Design Lane ESALs

Also known as design lane ESAL · directional distribution factor · lane distribution factor · w18 · W18 · 18-kip equivalent single axle loads · ESAL design lane · traffic distribution pavement design

w18=DDDLW18w_{18} = D_D \, D_L \, W_{18}
ESAL
ESAL

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

A pavement is not designed for the traffic on the road. It is designed for the traffic in one lane — the worst one — and this equation is how you get from the first to the second.

The two factors do different jobs. The directional distribution factor DDD_D splits the two-way total between the carriageways, and the default is 0.5 because most highways carry roughly the same traffic each way. Where it is not 0.5, it is usually badly not 0.5, and the reason is always the same: the haul is one-way. Quarry rock, logs, grain from an elevator, containers off a port, ore from a mine — loaded out, empty back. And because damage goes as roughly the fourth power of axle load, an empty return trip is very nearly free. A truck that grosses 80,000 lb loaded and 30,000 lb empty does something like fifteen times more damage in the loaded direction. The two carriageways of such a road genuinely need different pavements, and designing both to the average gives you one that is too thin and one that is too thick.

The lane distribution factor DLD_L then splits one direction's trucks between its lanes, and this is where the guidance stops being data and starts being judgement. On a single lane each way, DL=1D_L = 1 and there is nothing to discuss. On a multi-lane road, published values for the outer lane run from about 0.5 to 1.0, and the honest position is that truck lane discipline is a matter of law, enforcement, geometry and habit rather than of physics. It varies by jurisdiction, by time of day, by how congested the corridor is, and by whether trucks are legally restricted to the right-hand lanes. It also drifts: as a corridor fills up, trucks that used to stay right begin using the middle lane, and a factor measured a decade ago will be too high.

Which gives the practical rule: when you cannot count it, count it high. The outer lane is the one that fails, and a lane factor set too low produces a pavement that is too thin — an error that shows up as premature rutting eight years into a twenty-year design, by which time nobody remembers what number was assumed. Setting it too high costs a little asphalt now. The asymmetry is not close.

One more thing worth doing properly. When you measure DDD_D from counts, count trucks by direction, not vehicles. Cars contribute almost nothing to the ESAL total, so a lopsided truck haul buried inside balanced total traffic will look balanced and will not be. Classification counts, or better a weigh-in-motion station, are what settle this.

Design Lane ESALs
w18=DDDLW18w_{18} = D_D \, D_L \, W_{18}
W18w18DDDL
Where
  • w18w_{18}= Design lane ESALs (ESAL)
  • W18W_{18}= Total ESALs, both directions (ESAL)
  • DDD_D= Directional distribution factor
  • DLD_L= Lane distribution factor