Pyramid Frustum Formula for Computing Volumes at Roadway Transition Areas

Abstract

Intermediate transition and sidehill cross sections are normally established when the roadway section changes from cut to fill or vice versa. The average-end-area (AEA) and pyramid formulas are employed in practice for computing the cut and fill volumes. This technical note proposes a pyramid frustum (PF) formula that can be used instead of the AEA formula. Because the volumes formed in the transition areas are frustum-like solids, the PF formula is more accurate than the AEA formula. The proposed formula, which is a function of only the end areas and the distance between them, is as simple as the AEA formula. The PF formula should be of interest to the highway engineers concerned with achieving greater accuracy in volume computations.