Basic Experiments
Figure 2: Basic slope model
Preliminary experiments have been performed on two simple 2-dimensional environments. The simplest is shown in Figure 2. It involves a slope extending into a flat section and ending in a wall. The experiment was used to study the physical values of slides and validate against simple analytical solutions.
Figure 3: Simplified Köfels experiment.
The other is the simplified version of the Köfels slide shown in Figure 3 where 900 particles with a diameter of 10 meters are stacked loosely on a 60º slope. The slope originates at 1000 meters above the valley floor, falling to ground level and raising again as a 30º slope to a vertical wall starting at 1,000 meters altitude. The models were used mainly to investigate the various aspects of boulder dynamics and obtain some understanding of energy loss in rock avalanches. Based on evidence from Köfels that there is not rotation involved, we have in these models disregarded any exchange of angular momentum. Some results of the experiments are shown below. Figure 4 shows the loss in total energy during the first 25 seconds for a low β model with α in the range 0.1 (red) to 0.7 (blue). Notice the three separate sectors. First a gently loss as the slide descends the slope. Then a massive decline as the slide collides with the valley floor, followed by another gentle decrease as the slope traverses the valley and climbs the shallower slope. While the impact with the valley floor is clearly marked, the impact of the raising slope is hidden in the noise.
Figure 4: Energy loss for low β model.
Figure 5 shows the variation in pressure for the same model. Pressure is here a virtual value representing the forces acting on individual particles. The graphs clearly show the difference in forces between a gentle slope decent and the floor impact, but the is little variation observable as a result of changes to α.
Figure 5: Pressure variations for low β model.
Figure 6: Impact on valley floor.
The flows themselves are shown in Figure 6. Double click on each image to see an animation of the first 12.5 seconds of the slide. Both animations show the same slide, but in one the particles are coloured according to the pressure while the other show particles coloured to mark three layers at the start. We see that there is little mixing between the layers and that the bottom layers moves slightly faster than the top. Careful observations will reveal a separation of the slide into two parts; a slightly asymmetric head and a trailing tail. This is a tendency observed in most of the models but it is enhanced by friction. Figure 7 shows the pressure variations for a range of friction levels. We clearly see the a small separation in the peak of the red curve and this can be seen to grow as the friction is increased to form a clear double peak for the high friction, blue model.
Figure 7: Pressure variations with the friction parameter β.
The head of the slide forms a symmetric pile that slowly widens at the base. This widening is due to friction which is proportional to the force perpendicular to the slope and therefore strongest where the pile is thickest. Consequently, the head of the slide will run away from the rest. This effect is also responsible for the tail being composed primarily of material from the upper level, a tendency that is enhanced by stronger friction.
Figure 8: Models that initially are raised above the floor.
Two other models are shown in Figure 8, again a 12.5 second animation is available by clicking on each figure. Here the block of material is raised from the slope to give it an initial energy boost. Only the virtual pressure animations are shown. As expected this has little impact on the behaviour of the slide because of damping. The only way to impose energy on the slide is to feed energy continuously. One mechanism to accomplish that is to use an uneven surface.