manus_continuum_granular1

manuscript files for first continuum-till paper
git clone git://src.adamsgaard.dk/manus_continuum_granular1
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commit 90ed5d47b7711f1eb3d55ba5d5d1cc187e90a7fe
parent 26a64704be49a1cd97144d3bfe3ddfe9096b9700
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Thu,  7 Nov 2019 12:28:59 +0100

Small grammar fixes in intro

Diffstat:
Mcontinuum-granular-manuscript1.tex | 13+++++++------
1 file changed, 7 insertions(+), 6 deletions(-)

diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex @@ -72,19 +72,19 @@ The dynamic interplay of ice, water, and sediment is important for glacier and i \citet{Boulton1979} presented the pioneering idea that sedimentary beds and hydrological processes can significantly influence glacier and ice-sheet flow and stability. This discovery sparked interest in understanding the associated sediment physics. \citet{Boulton1987} argued that a viscous rheological model with mild stress non-linearity appropriately described their in-situ observations of a deforming bed. -The viscous rheology implies that stress required to deform the till is strongly dependent on how fast it is deformed. +A viscous rheology implies that the stress required to deform the till is strongly dependent on how fast it is deformed. Secondly, viscous materials have no upper bound to their strength with increasing strain rates. However, this result was hard to reproduce. \citet{Kamb1991}, \citet{Iverson1998}, and \citet{Tulaczyk2000} demonstrated from laboratory shear tests that rate-independent Mohr-Coulomb plasticity, as common for sedimentary materials, is a far better rheological description for subglacial till. -Mohr-Coulomb plastic materials have a yield strength that linearly scales with effective stress. +Mohr-Coulomb plastic materials have a yield strength that linearly scales with effective stress, regardless of strain rate. \citet{Iverson2010} reviewed possible viscous contributions during till-water deformation, but deemed them to be of minor importance. -In spite of a vaning observational basis, viscous rheologies continued to be applied as they allow for mathematical modeling of till advection. +In spite of a vaning observational basis, viscous rheologies continued to be applied as they allow for mathematical modeling of till advection under glaciers. Tills with viscous rheology were used to explain coupled ice-bed processes including subglacial sediment transport \citep[e.g.,][]{Jenson1995}, landform formation \citep[e.g.,][]{Hindmarsh1999, Fowler2000}, localization of water drainage \citep[e.g.,][]{Walder1994, Ng2000b}, and ice-sheet behavior in a changing climate \citep[e.g.,][]{Pollard2009}. Meanwhile, the Mohr-Coulomb plastic model continued to gain mounting empirical support from further laboratory testing \citep[e.g.,][]{Rathbun2008, Iverson2015}, as well as field observations on mountain glaciers \citep[e.g.,][]{Hooke1997, Truffer2006, Iverson2007} and ice sheets \citep[e.g.,][]{Tulaczyk2006, Gillet-Chaulet2016, Minchew2016}. Inconveniently, the plastic rheology caused a deadlock for the typical continuum modeling of ice and till, as the Mohr-Coulomb constitutive model offers no direct relation between stress and strain rate. \citet{Schoof2006} and \citet{Bueler2009} showed that Mohr-Coulomb friction can be included in ice-sheet models through mathematical reguralization. \citet{Ritz2015} demonstrated that the type of basal friction is highly influential for future Antarctic contributions to global-mean sea level rise. -However, the deformable bed is assumed to be devoid of reshaping through erosion, transport, and deposition as there exists no appropriate formulation for modeling strain in subglacial till and associated advective transport. +However, the methods allowing plastic beds in ice-flow models offer no treatment of sediment erosion, transport, and deposition as there exists no appropriate formulation for modeling strain in subglacial till and associated advective transport. \citet{Damsgaard2013} and \citet{Damsgaard2016} demonstrated that strain distribution and plasticity can be modeled in water-saturated tills by explicitly considering each sediment grain. Unfortunately, intense computational requirements associated with the grain-scale modeling entirely outrule model applicability for coupled ice-till simulations. @@ -92,13 +92,14 @@ Instead, simulation of landform to ice-sheet scale requires continuum models. In this study we build on continuum-modeling advances in granular mechanics and produce a model appropriate for water-saturated sediment deformation in the subglacial environment. The original model by \citet{Henann2013} is developed for critical state deformation of dry and cohesionless granular materials. However, subglacial tills are water saturated and often contain a certain amount of cohesion that generally increases with clay content \citep[e.g.,][]{Iverson1997}. -We extend the \citet{Henann2013} model by including sediment-strength contributions from cohesion and effective stress variations from pore-pressure diffusion. +We extend the \citet{Henann2013} model by including pore-pressure diffusion and add strength contributions from cohesion. The resultant model contributes the methodological basis required for understanding the coupled dynamics of ice flow over deformable beds. Different from previous continuum models for till, our model remains true to rheological properties observed in laboratory and field settings. In the following, we present the \citet{Henann2013} model and our modifications for modeling water-saturated subglacial till. We discuss its applicability and technical limitations before comparing the simulated sediment behavior to published results from laboratory experiments on tills. -The model produces stick-slip dynamics under variable water pressures, and remnants of pressure deviations within the modeled glacier bed constribute hysteresis to stress and strain. +The model produces stick-slip dynamics under variable water pressures. +Remnants of pressure deviations within the glacier bed provide hysteresis to stress and strain histories. In particular, the model demonstrates its ability to produce deformation deep away from the ice-bed interface, as occasionally observed in field settings \citep{Truffer2000, Kjaer2006}. The model source code is constructed with minimal external dependencies, is freely available, and is straight-forward to couple to models of ice-sheet dynamics and glacier hydrology.