How Fast a Gravel Road Loses Its Surface: Loss per Vehicle Pass, the Re-gravelling Interval, and the Traffic Level Below Which Keeping the Road Costs More Than Its Journeys Are Worth

A gravel road is a surface that traffic and weather steadily carry away, yet re-gravelling is often scheduled by habit or by complaint rather than by a loss rate. This paper computes the loss rate from stated traffic, gravel, and rainfall inputs and follows the money to two bounds. For a 5 m wide road carrying 150 vehicles per day (130 light, 20 heavy) under 800 mm of annual rainfall, the modelled surface loss is 7.8 mm per year, equal to 39.0 cubic metres per kilometre per year, or 1.14 kg of gravel lost per vehicle pass. Restoring a 50 mm layer therefore falls due every 6.41 years; each event places 400 tonnes per kilometre and costs 8,000 dollars, giving a total keeping cost, with grading and drainage, of 2,297 dollars per kilometre per year, or 0.042 dollars per journey over that kilometre. Loss rises to 9.8 mm per year at 1,400 mm of rainfall and 10.9 mm per year with excess fines, and the re-gravelling interval shortens to 1.64 years at 1,000 vehicles per day, where annual keeping cost reaches 5,914 dollars per kilometre. A sealed surface annualised at 14,500 dollars per kilometre per year becomes cheaper than gravel only above about 3,168 vehicles per day. The second bound is the uncomfortable one, and it is reported at full size: valuing a journey at 9.00 dollars, stated explicitly in the text, a single kilometre of gravel road costs more to keep than its journeys are worth only below about 1.0 vehicle per day — in other words, almost never. The bound becomes real only with length: a 20 km low-use spur costs more than its journeys are worth below 10.6 vehicles per day, and at 5 vehicles per day it charges 18.74 dollars of upkeep against each 9.00 dollar journey. Short gravel roads are almost always worth keeping; long, nearly empty spurs are where the arithmetic turns against the road.