Institute for Geotechnical Processes and Mine Surveying
Technical University of Clausthal,   Prof. Dr.-Ing. W. Busch 

Study project:   Calculation of the volume of cavities

Summary:

Within the scope of the study, various methods of three-dimensional modeling and volume calculation were investigated and compared with one another based on the cavern survey data provided by SOCON Sonar Control Kavernenvermessung GmbH (SOCON).

Qualitative displays and assessments were made for interpolation, approximation and alternative descriptions of volume models of caverns. An overview of possible combinations of methods and the current status of development were given. 3D-volume-based models and alternative stochastic and statistical techniques were presented.

In the method currently applied by SOCON (method combination A1/B1), the horizontal sections are plotted using measured distances to (cavern wall) segments and based on these partial volumes are calculated by multiplying each horizontal section area with half the interval to the adjacent horizontal sections. The total volume is determined by adding up all the partial volumes.

6 alternative volume models and 8 alternative area models were calculated for approximately 90 different cavern surveys and 10 cavern partial areas. The interpretation of about 360 volume calculations for 75 caverns with several alternative, area-based volume models revealed only slight differences. As the true volumes were not known, the differences between the various methods were considered so as to achieve a quantitative assessment.

Compared to the 'SOCON' method, the calculated volumes are on average 0.28% less when the areas are calculated alternatively using the Gaussian area equation (method combination A2/B1) (scatter of the volume differences 1.15%).

The 'SOCON' method did not reveal any significantly different results even in comparison with the volumes calculated from the vertical sections. If the vertical cross-sections are determined using the Gaussian method and the volume calculated by rotating these areas about the survey axis (method combination C1/D1), then the resulting volumes are on average 0.64% less than the volumes calculated using the 'SOCON' method (scatter 1.30%).

Compared with the other method combinations investigated, the 'SOCON' method revealed neither implausibilities nor any significant differences.

More details about the results: