manus_continuum_granular1

manuscript files for first continuum-till paper
git clone git://src.adamsgaard.dk/manus_continuum_granular1
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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:
MBIBnew.bib | 13+++++++++++++
Mcontinuum-granular-manuscript1.tex | 11+++++++++++
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}