Estimating Earthwork Volumes of Curved Roadways: Mathematical Model

The existing (average‐volume) method for estimating earthwork volumes of curved roadways is approximate and is suitable only for application to level terrains. For linear or fluctuating profiles, such as in hilly and mountainous terrains, no exact method is currently available. In this paper, a mathematical model that provides the exact volume of curved roadways with linear profiles between stations is developed. The model, which is based on triple integration, assumes that the ground cross slope is constant between stations. Closed‐form solutions are developed for cut (or fill) and transition sections, where the ground profile changes from cut to fill or vice versa. The application results indicate that the volume of the average‐volume method may deviate greatly from the exact volume and that the mathematical model is also reasonably accurate when the ground cross slope changes moderately.