Volumes
 Cross Sections
 End Area Method
 Prismoidal Formula
 Rectangular Base Method
 Triangular Base Method
 Balance of Cut and Fill
 Volumes From Contours
 Digital Terrain Models

Digital Terrain Models

All the previous methods for determining volumes depended on ordered data. These data are collected at predetermined points, positions that are in general invariant of the terrain. These methods are still in modern day usage but their roots lie in the past when it was most important to reduce the amount of computations.

Since 1978 several researchers have been working on alternatives. The basic premise was that points should be collected at locations that best define the terrain regardless of their locations. This had not been previously possible because of the large amount of computing involved. The mathematics is not complex but most tedious. With the advent of the computer it became possible to process large data sets to compute a volume. So Digital Terrain Models (DTMs) gained in acceptance, to the point where they are now the most frequently used method. The basic theory is that points are located (X, Y, Z, coordinates) on the terrain, the locations being the optimal places to define the surface (usually at changes of grade). Each point is connected to neighbouring points in a unique manner so that a series of triangles is formed that entirely covers the surface. As shown in the figure each of these right triangular prisms is a simple solution to an individual volume, their sums being the total volume between the surface and a datum plane. The procedure is also a very convenient way to compute and plot contours, cross sections, long sections, surface profiles and plans for complex surfaces. Numerous commercial packages are now available, most of which will run on an average size PC type computer. SOLVOL, COMPUTAS, RIDGE AND SPUR, INTERGRAPH and others are but a few examples. Research has reached the position where it is now possible to compute the volumes (cut and fill) between two complex intersecting surfaces; current research is attempting to solve the volumes of truly three dimensional surfaces such as an underground ore body or a statue.

In fact triangulated Irregular Networks (TIN) have become so advanced that it is possible to 'model' many irregular surfaces. Here a laboratory specimen cranium has been measured three dimensionally and modelled as a digital 'terrain' or surface model. They are the basis of most high order terrain analysis and volume determination computer packages.

If you would like to find out more about Digital Terrain Models visit this site:

web.ngdc.noaa.gov/seg/topo/topo.shtml 

This site is suggested for extra interest only - it is not part of the course material!

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