Rill and gully erosion on unpaved roads under heavy rainfall in agricultural watersheds on China’s Loess Plateau

•Main unpaved roads experienced more severe erosion than secondary roads and trails.•Gully erosion was over 100 times as much as rill erosion on main unpaved roads.•Contributing area and road segment gradient could better predict road erosion.•Changing cropland to woodland/shrubland could decrease road erosion.