| 1. |
- Bazargan, Mohsen, et al.
(författare)
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Evolution of the statistical distribution of crystal orientations in time- and space-varying viscous flows
- 2019
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Ingår i: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 218:2, s. 773-786
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Tidskriftsartikel (refereegranskat)abstract
- Magmas and other viscously deforming fluids in the Earth frequently contain embedded crystals or other solid inclusions. These inclusions generally rotate about their own axis and, under certain conditions, align themselves in a direction dictated by the details of the flow. This rotational behaviour has been studied extensively for homogeneous flows. Here, we couple the crystal rotation dynamics with the fluid mechanical Navier-Stokes equations for the large-scale flow, thus allowing the analysis of crystal rotations in settings that are variable in both space and time. The solution is valid provided that the intercrystal spacing is sufficiently large to preclude interaction between crystals. Additionally, we derive an evolution equation for the probability density function (PDF) of crystal orientations based on the fundamental concept of conservation of generic properties in continuum mechanics. The resulting system of equations is extensively tested against previous analytical and numerical solutions. Given the focus on method validation, we limit the fluid mechanics to simple systems with analytical solutions for the velocity field. Even for the simple examples computed, all of which are characterized by fluid flow that is constant in time, the crystal orientation patterns are spatially complex and change in time. Pressure-driven flow in a channel results in coherent bands of crystal orientations with band thickness decreasing towards the channel walls. In corner flow constrained by two mutually perpendicular walls, the pattern of crystal orientations does not exhibit any significant similarity with the flow field. Given that there is no local one-to-one correspondence between the flow and the PDF pattern, a combined and larger-scale solution of the two systems is generally required. The simple flow examples shown demonstrate the viability of this new approach. Application to more complex flow geometries which may commonly occur in nature is deferred to future studies.
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| 2. |
- Vachon, Rémi, et al.
(författare)
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Crystal rotations and alignment in spatially varying magma flows : 2-D examples of common subvolcanic flow geometries
- 2021
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Ingår i: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 226:1, s. 709-727
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Tidskriftsartikel (refereegranskat)abstract
- Elongate inclusions immersed in a viscous fluid generally rotate at a rate that is different from the local angular velocity of the flow. Often, a net alignment of the inclusions develops, and the resulting shape preferred orientation of the particle ensemble can then be used as a strain marker that allows reconstruction of the fluid’s velocity field. Much of the previous work on the dynamics of flow-induced particle rotations has focused on spatially homogeneous flows with large-scale tectonic deformations as the main application. Recently, the theory has been extended to spatially varying flows, such as magma with embedded crystals moving through a volcanic plumbing system. Additionally, an evolution equation has been introduced for the probability density function of crystal orientations. Here, we apply this new theory to a number of simple, 2-D flow geometries commonly encountered in magmatic intrusions, such as flow from a dyke into a reservoir or from a reservoir into a dyke, flow inside an inflating or deflating reservoir, flow in a dyke with a sharp bend, and thermal convection in a magma chamber. The main purpose is to provide a guide for interpreting field observations and for setting up more complex flow models with embedded crystals. As a general rule, we find that a larger aspect ratio of the embedded crystals causes a more coherent alignment of the crystals, while it has only a minor effect on the geometry of the alignment pattern. Due to various perturbations in the crystal rotation equations that are expected in natural systems, we show that the time-periodic behaviour found in idealized systems is probably short-lived in nature, and the crystal alignment is well described by the time-averaged solution. We also confirm some earlier findings. For example, near channel walls, fluid flow often follows the bounding surface and the resulting simple shear flow causes preferred crystal orientations that are approximately parallel to the boundary. Where pure shear deformation dominates, there is a tendency for crystals to orient themselves in the direction of the greatest tensile strain rate. Where flow impinges on a boundary, for example in an inflating magma chamber or as part of a thermal convection pattern, the stretching component of pure shear aligns with the boundary, and the crystals orient themselves in that direction. In the field, this local pattern may be difficult to distinguish from a boundary-parallel simple shear flow. Pure shear also dominates along the walls of a deflating magma chamber and in places where the flow turns away from the reservoir walls, but in these locations, the preferred crystal orientation is perpendicular to the wall. Overall, we find that our calculated patterns of crystal orientations agree well with results from analogue experiments where similar geometries are available.
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| 3. |
- Vachon, Remi, et al.
(författare)
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Effect of host-rock rheology on dyke shape, thickness and magma overpressure
- 2017
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Ingår i: Geophysical Journal International. - : Oxford University Press. - 0956-540X .- 1365-246X. ; 208:3, s. 1414-1429
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Tidskriftsartikel (refereegranskat)abstract
- The size and thickness of dykes is of fundamental importance for volcano dynamics because dykes are the primary path for magma transport, and because large numbers of dykes often comprise a major proportion of the volcanic edifice and of the underlying crust. Standard elastic models predict dyke geometry to be elliptic in cross-section for constant overpressure and uniform host-rock properties, whereas observations show that dyke thickness is typically more nearly constant with a sharp taper at the ends. Moreover, the predicted overpressures required to inflate dykes in a purely elastic medium are often significantly higher (> 150 MPa and up to 2 GPa) than those estimated by other means (about 1-50 MPa). In this study, we use 2-D finite element models to test whether other host-rock rheologies lead to more realistic dyke shapes and overpressures. We examine three different rheologies, each of which is affected by the presence of the dyke itself: (1) elasticity with reduced moduli in regions of low pressure or tension; (2) elastoplasticity with plastic failure in the high-stress regions surrounding the dyke tips; (3) viscoelasticity with a viscosity decrease due to heating by the dyke. We use rheological parameters obtained from laboratory experiments whenever possible, and assume static conditions for the final dyke shape. We find that all three rheologies tend to make the dyke more rectangular relative to the elliptical dykes of the linearly elastic models. The change in shape is due to enhanced deformation in the high-stress zone surrounding the dyke tip. We also find that the overpressure required to inflate an initially thin dyke to a given thickness is reduced for all three rheologies. The greatest decrease in overpressure by a factor of about 0.1 is observed for the elastoplastic model, and for the viscoelastic model if the dyke intrudes into moderately pre-heated host-rock. We discuss our results with respect to dyke observations from Rum Island (Scotland) and use these as a guide to evaluate our models.
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| 4. |
- Vachon, Remi, et al.
(författare)
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Mechanical energy balance and apparent fracture toughness for dykes in elastoplastic host rock with large-scale yielding
- 2019
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Ingår i: Geophysical Journal International. - : Oxford University Press (OUP). - 0956-540X .- 1365-246X. ; 219:3, s. 1786-1804
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Tidskriftsartikel (refereegranskat)abstract
- The dynamics of dyke emplacement are typically modelled by assuming an elastic rheology for the host rock. However, the resulting stress field predicts significant shear failure in the region surrounding the dyke tip. Here, we model the dyking process in an elastic-perfectly plastic host rock in order to simulate distributed shear fracturing and subsequent frictional slip on the fracture surfaces. The fluid mechanical aspects of the magma are neglected as we are interested only in the fracture mechanics of the process. Magma overpressure in dykes is typically of the same order of magnitude as the yield stress of the host rock in shear, especially when the pressure effect of volatiles exsolving from the magma is taken into account. Under these conditions, the plastic deformation zone has spatial dimensions that approach the length of the dyke itself, and concepts based on linear elastic fracture mechanics (LEFM) no longer apply. As incremental plasticity is path dependent, we describe two geologically meaningful endmember cases, namely dyke propagation at constant driving pressure, and gradual inflation of a pre-existing crack. For both models, we find that plastic deformation surrounding the fracture tip enhances dyke opening, and thus increases the energy input into the system due to pressure work integrated over the fracture wall. At the same time, energy is dissipated by plastic deformation. Dissipation in the propagation model is greater by about an order of magnitude than it is in the inflation model because the propagating dyke tip leaves behind it a broad halo of deformation due to plastic bending and unbending in the relict process zone. The net effect is that plastic deformation impedes dyke growth in the propagation model, while it enhances dyke growth in the inflation model. The results show that, when the plastic failure zone is large, a single parameter such as fracture toughness is unable to capture the physics that underpin the resistance of a fracture or dyke against propagation. In these cases, plastic failure has to be modelled explicitly for the given conditions. We provide analytical approximations for the propagation forces and the maximum dyke aperture for the two endmember cases, that is, the propagating dyke and the dyke formed by inflation of a crack. Furthermore, we show that the effect of plasticity on dyke energetics, together with an overestimate of magma pressure when interpreting dyke aspect ratios using elastic host rock models, offers a possible explanation for the long-standing paradox that laboratory measurements of fracture toughness of rocks consistently indicate values about two orders of magnitude lower than those derived from dyke observations.
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