Large particle segregation, transport and accumulation in granular free-surface flows

Particle size segregation can have a significant feedback on the motion of many hazardous geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches. This paper develops a new depth-averaged theory for segregation that can easily be incorporated into the existing depth-averaged structure of typical models of geophysical mass flows. The theory is derived by depth-averaging the segregation-remixing equation for a bi-disperse mixture of large and small particles and assuming that (i) the avalanche is always inversely graded and (ii) there is a linear downslope velocity profile through the avalanche depth. Remarkably, the resulting ‘large particle transport equation’ is very closely related to the segregation equation from which it is derived. Large particles are preferentially transported towards the avalanche front and then accumulate there. This is important, because when this is combined with mobility feedback effects, the larger less mobile particles at the front can be continuously shouldered aside to spontaneously form lateral levees that channelize the flow and enhance run-out. The theory provides a general framework that will enable segregation-mobility feedback effects to be studied in detail for the first time. While the large particle transport equation has a very simple representation of the particle size distribution, it does a surprisingly good job of capturing solutions to the full theory once the grains have segregated into inversely graded layers. In particular, we show that provided the inversely graded interface does not break it has precisely the same solution as the full theory. When the interface does break, a concentration shock forms instead of a breaking size segregation wave, but the net transport of large particles towards the flow front is exactly the same. The theory can also model more complex effects in small-scale stratification experiments, where particles may either be brought to rest by basal deposition or by the upslope propagation of a granular bore. In the former case the resulting deposit is normally graded, while in the latter case it is inversely graded. These completely opposite gradings in the deposit arise from a parent flow that is inversely graded, which raises many questions about how to interpret geological deposits

Timing, relations and cause of plutonic and volcanic activity of the Siluro-Devonian post-collision magmatic episode in the Grampian Terrane, Scotland

<p>Calc-alkaline magmatism in the Grampian Terrane started at <em>c</em>. 430 Ma, after subduction of the edge of continental Avalonia beneath Laurentia, and it then persisted for at least 22 Ma. Isotope dilution thermal ionization mass spectrometry U–Pb zircon dating yields 425.0 ± 0.7 Ma for the Lorn Lava Pile, 422.5 ± 0.5 Ma for Rannoch Moor Pluton, 419.6 ± 5.4 Ma for a fault-intrusion at Glencoe volcano, 417.9 ± 0.9 Ma for Clach Leathad Pluton in Glencoe, and, in the Etive Pluton, 414.9 ± 0.7 Ma for the Cruachan Intrusion and 408.0 ± 0.5 Ma for the Inner Starav Intrusion. The Etive Dyke Swarm was mostly emplaced during 418–414 Ma, forming part of the plumbing of a large volcano (≥2000 km³) that became intruded by the Etive Pluton and was subsequently removed by erosion. During the magmatism large volumes (thousands of km³) of high Ba–Sr andesite and dacite were erupted repeatedly, but were mostly removed by contemporaneous uplift and erosion. This volcanic counterpart to the ’Newer Granite' plutons has not previously been fully recognized. The intermediate magmas forming both plutons and volcanoes originated mainly by partial melting of heterogeneous mafic to intermediate lowermost crust that had high Ba–Sr derived from previous melting of large ion lithophile element (LILE)-enriched mantle, possibly at <em>c</em>. 1.8 Ga. This crustal recycling was induced by heat and volatiles from underplated small-degree melts of LILE- and light REE-enriched lithospheric mantle (appinite–lamprophyre magmas). The post-collision magmatism and uplift resulted from breakoff of subducted oceanic lithosphere and consequent rise of asthenosphere. </p

Timing, relations and cause of plutonic and volcanic activity of the Siluro-Devonian post-collision magmatic episode in the Grampian Terrane, Scotland

<p>Calc-alkaline magmatism in the Grampian Terrane started at <em>c</em>. 430 Ma, after subduction of the edge of continental Avalonia beneath Laurentia, and it then persisted for at least 22 Ma. Isotope dilution thermal ionization mass spectrometry U–Pb zircon dating yields 425.0 ± 0.7 Ma for the Lorn Lava Pile, 422.5 ± 0.5 Ma for Rannoch Moor Pluton, 419.6 ± 5.4 Ma for a fault-intrusion at Glencoe volcano, 417.9 ± 0.9 Ma for Clach Leathad Pluton in Glencoe, and, in the Etive Pluton, 414.9 ± 0.7 Ma for the Cruachan Intrusion and 408.0 ± 0.5 Ma for the Inner Starav Intrusion. The Etive Dyke Swarm was mostly emplaced during 418–414 Ma, forming part of the plumbing of a large volcano (≥2000 km³) that became intruded by the Etive Pluton and was subsequently removed by erosion. During the magmatism large volumes (thousands of km³) of high Ba–Sr andesite and dacite were erupted repeatedly, but were mostly removed by contemporaneous uplift and erosion. This volcanic counterpart to the ’Newer Granite' plutons has not previously been fully recognized. The intermediate magmas forming both plutons and volcanoes originated mainly by partial melting of heterogeneous mafic to intermediate lowermost crust that had high Ba–Sr derived from previous melting of large ion lithophile element (LILE)-enriched mantle, possibly at <em>c</em>. 1.8 Ga. This crustal recycling was induced by heat and volatiles from underplated small-degree melts of LILE- and light REE-enriched lithospheric mantle (appinite–lamprophyre magmas). The post-collision magmatism and uplift resulted from breakoff of subducted oceanic lithosphere and consequent rise of asthenosphere. </p

Segregation-induced fingering instabilities in granular free-surface flows

Particle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance run-out distance. This is particularly important in geophysical mass flows, such as pyroclastic currents, snow avalanches and debris flows, where run-out distance is of crucial importance in hazards assessment. A model for finger formation in a bidisperse granular avalanche is developed by coupling a depth-averaged description of the preferential transport of large particles towards the front with an established avalanche model. The coupling is achieved through a concentration-dependent friction coefficient, which results in a system of non-strictly hyperbolic equations. We compute numerical solutions to the flow of a bidisperse mixture of small mobile particles and larger more resistive grains down an inclined chute. The numerical results demonstrate that our model is able to describe the formation of a front rich in large particles, the instability of this front and the subsequent evolution of elongated fingers bounded by large-rich lateral levees, as observed in small-scale laboratory experiments. However, our numerical results are grid dependent, with the number of fingers increasing as the numerical resolution is increased. We investigate this pathology by examining the linear stability of a steady uniform flow, which shows that arbitrarily small wavelength perturbations grow exponentially quickly. Furthermore, we find that on a curve in parameter space the growth rate is unbounded above as the wavelength of perturbations is decreased and so the system of equations on this curve is ill-posed. This indicates that the model captures the physical mechanisms that drive the instability, but additional dissipation mechanisms, such as those considered in the realm of flow rheology, are required to set the length scale of the fingers that develop

Timing, relations and cause of plutonic and volcanic activity of the Siluro-Devonian post-collision magmatic episode in the Grampian Terrane, Scotland

Calc-alkaline magmatism in the Grampian Terrane started at c. 430 Ma, after subduction of the edge of continental Avalonia beneath Laurentia, and it then persisted for at least 22 Ma. Isotope dilution thermal ionization mass spectrometry U–Pb zircon dating yields 425.0 ± 0.7 Ma for the Lorn Lava Pile, 422.5 ± 0.5 Ma for Rannoch Moor Pluton, 419.6 ± 5.4 Ma for a fault-intrusion at Glencoe volcano, 417.9 ± 0.9 Ma for Clach Leathad Pluton in Glencoe, and, in the Etive Pluton, 414.9 ± 0.7 Ma for the Cruachan Intrusion and 408.0 ± 0.5 Ma for the Inner Starav Intrusion. The Etive Dyke Swarm was mostly emplaced during 418–414 Ma, forming part of the plumbing of a large volcano (2000 km3) that became intruded by the Etive Pluton and was subsequently removed by erosion. During the magmatism large volumes (thousands of km3) of high Ba–Sr andesite and dacite were erupted repeatedly, but were mostly removed by contemporaneous uplift and erosion. This volcanic counterpart to the ’Newer Granite' plutons has not previously been fully recognized. The intermediate magmas forming both plutons and volcanoes originated mainly by partial melting of heterogeneous mafic to intermediate lowermost crust that had high Ba–Sr derived from previous melting of large ion lithophile element (LILE)-enriched mantle, possibly at c. 1.8 Ga. This crustal recycling was induced by heat and volatiles from underplated small-degree melts of LILE- and light REE-enriched lithospheric mantle (appinite–lamprophyre magmas). The post-collision magmatism and uplift resulted from breakoff of subducted oceanic lithosphere and consequent rise of asthenosphere