Estimating Pit Excavation Volume Using Nonlinear Ground Profile

Abstract

The formula used in surveying applications for estimating excavation volume for a rectangular pit assumes that the ground profile between the grid points is linear. In this paper, formulas that consider a nonlinear ground profile (NLP) between the grid points are presented. The NLP formulas are based on an extension of the known Simpson 1/3 and 3/8 formulas for calculating area of a region with irregular boundary. For an even number of intervals in each direction of the rectangular grid, the NLP formula is based on Simpson 1/3 formula. For an odd number of intervals in one or both directions of the rectangular grid, the NLP formula is based on a combination of Simpson 1/3 and 3/8 formulas. The NLP formulas are simple and amenable to computations by calculators or computers. The formulas should provide a better accuracy than the linear profile formula currently in use. Application of the NLP formulas is illustrated by a numerical example.