Finite‐Element Volumes

The finite‐element‐volumes method is a new earthwork volumes technique quite unlike conventional methods. The algorithm provides automatic curvature and prismoidal correction using ordinarily available cross‐section data in conjunction with horizontal baseline geometry. The cross sections are approximated as a series of rectangular elements of equal, user‐specified width. As this width approaches zero, cross‐sectional area and centroid location approach that of the original cross section. Every element is assumed to transition linearly along an offset curve concentric with the baseline to an opposing element upstation or to terminate on a tapered offset curve when an opposing element does not exist. The resulting volume elements are thus curvilinear wedges or frustums of wedges. Linear, circular, and Cornu spiral baseline (clothoidal spline) components are accommodated by the method. Numerical examples show excellent agreement with exact results even when the mass components are not prismoidal. A general formula for the volume of a curvilinear mass component and a new, high‐precision, prismoidal curvature‐correction technique are also presented.