-20% reduction).

Nowadays, we use layered elastic design or finite element design methods, but the ESWL is still floating around in the background and giving some pretty reasonable results. I use it as a rough check on what the other methods have computed.

[pilotho]

Ok, just to clarify.

Over run, you said that "So a 4 wheels unit off a Boeing 747, with say 20 t per wheel, is 80 tonnes on the leg. This is equivalent to a loading by 2.25 * 20 = 45 tonnes on a single wheel on the leg"

Does that mean if the leg only had one wheel, it would be exerting a load of 45T on the ground? However, if there were 4 wheels, there would only be a load of 20T on the ground from each wheel.

[OverRun]

Pilotho,
Correct.

Does that mean if the leg only had one wheel, it would be exerting a load of 45T on the ground? However, if there were 4 wheels, there would only be a load of 20T on the ground from each wheel = 4 * 20T = 80T.

The load spreads down from the top layers to the subgrade through load transfer by the layers through a cone of about 45 degrees as shown in this figure (http://www.geocities.com/profemery/cone.jpg).

If there are 4 wheels each of 20 tonnes, there is a total load of 80 tonnes on the ground. Immediately under a single wheel, where only the effect of that single wheel can be felt by the soil particles, the load on a soil particle is 20 tonnes. This is the same effect as if the pavement was loaded with a single wheel of 20 tonnes. Hence at the surface, the ESWL is 20 tonnes, even though there is an 80 tonnes load on the ground spread over 4 wheels.

As you go deeper, the effect of the other wheels starts to become felt as the load 'cones' start to overlap. Eventually you get deep enough so that all the load cones are overlapping. At that point, you have the effect of all 4 wheels of 20 tonnes each (= 80 tonnes) on the soil particles, and this is the same effect as if the pavement was loaded with a single wheel of 80 tonnes. The ESWL is 80 tonnes.

In between, the ESWL varies between 20 tonnes and 80 tonnes, depending on how deep you are and the extent to which the load cones overlap. The typical pavement is say 750mm deep, and at that depth, the overlap is such the vertical load on the soil particles is the same as would be induced by an ESWL of 45 tonnes.

Of course as you go deeper, the load(s) spread or dissipate, and while the load seems to increase as load cones overlap, it is decreasing rather more quickly because the load(s) are being spread over a bigger area. What an awkward clunky workaround the ESWL concept was, IMHO. Almost as awkward as PCN, but don't get me started on that.

[pilotho]

Thats great over run, concept almost understood.

I have looked at the diagram, does it mean that the deeper layers are exerted with a greater load? What are the implications for this because I would have thought it is better to have a thicker set of concrete or is it because the load is spread over a greater area on the bottom layer, so it wouldn't affect in terms of crack propagation??

[OverRun]

In the diagram, as you go deeper, the load spreads which means it is spread over more and more soil particles and each particle supports less of the load. The load per soil particle drops off quickly. But as you go deeper, the effect of the other wheels starts to become felt as the load 'cones' start to overlap, and the load per soil particle increases. However the load spreading reduces the load more quickly than the overlapping cones effect increases the load.

Better to have thicker concrete at the top where there isn't yet much load spreading, because the strong concrete particles can take all the load without squashing.

[GotTheTshirt]

I see there was no mention of LCN !:confused:

[OverRun]

LCN is covered a bit in this post (http://www.pprune.org/forums/showthread.php?t=239066)

and a graph relating the two is here (http://www.geocities.com/profemery/aviation/lcn.pdf)