commit 4fc3c4fee99da069042e9cac219bc5cb2222bfb7
parent d11cc47f2f2165b487410373ee5cc7876cafddbb
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Mon, 8 Jul 2019 13:34:53 +0200
Update figures to reflect 1d_fd_simple_shear update
Diffstat:
7 files changed, 3 insertions(+), 4 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -56,8 +56,8 @@ We show that past pulses in water pressure can transfer shear away from the ice-
\subsection{Granular flow}%
\label{sub:granular_flow}
-We expand a steady-state continuum model for granular flow by \citet{Henann2013} with a coupling to pore-pressure diffusion.
-The sediment deforms as a highly nonlinear Bingham material with yield beyond the Mohr-Coulomb failure limit for a cohesionless material.
+We expand a steady-state continuum model for granular flow by \citet{Henann2013} with material cohesion and a coupling to pore-pressure diffusion.
+The sediment deforms as a highly nonlinear Bingham material with yield beyond the Mohr-Coulomb failure limit.
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,
@@ -66,12 +66,11 @@ We assume that the elasticity is negligible and set the total shear rate $\dot{\
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.
-We expand the fluidity term in \citet{Henann2013} to account for material cohesion.
The local fluidity is defined as:
\begin{equation}
g_\text{local}(\mu, \sigma_\text{n}') =
\begin{cases}
- \sqrt{d^2 \sigma_\text{n}' / \rho_\text{s}} ((\mu - C/\sigma_\text{n}' - \mu_\text{s})/(b\mu) &\text{if } \mu - C/\sigma_\text{n}') > \mu_\text{s} \text{, and}\\
+ \sqrt{d^2 \sigma_\text{n}' / \rho_\text{s}} ((\mu - C/\sigma_\text{n}') - \mu_\text{s})/(b\mu) &\text{if } \mu - C/\sigma_\text{n}' > \mu_\text{s} \text{, and}\\
0 &\text{if } \mu - C/\sigma_\text{n}' \leq \mu_\text{s}.
\end{cases}
\label{eq:g_local}
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diff --git a/experiments/fig6.pdf b/experiments/fig6.pdf
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