Frictional Hysteresis in Granular Avalanches

  • Aaron Russell

Student thesis: Phd


Geophysical mass flows often occur on inclines covered by a static layer of erodible granular material, which once disturbed initiates a flow downslope that grows in size as it erodes additional material, posing a hazard to the local population. If the slope is sufficiently steep, material upslope of the disturbance can also be eroded via an upslope-propagating erosion wave, or retrogressive failure, which increases the volume of the flow, posing an increased hazard. This thesis aims to gain an insight into this complex phenomenon using a combination of continuum models, small-scale laboratory experiments and numerical simulations. Shallow dry granular flows over a rough plane inclined at an angle ζ to the horizontal exhibit a wide range of hysteretic behaviour, the simplest of which is that when a steady uniform granular flow is brought to rest it leaves a deposit of thickness hstop(ζ), but this layer will not start to flow spontaneously unless it is inclined to a greater angle ζstart. This frictional hysteresis is directly responsible for flows with co-existing regions of solid-like and fluid-like behaviour such as retrogressive failures, self channelised flows with static levees and erosion-deposition waves. This thesis proposes a new non-monotonic friction law for granular materials, consisting of static, intermediate and dynamic friction regimes, that when combined with a depth-averaged avalanche model can capture all the hysteretic phenomena observed as well as predicting the correct deposit depths left behind by steady uniform flows. Retrogressive failures can be observed in small-scale dry granular flow experiments by creating a static layer of thickness hstop(ζ), which due to frictional hysteresis can remain static when inclined to a steeper angle. If the increase in angle is small, a perturbation to the layer results in only a downhill propagating avalanche, but if the increase in angle is large enough an additional upward retrogressive failure is observed. These retrogressive failure experiments give indirect measurements of the functional form of the inherently unstable intermediate friction regime. This thesis shows that a simple depth-averaged avalanche model combined with the hysteretic non-monotonic friction law proposed here is sufficient to capture the observed planar retrogressive failures. An investigation into the stability of the downstream flow produced by retrogressive failures provides further constraints on the functional form of the friction law.
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorNico Gray (Supervisor) & Christopher Johnson (Supervisor)


  • Geophysical and geological flows
  • Granular flow
  • Shallow water flows
  • Waves/free-surface flows

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