commit 2f01a826e703dc0251dca1eddce1d3aeac8580cb
parent 5e9c0117e6b35d69e338ed89c857d718ef7fc19c
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Wed, 26 Jun 2019 15:29:00 +0200
Fix references
Diffstat:
1 file changed, 13 insertions(+), 11 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -23,7 +23,7 @@
%% Links, colors, citations
\usepackage{color}
-\usepackage{hyperref}https://www.overleaf.com/6436856223rspxdsvynfyk
+\usepackage{hyperref}
\usepackage[natbib=true, style=authoryear, bibstyle=authoryear-comp, maxbibnames=10,
maxcitenames=2, backend=bibtex8]{biblatex}
\bibliography{BIBnew.bib}
@@ -61,7 +61,7 @@ In our model, the sediment deforms as a highly nonlinear Bingham material with y
We assume that the elasticity is negligible and set the total shear rate $\dot{\gamma}$ to consist of a plastic contribution $\dot{\gamma}^\text{p}$:
\begin{equation}
\dot{\gamma} \approx \dot{\gamma}^\text{p} = g(\mu_\text{c}, \sigma_\text{n}') \mu,
- \label{eq:shear-strain-rate}
+ \label{eq:shear_strain_rate}
\end{equation}
where $\mu = \tau/\sigma_\text{n}'$ is the dimensionless ratio between shear stress ($\tau$ [Pa]) and effective normal stress ($\sigma_\text{n}' = \sigma_\text{n} - p_f$ [Pa]).
Water pressure is $p_\text{f}$ [Pa] and $g$ [s$^{-1}$] is the granular fluidity. The fluidity consists of local and non-local components.
@@ -94,7 +94,7 @@ We prescribe the transient evolution of pore-fluid pressure ($p_\text{f}$) by Da
\end{equation}
where $\mu_\text{f}$ denotes dynamic fluid viscosity [Pa s], $\beta_\text{f}$ is adiabatic fluid compressibility [Pa$^{-1}$], and $k$ is intrinsic permeability [m$^2$].
The sediment is assumed to be in the critical state throughout the domain, as in the original formulation by \citet{Henann2013}.
-The fluid pressure is used to determine the effective normal stress used in the granular flow calculations (Eq.~\ref{eq:shear-strain-rate} and~\ref{eq:g_local}).
+The fluid pressure is used to determine the effective normal stress used in the granular flow calculations (Eq.~\ref{eq:shear_strain_rate} and~\ref{eq:g_local}).
\subsection{Numerical solution procedure}%
\label{sub:numerical_solution_procedure}
@@ -160,7 +160,7 @@ The above relation implies that the amplitude in water-pressure forcing does not
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=7.5cm]{experiments/fig1.pdf}
- \caption{\label{fig:rate-dependence}%
+ \caption{\label{fig:rate_dependence}%
Influence of rate-dependence factor $b$ in Eq.~\ref{eq:g_local} on post-failure friction.
Plot limits equal to \citet{Iverson2010}.
The effective normal stress is held constant at $\sigma_\text{n}' = 100$ kPa.
@@ -171,7 +171,7 @@ The above relation implies that the amplitude in water-pressure forcing does not
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=7.5cm]{experiments/fig2.pdf}
- \caption{\label{fig:stick-slip}%
+ \caption{\label{fig:stick_slip}%
Stick-slip dynamics during sinusoidal water-pressure forcing from the top.
Stress and shear velocity are measured at the top of the sediment bed.
}
@@ -181,8 +181,8 @@ The above relation implies that the amplitude in water-pressure forcing does not
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=15.0cm]{experiments/fig3.pdf}
- \caption{\label{fig:stick-slip-depth}%
- Pore-pressure diffusion and strain distribution with depth with a sinusoidal water-pressure forcing from the top (Fig.~\ref{fig:stick-slip}).
+ \caption{\label{fig:stick_slip_depth}%
+ Pore-pressure diffusion and strain distribution with depth with a sinusoidal water-pressure forcing from the top (Fig.~\ref{fig:stick_slip}).
The forcing has a daily periodocity, and plot lines are one hour in simulation time apart.
}
\end{center}
@@ -191,8 +191,8 @@ The above relation implies that the amplitude in water-pressure forcing does not
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=15.0cm]{experiments/fig4.pdf}
- \caption{\label{fig:stick-slip-depth}%
- Pore-pressure diffusion and normalized strain distribution with depth with a sinusoidal water-pressure forcing from the top (Fig.~\ref{fig:stick-slip}).
+ \caption{\label{fig:stick_slip_depth_normalized}%
+ Pore-pressure diffusion and normalized strain distribution with depth with a sinusoidal water-pressure forcing from the top (Fig.~\ref{fig:stick_slip}).
The forcing has a daily periodocity, and plot lines are one hour in simulation time apart.
}
\end{center}
@@ -200,8 +200,10 @@ The above relation implies that the amplitude in water-pressure forcing does not
\begin{figure}[htbp]
\begin{center}
- \includegraphics[width=5.0cm]{experiments/fig5.pdf}
- \caption{\label{fig:skin-depth}%
+ \includegraphics[width=7.5cm]{experiments/fig5.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.
+ The permeability range spans commonly encountered tills \citep{Schwartz2003}.
}
\end{center}
\end{figure}
