Most damage to roads is done by semis. The damage a vehicle does to a road surface is proportional to axle load^4. The logistics industry's miniscule share of road usage fees amounts to the single largest subsidy in the US when you consider trucking accounts for nearly all vehicle-related damage to roads surfaces.
But vehicle related damage to road surfaces is not the main cause of road deterioration. Weather causes most of the damage anywhere with freeze thaw cycles. A completely unused road will pretty quickly deteriorate just sitting there.
That "Fourth power law" appears to be based on very old tests using specialized equipment. I don't think it probably carries weight that is properly applied to modern trucks and vehicles. One simplification of the testing was the truck "rig" that only had four large wheels on two axles rather than the modern "18 wheeler" with five axles distributing the load.