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Discrete element modelling of scree dynamics

Discrete element modelling of scree dynamics

The issue of how scree slopes form has been under investigation at least since the time of the Reverend Oswald Fisher in 1866. He deduced analytically that the shape of the rock core under the scree should be quadratic in form, with the underlying rock slope being just tangential to the debris as the scree approached the full cliff height. Numerous investigations of this rock-core shape have since been undertaken, but few investigations have looked at the dynamics of the accumulating debris at the cliff foot. Here we use a discrete element model to simulate the falling material that is loosened from the cliff by weathering. We simulate the interactions between all particles that fall to the cliff foot, approximating the interactions by damped linear springs, and constraining our spherical particles to move in only 2 dimensions.

We have varied the model parameters (such as coefficient of restitution and internal friction angle, rock fragment size distribution) to give 12 parameter sets, and run the model 32 times for each set of parameters with different pseudo-random number sequences for a total of 384 model runs, each one comprising approximately 10,000 particles with radii between 0.3 and 0.6 m.

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Particles fall the cliff foot and accumulate there. As the material build up, the debris becomes unstable and undergoes repeated failures resulting in large avalanches.

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The statistics of the avalanches changes gradually over time, as early high energy-input events dominated by rock-fall are replaced by sliding events.

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The rock core shows the classic quasi-quadratic shape, although the fit to the DEM model requires use of an effective cliff height rather larger than the actual cliff height as a result of the repeated slides.

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The above results seem to be very insensitive to model parameters, although the resulting scree slopes currently have angles of repose that are rather small (between 18 and 20 degrees, more or less independent of particle internal friction angle).

Acknowledgements

This work was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service, provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England. Discrete element simulations were parallelized using the CUDA Thrust library.

References

  • Bithell,M. And Richards, K.S. "Cliffs and screes: The Reverend Fisher, Nakker and LeHeux, Statham, Kirkby and DEM" IAG conference 2013
  • Bithell, M., Richards, K.S., and Bithell, E.G., (2014), "Simulation of scree slope dynamics: investigating the distribution of debris avalanche evets in an idealised two dimensional model" Earth Surface Processes and Landforms doi:10.1002/esp.3548