Triangulation Applications in Volume Calculation

Abstract

Results from volume calculation of soils are a major input in heavy construction and earth‐moving operations. Traditional methods for volume calculation have been based on the application of the end‐area method or prismoidal method to a grid covering the site. This paper discusses the weaknesses of griding techniques and introduces triangulation as a powerful and viable alternative. Delaunay triangulation is chosen to demonstrate the benefits of triangulation that include higher accuracy, better ability to deal with volumes for different soil types, and faster development of “in‐between” elevations (i.e., elevations of the site after some cut and/or fill is performed). This paper also addresses some problems with triangulation and the modifications needed to adapt triangulation to volume calculation. A volume‐calculation program using Delaunay triangulation was developed in FORTRAN and used to demonstrate the merits of the proposed method. The program developed also includes an implementation of an algorithm developed by the writer (referred to as the lot‐inclusion algorithm) to enable the user to calculate volumes of divisions with any shape including those with holes.