Periodic Reporting for period 1 - kelbus2 (Experimental and numerical study of long runout landslides)
Berichtszeitraum: 2020-01-15 bis 2022-01-14
The result of both the experimental and parallel numerical study was that a relevant parameter absent in prevalent theories of landslide runout was the landslide grain size. We made a radical improvement on our ability to predict landslide runout by using systematic laboratory experiments of granular flow with a simplified landslide geometry combined with a scaling analysis. We found that additionally accounting for the granular nature of the flow through the constituent grain size, and correctly accounting for the fall height, reveals a striking correlation of normalized runout with landslide size which when combined with field data extends to nearly ten orders of magnitude in size. We thus united seemingly disparate fields such as small-scale laboratory granular experiments, landslides, and snow avalanches, and dramatically enhanced runout prediction for dense flows. Our work thus alleviates the need for special theories and removes some of the mystery clouding the discussion of these fascinating, if extremely dangerous, phenomena.
In addition, we also determined the minimum landslide size required to observe this scaling, which we find is set by a combination of air drag, grain size, and fall height. The scaling of this minimum size was determined with the assumption that for small total volumes, landslides behave as a granular gas, while at large volumes they behave as a dense granular liquid. This result will help to guide the design of any future laboratory experiments aimed at understanding natural landslide behavior.
We started by doing studies of landslide runout for a single fall height and grain size as well but changing systematically the landslide total volume. For a single grain size and fall height we observed the classical result that the runout distance increases with landslide volume. When we either changed the fall height or changed the grain size we found the same classical behavior, but when plotted in the traditional way (fall height divided by runout distance versus volume) we ended up with many distinct curves. This lack of agreement between the data caused by different fall height and diameter meant that the traditional plot, which is an attempt to account for the influence of the fall height and the volume on the runout distance, does not work. We thus performed a standard scaling analysis often used in the fields of applied mathematics, fluid mechanics, and physics, and revealed the true dependence of the runout distance on fall height, landslide size (which became the number of grains), and the average landslide grain size. Plotting in our new way, the normalized landslide runout distance for a wide range of parameter values collapse onto a common, universal curve.
In fact, we observed that for small landslide volumes the scaling analysis breaks down, which is not uncommon. A given scaling does not always work for all ranges of a parameter. We were able to determine when this breaks down as a function of landslide size, fall height, grain diameter, and the viscosity of the surrounding air, by assuming that the breakdown is caused by a transition from a granular gas to granular liquid behavior. This observation of a granular phase transition is novel in its own right, but the scaling result that we found is also of practical value in designing laboratory experiments to study natural landslides. The scaling of the landslide runout as well as its breakdown are in a publication under review.
Finally, using the new scaling that we found as a foundation, we began to add new parameters into our experiments that are also of relevance to natural landslides. Our original experiments were performed on a flat, smooth substrate, but natural landslides have a variety of complicated terrain. To account for this systematically we performed a large number of experiments for which we varied the roughness of the substrate. We did this by attaching standard sandpaper, which we characterized using a microscope, as well as our own laboratory-made rough substrates. Again using the same standard scaling analysis revealed a new dependence on the ratio of grain size to roughness. This result is not only of interest to landslide runout prediction, but it also continuously bridges the gap between two standard laboratory approaches: the smooth and rough substrates. This work is being written up into a manuscript for publication.