commit ded858fb3e946b140ae036f79887dc573711a9f2
parent 3c0e8142b468e46540cac0f83edbbfa2399700ba
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Wed, 26 Jun 2019 15:54:13 +0200
Add section on simulation setup
Diffstat:
2 files changed, 24 insertions(+), 0 deletions(-)
diff --git a/BIBnew.bib b/BIBnew.bib
@@ -8825,3 +8825,16 @@ Winton and A. T. Wittenberg and F. Zeng and R. Zhang and J. P. Dunne},
author = {D. L. Turcotte and G. Schubert},
title = {Geodynamics},
}
+
+@article{Henann2016,
+ doi = {10.1002/nme.5213},
+ year = 2016,
+ month = {feb},
+ publisher = {Wiley},
+ volume = {108},
+ number = {4},
+ pages = {273--302},
+ author = {D. L. Henann and K. Kamrin},
+ title = {A finite element implementation of the nonlocal granular rheology},
+ journal = {Int. J. Num. Meth. Eng.}
+}
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -144,9 +144,18 @@ We then use Jacobian iterations to find an implicit solution to the same equatio
For the final pressure field at $t + \Delta t$ we mix the explicit and implicit solutions with equal weight, which is known as the Crank-Nicholson method \citep[e.g.][]{Patankar1980, Ferziger2002, Press2007}.
The method is unconditionally stable and second-order accurate in time and space.
+\subsection{Simulation setup}
+The spatial domain is two meters long and is discretized into 50 cells.
+We use a representative grain size of 0.04 m, a grain material density of 2600 kg/m$^3$, a porosity of 0.25, and a Coulomb-friction coefficient of 0.37.
+Dimensionless material parameters $A$ and $b$ from Eq.~\ref{eq:g_local} and~\ref{eq:cooperativity} are 0.4 and 0.9377, respectively.
+These values are commonly reported on glass beads \citep{Damsgaard2013, Henann2016}.
+
+For the first experiment with variable water pressure, we apply a water-pressure forcing amplitude of 50 kPa that modulates effective stress at the top around 100 kPa (Fig.~\ref{fig:stick_slip}).
+
\section{Results}%
\label{sec:results}
+
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=7.5cm]{experiments/fig1.pdf}
@@ -211,6 +220,8 @@ As long as fluid and diffusion properties are constant,
\label{eq:skin_depth}
\end{equation}
The above relation implies that the amplitude in water-pressure forcing does not influence the maximum depth of slip.
+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} to~\ref{fig:stick_slip_depth_normalized}) correspond to a skin depth of 2.2 meter.
\section{Conclusion}%
\label{sec:conclusion}