Modelling shear bands in a volcanic conduit: Implications for over-pressures and extrusion-rates

Shear bands in a volcanic conduit are modelled for crystal-rich magma flow using simplified conditions to capture the fundamental behaviour of a natural system. Our simulations begin with magma crystallinity in equilibrium with an applied pressure field and isothermal conditions. The viscosity of the magma is derived using existing empirical equations and is dependent upon temperature, water content and crystallinity. From these initial conduit conditions we utilize the Finite Element Method, using axi-symmetric coordinates, to simulate shear bands via shear localisation. We use the von Mises visco-plasticity model with constant magma shear strength for a first took into the effects of plasticity. The extent of shear bands in the conduit is explored with a numerical model parameterized with values appropriate for Soufriere Hills Volcano, Montserrat, although the model is generic in nature. Our model simulates shallow (up to approximately 700 in) shear bands that occur within the upper conduit and probably govern the lava extrusion style due to shear boundaries. We also model the change in the over-pressure field within the conduit for flow with and without shear bands. The pressure change can be as large as several MPa at shallow depths in the conduit, which generates a maximum change in the pressure gradient of 10's of kPa/m. The formation of shear bands could therefore provide an alternative or additional mechanism for the inflation/deflation of the volcano flanks as measured by tilt-metres. Shear bands are found to have a significant effect upon the magma ascent rate due to shear-induced flow reducing conduit friction and altering the over-pressure in the upper conduit. Since we do not model frictional controlled slip, only plastic flow, our model calculates the minimum change in extrusion rate due to shear bands. However, extrusion rates can almost double due to the ton nation of shear bands, which may help suppress volatile loss. Due to the paucity of data and large parameter space available for the magma shear strength our model results can only allow for a qualitative comparison to a natural system at this stage. (c) 2007 Elsevier B.V. All rights reserved

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 3.2.1 (r3613)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of four major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. The current version supports parallelization through both MPI for distributed memory and OpenMP for distributed shared memory. Please see Chapter 2 for changes to the way to launch esys.escript scripts. For more info on this and other changes from previous releases see Appendix B. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 3.3.1 (r4302)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of five major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. • an inversion library. The current version supports parallelization through both MPI for distributed memory and OpenMP for distributed shared memory. In this release there are a number of small changes which are not backwards compatible. Please see Appendix B to see if your scripts will be affected. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D. For Python3 support, see Appendix E

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley. Release - 3.4.1 (r4596)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of four major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. The current version supports parallelization through both MPI for distributed memory and OpenMP for distributed shared memory. Please see Chapter 2 for changes to the way to launch esys.escript scripts. For more info on this and other changes from previous releases see Appendix B. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 3.4 (r4488)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of five major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. • an inversion library. The current version supports parallelization through both MPI for distributed memory and OpenMP for distributed shared memory. In this release there are a number of small changes which are not backwards compatible. Please see Appendix B to see if your scripts will be affected. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D. For Python3 support, see Appendix E

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 3.4.2 (r4925)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of five major components • esys.escript core library • finite element solver esys.finley (which uses fast vendor-supplied solvers or our paso linear solver library) • the meshing interface esys.pycad • a model library. • an inversion library. The current version supports parallelization through both MPI for distributed memory and OpenMP for shared memory. In this release there are a number of small changes which are not backwards compatible. Please see Appendix B to see if your scripts will be affected. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D. For Python 3 support, see Appendix E

esys-Escript User’s Guide: Solving Partial Differential Equations with Escript and Finley Release - 4.0 (r5402)

esys.escript is a python-based environment for implementing mathematical models, in particular those based on coupled, non-linear, time-dependent partial differential equations. It consists of five major components: • esys.escript core library • finite element solvers esys.finley, esys.dudley, esys.ripley, and esys.speckley (which use fast vendor-supplied solvers or the included PASO linear solver library) • the meshing interface esys.pycad • a model library • an inversion module. All esys.escript modules should work under both python 2 and python 3, see Appendix E. The current version supports parallelization through MPI for distributed memory, OpenMP for shared memory on CPUs, as well as CUDA for some GPU-based solvers. This release comes with some significant changes and new features. Please see Appendix B for a detailed list. If you use this software in your research, then we would appreciate (but do not require) a citation. Some relevant references can be found in Appendix D

Micromechanical investigation of soil plasticity using a discrete model of polygonal particles

The mechanical behavior of soils has been traditionally described using continuum-mechanics-based models. These are empirical relations based on laboratory tests of soil specimens. The investigation of the soils at the grain scale using discrete element models has become possible in recent years. These models have provided valuable understanding of many micromechanical aspects of soil deformation. The aim of this work is to draw together these two approaches in the investigation of the plastic deformation of non-cohesive soils. A simple discrete element model has been used to evaluate the effect of anisotropy, force chains, and sliding contacts on different aspects of soil plasticity: dilatancy, shear bands, ratcheting etc. The discussion of these aspects raises important questions such as the width of shear bands, the origin of the stress-dilatancy relation, and the existence of a purely elastic regime in the deformation of granular material