commit 33b45ecbfa70b2cba4b9a06306414cb625a45154
parent 574096d99e66aa06c735706ec9fc6504c57c2014
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Mon, 24 Jun 2019 13:40:50 +0200
Clean up methods text
Diffstat:
1 file changed, 2 insertions(+), 3 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -87,17 +87,16 @@ where
\label{eq:cooperativity}
\end{equation}
-Unlike \citet{Pailha2009} we do not implicitly prescribe the viscous drag during dilation and equation, and instead solve for the fluid pressure.
-
\subsection{Fluid-pressure evolution}%
\label{sub:fluid_pressure_evolution}
-The transient evolution of pore-fluid pressure ($p_\text{f}$) is governed by Darcian pressure diffusion \citep[e.g.]{Goren2010, Goren2011, Damsgaard2017}:
+We prescribe the transient evolution of pore-fluid pressure ($p_\text{f}$) by Darcian pressure diffusion \citep[e.g.][]{Goren2010, Goren2011, Damsgaard2017}:
\begin{equation}
\frac{\partial p_\text{f}}{\partial t} = \frac{1}{\phi\mu_\text{f}\beta_\text{f}} \nabla \cdot (k \nabla p_\text{f})
\label{eq:p_f}
\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}).
\subsection{Numerical solution procedure}%
\label{sub:numerical_solution_procedure}