commit c302d2c9abe63ca642d8c82fecf931973746e05a
parent f956269266b08d86a1c8061f7c5717cecd257da8
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Tue, 3 Dec 2019 15:43:16 +0100
Reorder SI figures, improve results presentation
Diffstat:
2 files changed, 19 insertions(+), 22 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -254,6 +254,8 @@ Under the stress-controlled conditions the till flux peaks during rapid slip as
In the rate-controlled configuration (Fig.~\ref{fig:stick_slip}b), the shear stress varies as effective normal stress oscillates, as expected from a Mohr-Coulomb material.
As in the stress-controlled configuration, deformation propagates into the bed as effective normal stress increases at the top.
Contrary to the stress-controlled setup, the till flux is under rate-controlled shear largest during deep deformation events, which occur when the ice-bed water pressure is at its minimum value.
+We find that pulse perturbations of various shape in water pressure are also able to cause deep deformation (Fig.~S1).
+The maximum deformation depth increases with increasing perturbation amplitude, with a temporal lag governed by pressure diffusion.
\begin{figure}[htbp]
\begin{center}
@@ -283,18 +285,13 @@ On the other hand, under rate-controlled conditions the majority of sediment flu
\end{center}
\end{figure*}
-Strong water pressure decrease at the ice-bed interface can cause reversal of the effective normal stress at some depth beneath the ice-bed interface (Fig.~\ref{fig:stick_slip_depth}).
-The depth of maximum shear-strain rate corresponds to the depth of minimum in effective normal stress.
-Figure~\ref{fig:stick_slip_depth} shows a time-stacked series of simulation state with depth.
-The experimental setup is rate-controlled and identical to Fig.~\ref{fig:stick_slip}b and~\ref{fig:hysteresis}b.
-The water pressure perturbations decay exponentially with depth with a phase shift.
-Deep deformation occurs when the effective normal stress is smaller at depth than at the top.
+Figure~\ref{fig:stick_slip_depth} shows depth variations through a day of simulation time, which corresponds to a single wavelength of water-pressure forcing.
+The effective normal stress generally increases with depth according to the difference in grain and fluid density.
+However, water pressure variations at the ice-bed interface can reverse this depth trend.
+Granular failure generally occurs where effective normal stress is at its minimum, as long as there is enough space to accomodate shear zone size.
+Due to diffusion, water pressure perturbations decay exponentially with depth and travel with a phase shift.
-We next perturb the top water pressure with pulses of triangular and square shape (Fig.~\ref{fig:pulse}).
-Regardless of perturbation shape, the maximum deformation depth increases with increasing perturbation amplitude.
-
-Figure~S1 contains a systematic analysis of parameter influence in the model equations.
-All experiments are at a shear rate of 300 m a$^{-1}$ and a normal stress of $\sigma_\mathrm{n}'$ = 100 kPa.
+Figure~S2 contains a systematic analysis of parameter influence in the model equations.
Several observations emerge from this parameter sensitivity analysis.
The representative grain size $d$ has a major influence on the strain distribution, where finer materials show deeper deformation.
The material is slightly weaker with larger grain sizes.
diff --git a/si.tex b/si.tex
@@ -428,17 +428,6 @@ In rate-\emph{limited} experiments, the iterative procedure is only performed fo
\begin{figure}[htbp]
\begin{center}
- \includegraphics[width=15cm]{experiments/fig-parameter_test.pdf}
- \caption{\label{fig:parameter_test}%
- Analysis of parameter influence on steady-state strain distribution and bulk friction during shear.
- All experiments are performed under constant shear rate of 300 m a$^{-1}$ and a normal stress of $\sigma_\mathrm{n}'$ = 100 kPa.
- Parameter values marked with an asterisk (*) are used outside of the individual parameter sensitivity tests.
- }
- \end{center}
-\end{figure}
-
-\begin{figure}[htbp]
- \begin{center}
\includegraphics[width=0.49\textwidth]{experiments/fig-pulse_triangle.pdf}
\includegraphics[width=0.49\textwidth]{experiments/fig-pulse_square.pdf}
\caption{\label{fig:pulse}%
@@ -451,6 +440,17 @@ In rate-\emph{limited} experiments, the iterative procedure is only performed fo
\begin{figure}[htbp]
\begin{center}
+ \includegraphics[width=15cm]{experiments/fig-parameter_test.pdf}
+ \caption{\label{fig:parameter_test}%
+ Analysis of parameter influence on steady-state strain distribution and bulk friction during shear.
+ All experiments are performed under constant shear rate of 300 m a$^{-1}$ and a normal stress of $\sigma_\mathrm{n}'$ = 100 kPa.
+ Parameter values marked with an asterisk (*) are used outside of the individual parameter sensitivity tests.
+ }
+ \end{center}
+\end{figure}
+
+\begin{figure}[htbp]
+ \begin{center}
\includegraphics[width=7.5cm]{experiments/fig-skin_depth.pdf}
\caption{\label{fig:skin_depth}%
Skin depth of pore-pressure fluctuations (Eq.~\ref{eq:skin_depth}) with forcing frequencies ranging from yearly to hourly periods.
