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 $$\text{ Bo }$$ Bo , the Capillary number $$\text{ Ca }$$ Ca , the system size $$r^*$$ r ∗ , and the grain-fluid density ratio $$\rho ^*$$ ρ ∗ . This analysis demonstrated that collapses as characterised by pore pressure evolution and front positions were controlled by the ratio of $$\text{ Bo}/\text{Ca}$$ 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. Graphical 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.
<p>Debris flows are subaerial, gravity-driven mass movements of water, soil and rocks. &#160;High fluid volume fractions and the presence of a wide particle-size distribution lead to highly heterogeneous flow states, and the mechanisms giving rise to this phenomenology open to debate. For tractable modelling, assumptions around the interaction between grains and fluid must be made, but it is not clear whether those assumptions are reasonable across the wide range of length-scales observed. For example, recent studies have shown that the inclusion of a significant proportion of fine granular material within the flow&#8217;s composition limits the dissipation of excess pore pressures. Here we explore the possibility that these crucial pore pressure processes are governed at length scales that might otherwise seem insignificant to the macroscopic flow behaviour. Hence, we aim to provide insight on the underlying mechanisms controlling pore pressure through a scaling analysis describing the idealised scenario of sub-aerial axisymmetric column collapses of just-saturated fluid-grain mixtures. Glass beads provide the prototype for inertial particles within the debris flow, and Newtonian fluids carrying varying mass concentrations of fine kaolin clay particles provide the microscopic processes that can control the pore spaces. A geotechnical centrifuge permits elevated gravitational acceleration that when varied alongside particle size, fluid viscosity and mass concentration of fines, allows a wide parameter space to be explored. Pore pressure measurements from these collapses indicate two competing mechanisms, stemming from drainage related pore pressure dissipation and inertial collision related pore pressure generation. An empirical description of these processes is proposed based on our experimental data. This expression is then implemented to describe the fluid-particle coupling within a multiphase Saint-Venant inspired central-upwind scheme in an attempt to simulate the experimental observations.</p>
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