That is true, the fatigue damage to the road goes up as the cube of the weight. What this means is that cars don't cause much fatigue damage to the roads - it's the trucks that do. A semi loaded to the legal limit causes 9,000 times as much damage as a car.
Really, the heavy loads need to go by rail, not highway.
It just seems like we let good infrastructure go to waste. It’s probably a tax thing, iirc the rail companies pulled up half their mileage because they were on the hook for property taxes on all that acreage (turned lots of double tracks into single tracks, and old single tracks into recreational bike trails)
> old single tracks into recreational bike trails
This is rampant in Seattle. They've not only torn up the tracks and turned them into bike trails, in order to install light rail, they've had to blast new right-of-ways at incredible cost.
Slight correction - damage per axle is proportional to 4th power of load per axle. In practice it means slightly less than 4th power of weight (due to semis usually having more axles).
https://www.insidescience.org/news/how-much-damage-do-heavy-...