Kesseler, Matthew
(2019)
Laboratory-numerical investigation of scale effects in granular slides.
PhD thesis, University of Nottingham.
Abstract
Granular slides are omnipresent phenomena, occurring in both natural contexts such as avalanches and landslides, and in industrial applications such as blenders, chutes, hoppers, and rotating drums. The correct modelling of these events is paramount to the safety of populations that are at risk from granular slides themselves and other slide-related hazards such as landslide tsunamis. Many granular slides are strongly influenced by their interactions with fluid-phases, such as moisture or entrained snow and ice; nevertheless, this study focuses on "dry" granular slides where the surrounding and interstitial airflow is the dominant fluid phase.
Scale effects are changes in physical behaviour of a phenomenon at different geometrically similar scales, such as between a large event observed in nature and a smaller laboratory representation. These scale effects can be considerable and cause small-scale models to become misleading in their prediction of key slide characteristics including maximum velocity and runout distance. Although scale effects are highly relevant to granular slides due to the multiplicity of time and length scales involved, they are currently not well understood. This study aims to provide evidence of and quantify these scale effects, and to clarify whether these scale effects are inherent to the physical grains and their structure, or whether they are more dependent on other characteristics such as the grain Reynolds number (Re), which quantifies the turbulent or viscous manner in which the drag force acts on particles.
A versatile laboratory set-up has been developed to investigate dry granular slides of different scales and initial conditions, with a scale series of experiments being conducted under Froude similarity. The scale series allowed the slide geometry of different experiments to be directly up- or down-scaled, allowing key slide parameters to be measured, non-dimensionalised, and compared directly to quantify scale effects. While many studies addressed granular slides, none of them directly compare geometrically similar slides in this scale series approach.
This set-up has a configurable channel width of 0.25-1.00 m, with an inclined surface up to 3.00 m in length leading to a flat runout zone via interchangeable transition curves. The slide masses investigated in the scale series ranged from 1--110 kg, while Re varied from 100-1000. Particle image velocimetry was used to measure the slide surface velocity at specific points on the inclined ramp section, while laser-trigonometry was used to measure the slide thickness, and photogrammetry was used to measure the final deposit dimensions. The particles investigated in the present study were polydisperse mixtures of angular sand (quartz) grains, with mean diameters ranging from 0.675-2.7 mm across the scale series. Discrete element modelling (DEM) simulations were also conducted, modelling the laboratory scale series and much larger and smaller granular slides. This DEM approach was validated against an axisymmetric column collapse and a granular slide experiment from the technical literature, showing that these two slide conditions could be described well without the need for coupling with computational fluid dynamics.
The data from the experiments conducted in this study has been compared to many slide events in nature and analysed to quantify the influence of Re on slide dynamics, and to evaluate the match between simulated and laboratory events. Overall, significant scale effects have been identified in the laboratory experiments with respect to the slide surface velocity, total runout distance, and deposit morphology. The slide surface velocity increased by up to 34.8% as the experimental scale increased by a factor of 4, and became increasingly Re-dependent as the slide progressed further down the inclined channel section. Normalisation of the slide surface velocity with the estimated drag force on particles shows that the particle drag force becomes increasingly influential over Re scale effects as the velocity increases.
Meanwhile, the deposit runout distance increased by up to 38.1% as scale increased across the range of initial conditions that were investigated, and morphological parameters show greater dependence on the maximum Re achieved by the slide before it starts to settle. Additionally, the slide deposit volume and porosity decreased by over 10% as scale increased, showing a weak inverse dependence on Re. Normalising key laboratory data by multiplying them by a power of Re significantly improved the match of similar experiments of differing scales, allowing the influence of Re to be directly quantified. Simultaneously, characteristics such as the maximum slide thickness in motion remain scale-independent, highlighting that scale effects affect granular slide in heterogeneous and non-linear ways. Furthermore, other physical factors such as increasing dust formation with increasing scale were also observed in the laboratory-scale experiments, which may become increasingly important at geophysical scales. However, the magnitude of the effects induced by these secondary mechanisms is seen to be small compared to the influence of Re, particularly in the deposit position data.
The DEM shows general agreement with the small-scale laboratory experiments. The DEM also provides insight into the processes that may occur in the laboratory slides; analysis of the simulated depth-velocity profiles show the granular slide alternating between Bagnold- and plug-like flow conditions as it traverses the inclined channel. The main difference of the simulations in comparison to the laboratory experiments was the former not being strongly influenced by scale effects. This highlights the importance of laboratory models and experiments in capturing and quantifying scale effects. Overall, the clear importance of Re to these slides suggests that modelling of the airflow surrounding the granular slides is an essential component for capturing scale effects in dry granular slides in numerical contexts.
Furthermore, comparisons of the laboratory data to that of other studies and of relevant natural events show that data calibration with Re is an effective method of correctly upscaling laboratory results to natural events. This upscaling technique can improve hazard assessment in natural contexts and is potentially useful for modelling industrial flows.
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