Inertial effects in just-saturated axisymmetric column collapses

Abstract

This work introduces a scaling analysis of sub-aerial axisymmetric column collapses of glass beads and Newtonian glycerol-water solutions mimicking some of the behaviours of debris flows. The beads were in a size range where their inertia partly decouples their collapse behaviour from the water column. Experiments explored a range of viscous, surface tension and particle inertia effects through systematic variation of particle size and fluid viscosity. Crucially a geotechnical centrifuge was used to access elevated effective gravitational accelerations driving the collapse, allowing field-scale viscous and surface tension effects to be replicated. Temporal pore pressure and run out front position evolution data was extracted using a pressure transducer and high speed imaging, respectively. A least-squares fitted scale analysis demonstrated that all characteristic dimensionless quantities of the acceleration phase could be described as a function of the column-scale Bond number \(\text{ Bo }\), the Capillary number \(\text{ Ca }\), the system size \(r^*\), and the grain-fluid density ratio \(\rho ^*\). This analysis demonstrated that collapses as characterised by pore pressure evolution and front positions were controlled by the ratio of \(\text{ Bo}/\text{Ca}\). This indicates that grain-scale surface tension effects are negligible in such inertial column collapses where they may dominate laboratory-scale granular-fluid flow behaviour where geometric similarity between grain and system size is preserved.

Graphical abstract