Anders et al.  I concur completely with the advice from our Swedish colleagues.  Our research in New Zealand indicates that the power relationship will vary with pavement type, and that the exponent of 4 probably relates to an average pavement type.  I think the AASHTO research investigated cracking of thick asphalt pavements, which are common in heavy trafficked situations e.g. motorways.  In New Zealand (and I believe Australia also) the maintenance intervention level mostly takes place based upon rutting (i.e. loss of shape) in the flexible road surface, which is typically earlier in the pavement's life cycle.  Our initial research (research is never completed!) has suggested that an exponent less than 4 may apply here.  We also have the added complication that the same exponent is also used in the calculation of our road user charges.  So we also have to convince economists and policy makers if we wish to generate new exponents.  Their immediate response is "is it broken?  if not we won't change it".

I also agree with the comments about the exponent being related to the road hierarchy.  In fact, I am on record as suggesting a couple of years ago that the vertical pavement wear measure in the Australian PBS project (proposed at about 7 I think) could vary with road hierarchy, and could possibly involve four separate exponents for the four Levels 1-4 that are already included in that project.  This would encourage productivity and innovative vehicles more that the selection of a single, somewhat conservative, exponent.

Lynn Sleath
Network Operations
National Office
Transit New Zealand.


>>> Lundström Anders A              <[log in to unmask]> 22/02/2007 01:33 >>>
The discussions by David Cebon and Johan Lang below are enlightening. 
 
Different mechanisms for cracking, deformation etcetera need different 
theories. I agree completely with David that rut (or track) formation must 
be some kind of viscous or creep mechanism including stresses, 
temperature (this is a dominantly a summer thing in Sweden) and 
duration ("inversely proportional to speed", that is why this is particularly 
noted at red lights and bus stops). 
 
As a consequence, when looking at different axle configurations of 
heavy vehicles (a Swedish timber combination may pass "off-road", 
gravel roads, thin pavement roads and rigid highways in one trip) the 
proposed practice should be to investigate using different exponents 
as one, four, eight or even twelwe as in the Australian PBS 
recommendations. 
 
Are there other suggestions? 
 
Regards 
 
Anders 

	-----Original Message-----
	From: Technical, operational and economic aspects of road freight transportation [mailto:[log in to unmask]] On Behalf Of David Cebon
	Sent: den 20 februari 2007 23:42
	To: [log in to unmask] 
	Subject: Fwd: SV: Does the 4th Power Law apply to cars?
	
	
	The way that roads fail is dependent on their design, materials, vehicle loads, environment, etc.  The sensitivity to loads depends critically on the mode of failure.  For example, consider asphalt roads in temperate climates, as in the UK:  
	
	(i)  Failure of light construction asphalt roads, used for local and rural roads, is often by cracking and pot-holing - ie fatigue.
	
	As Anders mentions in his contribution, fatigue damage is often very sensitive to load level.  A power of 4 is not unreasonable for high-cycle fatigue of many materials, including asphalt.  We might expect, therefore, that for local and rural roads that fail by fatigue, a fourth power dependence on axle load is plausible.  Note that if a 4th power law applies, dynamic tyre forces are critical.  An instantaneous dynamic tyre force that is 30% higher than the static load  translates into nearly a factor of 3 increase in fatigue damage at that point on the road.  In our models, this type of dynamic overload (when spread out suitably over the road to account for the load patterns generated by traffic stream) causes local fatigue damage and potholes.  Conclusion:  local and rural roads of light construction (much like the AASHO Road Test sections) are very sensitive to static load levels and dynamic tyre forces... and a fourth power law is plausible.  BUT:  this still doesn't mean you can extrapolate the fourth power law for cars.
	
	
	(ii)  Failure of full-depth (strong) asphalt roads is most often by permanent deformation - ie formation of longitudinal ruts.  We see this very frequently on UK motorways.
	
	The literature on permanent deformation of asphalt indicates that a reasonable constitutive model is linear viscous.  This means that the permanent deformation per axle pass is proportional to F/V...  Linear in load, inversely proportional to vehicle speed.  Linear in load... this means a power of 1 not 4.  The consequence is that the ruts in these roads are essentially uniform in depth - because they only depend on the static loads of the passing vehicles.  They don't oscillate wildly in depth as would be expected if they depended on dynamic tyre forces.  Conclusion: full-depth asphalt roads like UK motorways are not very sensitive to static load levels.  Dynamic tyre forces are irrelevant on these roads.  A first power law is a reasonable guess.
	
	In the UK, Local Authorities are responsible for local and rural roads, whereas the Highways Agency is responsible for the motorways.  Local Authorities should be very worried about overloaded trucks and trucks that bounce up and down as they drive over their roads.  For the Highways Agency, axle loads are much less important.... and suspension dynamics (and 'road-friendly suspensions') are irrelevant.
	
	
	-David Cebon
	
	
	
	

		From: <[log in to unmask]>
		To: <[log in to unmask]>
		X-OriginalArrivalTime: 20 Feb 2007 12:28:19.0809 (UTC) FILETIME=[9AB6A510:01C754EA]
		
		Dear all,
		I agree with Steven Karamias that using the 4th power law in the comparision of cars and trucks should embarass politicians and reporters, but it should even embarass me as an road administrator to let it go so far. I believe that the 4th power law is so easy to explain that even a non-technichian can understand it and therefore, it has been used to illustrate the relation cars/trucks. But the political interest (road tolling) is really not about the axle load relation, it is more about the damage cost of different vehicles. And the cost is affected not only by fatigue (4th power law), but also by permanent deformation and, as in Sweden, by wear of studded tires. My opinion is that permanent deformation and wear of studded tires is a more common reason why pavement maintenance is carried out than fatigue. The permanent deformation is of course affected by the axle load so the the damage cost of trucks is higher than the damage cost of passenger cars but the relation is not in the magnitude that the 4th power law shows.
		
		Concerning the exponent. Different studies have shown that the exponent varies depending on pavement design, climate etc. I have in the literature seen exponents from 2 to 8.
		
		Regards,
		Johan Lang
		Swedish Road Administration
		
		
		
		-----Ursprungligt meddelande-----
		Från: Technical, operational and economic aspects of road freight transportation [ mailto:[log in to unmask] <mailto:[log in to unmask]> ] För David Cebon
		Skickat: den 20 februari 2007 00:01
		Till: [log in to unmask] 
		Ämne: Does the 4th Power Law apply to cars?
		
		Dear All
		
		Anders Lundström recently asked the question "Does the 4th Power Law (of road damage) apply to cars"?  A brief flurry of emails resulted.  Anders collected these together into a file which I have put on the road-transport-technology mailing list web site.  We would welcome more discussion of this topic on the mailing list.
		
		Please go to
		http://www.jiscmail.ac.uk/cgi-bin/filearea.cgi?LMGT1=ROAD-TRANSPORT-TECHNOLOGY&X=&Y=&f=/Discussions 
		and click on the file name '0702 fourth power relation and cars.pdf' to read the discussion.
		
		Best wishes
		
		-David Cebon
		
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