manus_continuum_granular1

commit 62bbbfc299f971f9a0256279820b216b676870ab
parent 49c88bd8a879487f69798fd57c98e291ea11e7f8
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Wed,  9 Oct 2019 15:11:51 +0200

Continue writing results

Diffstat:
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continuum-granular-manuscript1.tex
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12
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1 file changed, 10 insertions(+), 2 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -417,8 +417,8 @@ There is a significant strengthening when the bed thickness $L_z$ begins to cons
 \end{figure}
 
 Next we vary the top water pressure and observe the shear dynamics over a simulation time of seven days Figure~\ref{fig:stick_slip}.
-We perform tests under both stress- and rate-controlled configurations.
-The shear velocities during the first cycle ($t<1$ d) is slightly different from later cycles ($t>1$ d) since the model is initialized with a hydrostatic water-pressure distribution.
+We perform tests under both stress and rate-controlled configurations.
+The response during the first cycle ($t<1$ d) is slightly different from later cycles ($t>1$ d) since the model is initialized with a hydrostatic water-pressure distribution.
 
 \begin{figure}[htbp]
 	\begin{center}
@@ -430,6 +430,14 @@ The shear velocities during the first cycle ($t<1$ d) is slightly different from
 	\end{center}
 \end{figure}
 
+Under both stress and rate-controlled conditions, the grain/fluid system displays strong hysteresis in shear velocity and strain distribution (Fig.~\ref{fig:stick_slip_depth}).
+The granular deformation primarily occurs where the effective normal stress is the lowest value.
+When water pressure drops at the ice-bed interface, there is a remnant of high fluid-pressure diffusing downwards.
+The depth of maximum shear-strain rate follows the minimum in effective normal stress into the bed, until the effective normal stress at the top exceeds the minimum at depth.
+It is worth noting that the minima in $\sigma'_\text{n}$ need a width comparable to the shear zone thickness, due to granular non-locality.
+Otherwise the material rather deforms in a zone where the depth integral of effective normal stress is lower.
+
+
 \begin{figure*}[htbp]
 	\begin{center}
 		\includegraphics[width=15.0cm]{experiments/fig6.pdf}