Zur Ausbreitung einer Granulatlawine entlang gekrümmter Flächen
This paper deals with the theoretical, numerical and experimental treatment of two- and three-dimensional flow avalanches. A depth-averaged theory for three-dimensional flow avalanches is introduced, basing upon a MOHR-COULOMB yield criterion and a COULOMB dry friction law, and the specialization to two dimensions is carried out. The three-dimensional model equations are width-averaged in a further step in order to receive equations that can more easily be numerically handled. Furthermore, numerical calculation schemes are given for the two- and three-dimensional model equations, making use of material cells that follow the motion of the avalanche.
Experiments are carried out with different granular materials in a chute with a partly convex, partly concave curved geometry. In these experiments the avalanche motion from the moment of release to its standstill is followed by high speed photography. The results are compared with numerical calculations in order to get information about the applicability of the model. Moreover, experiments are performed on a surface without constraining walls, consisting of an inclined and a horizontal plane connected by a curved area. These experiments are followed by stereoscopic high speed photography, for which a mirror attachment, constructed during this work, is applied. The photogrammetric evaluation of the photos with the aim of obtaining relief maps as time series could not be accomplished, but the applicability of this method is demonstrated in principle by using a calibration body.
In case of two-dimensional avalanches a very good correspondence between experiment and theory is observed. Even the development of the detailed avalanche geometry can be reproduced in good agreement by the model. In case of three-dimensional avalanches, however, the model produces a considerable overprediction of the length and an underprediction of the width of the avalanche body in comparison with the experiment; a fact indicating that too much information of the motion process is lost because of the width-averaging of the model equations.
Diploma thesis, Department of Mechanics, Darmstadt University of Technology, Germany, 171 pp. (1991).