FINITE-ELEMENT VOLUMES

The finite-element-volumes method is a new earthwork volumes technique quite unlike conventional methods. The algorithm provides automatic c urvature and prismoidal correction using ordinarily available cross-se ction data in conjunction with horizontal baseline geometry. The cross sections are approximated as a series of rectangular elements of equa l, user-specified width. As this width approaches zero, cross-sectiona l area and centroid location approach that of the original cross secti on. Every element is assumed to transition linearly along an offset cu rve concentric with the baseline to an opposing element upstation or t o terminate on a tapered offset curve when an opposing element does no t exist. The resulting volume elements are thus curvilinear wedges or frustums of wedges. Linear, circular, and Cornu spiral baseline (cloth oidal spline) components are accommodated by the method. Numerical exa mples show excellent agreement with exact results even when the mass c omponents are not prismoidal. A general formula for the volume of a cu rvilinear mass component and a new, high-precision, prismoidal curvatu re-correction technique are also presented.