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 runout 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 Bo, the Capillary number Ca, the system size r*, and the grain-fluid density ratio ρ*. This analysis demonstrated that collapses as characterised by pore-pressure evolution and front positions were controlled by the ratio of Bo/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.

DEM-LBM insights into unsteady grain-fluid collapses on a geotechnical centrifuge

“…This transformation results in, approximately, a family of curves dependent on B, with increasing B indicating a higher relative influence of column-scale inertia, leading to the faster propagation of r * v ρ * . Encouragingly, a similar result was obtained previously when modelling the collapses using a two-phase shallow water model [42].…”

“…In particular, it predicts well the time after release of the phase peak velocity, and achieves runout distances comparable to the physical experiments. However, there are two main sources of discrepancies between the simulations and the physical experiments, as discussed in detail by Webb et al [42] and summarised below.…”

“…41]. Following the approach of Webb et al [42], the anticipated behaviour of the numerically modelled just-saturated column configuration can be characterised using three dimensionless parameters: a, the fluid-grain density ratio ρ * = ρ f /ρ p and B = (N gD 4 ρ 2 )/(h 0 µ 2 f ). Here ρ represents the effective column density, defined as = ϕ p ρ p + (1 − ϕ p )ρ f .…”

“…Here ρ represents the effective column density, defined as = ϕ p ρ p + (1 − ϕ p )ρ f . The parameter B, analogous to the square of the ratio of the column Bond and Capillary numbers (Bo/Ca) 2 [42], quantifies the relative influence of column-scale inertial and viscous forces on collapse dynamics [15]. Since a is held constant, we plot the evolution of the phase radial position in dimensionless density-weighted ρ * r * v -t * space (Figure 7b), where r * v = (r v − r 0 )/r 0 and t * = t/ h 0 /(N g).…”

Fines-controlled drainage in just-saturated, inertial column collapses

“…A recent study [8] attempted to isolate the influence of inertial grains on flow dynamics over a wide parameter space by conducting g-elevated, fluid-saturated granular column collapse experiments where water-glycerol mixtures were used as a pseudo-fluid. The current study attempts to build on this work and introduce an extreme bimodal grain size distribution by using a fluid phase comprised of kaolin clay particles and water.…”