commit 42bf9843466496adbefb06de4726d4138671d3eb
parent daab23d5708c7d6756eee417834df7c338510e01
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Thu, 10 Oct 2019 19:01:03 +0200
Add analysis of pulse perturbations
Diffstat:
1 file changed, 4 insertions(+), 3 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -506,7 +506,8 @@ Deep deformation occurs when top water pressure is at a minimum, and the effecti
\end{figure}
We next perturb the top water pressure with pulses of triangular and square shape (Fig.~\ref{fig:pulse}).
-\textbf{ANALYSIS OF AMPLITUDE EFFECT}
+Regardless of perturbation shape, the maximum deformation depth increases with increasing perturbation amplitude.
+The response in maximum deformation depth is non-linear for triangular perturbations, and linear with square perturbations.
\section{Discussion}%
@@ -535,8 +536,7 @@ As long as fluid and diffusion properties are constant, an analytical solution t
\end{linenomath*}
where $D$ is the hydraulic diffusivity [m$^2$/s] and $P$ [s] is the period of the oscillations.
The remaining terms were previously defined.
-The relation implies that the amplitude in water-pressure forcing does not influence the maximum depth of slip.
-However, the forcing amplitude determines if pressure anomalies at depth are sufficiently large to facilitate shear.
+Unrelated to skin depth, the forcing amplitude determines if pressure anomalies at depth are sufficiently large to facilitate shear (Fig.~\ref{fig:pulse}).
Figure~\ref{fig:skin_depth} shows the skin depth for water under a range of permeabilities and forcing frequencies.
The stick-slip experiments (Fig.~\ref{fig:stick_slip}) correspond to a skin depth of 2.2 meter.
Practically all of the shear strain through a perturbation cycle occurs above the skin depth (magenta line in Fig.~\ref{fig:stick_slip_depth}).
@@ -570,6 +570,7 @@ The rate dependence is only significant as kinematics approach a landslike-like
A simple shear experimental setup is adapted for analyzing the mechanical response under different stresses and water-pressure variations.
With cyclical water-pressure variations at the ice-bed interface, deep deformation occurs when remnant high water pressures at depth overcome the lithostatic gradient.
Deep deformation may be common in coarse-grained subglacial tills with strong annual water-pressure differences.
+Similarly, sudden water-pressure pulses are powerful drivers for single events of deep deformation.
\section*{Appendix}%
