Smooth Surface Approximation for Computing Pit Excavation Volume
Publication: Journal of Surveying Engineering
Volume 124, Issue 3
Abstract
In this paper, a method of volume computation that combines the advantages and avoids the drawbacks of current methods is presented. Earlier methods of computing pit excavation volume were based on the trapezoidal or Simpson-type rules. These methods provide direct formulas for volume computation, but their disadvantage is that they approximate the ground surface by piecewise surfaces that have sharp connections. The existing cubic spline method is based on a smooth ground surface, but its disadvantage is that it requires solving a system of linear equations and integrating a function many times. The proposed method provides a direct formula for volume computation and is based on a smooth approximating surface. The method employs a cubic Hermite polynomial for individual intervals in both directions of the grid, the intervals of which may be unequal. A cubic Hermite volume formula is developed by integrating the surface function in both coordinate directions. The proposed method, which provided comparable accuracy to that of the more elaborate cubic spline method, should be of interest to surveyors concerned with both accuracy and ease of volume computations.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderson, J. M., Michael, E. M., and Woolnough, D. E. (1985). Introduction to surveying. McGraw-Hill Book Co., Inc., New York, N.Y.
2.
Chambers, D. W.(1989). “Estimating pit excavation volume using unequal intervals.”J. Surv. Engrg., ASCE, 115(4), 390–401.
3.
Chen, C.-S., and Lin, H.-C.(1991). “Estimating pit excavation volume using cubic spline volume formula.”J. Surv. Engrg., ASCE, 117(2), 51–66.
4.
Easa, S. M.(1993). “Smooth boundary approximation for computing area of irregular region.”J. Surv. Engrg., ASCE, 119(3), 86–101.
5.
Easa, S. M.(1992). “Discussion of `Estimating pit-excavation volume using cubic spline volume formula,' by C.-S. Chen and H.-C. Lin.”J. Surv. Engrg., ASCE, 118(2), 66–67.
6.
Easa, S. M.(1988). “Estimating pit excavation volume using nonlinear ground profile.”J. Surv. Engrg., ASCE, 114(2), 71–83.
7.
Gerald, C. F., and Wheatley, P. O. (1989). Applied numerical analysis. Addison-Wheatley Publishing Co., Reading, Mass.
8.
Moffit, F. H., and Bossler, J. D. (1998). Surveying. Harper & Row, Publishers, Inc., New York, N.Y.
9.
Schmidt, M. O., and Wong, K. W. (1985). Fundamentals of surveying. Harper & Row, Publishers, Inc., New York, N.Y.
10.
Wolf, P. R., and Brinker, R. C. (1989). Elementary surveying. Harper & Row, Publishers, Inc., New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Aug 1, 1998
Published in print: Aug 1998
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.