David L. George
Richard M. Iverson
2014
<p style="text-align: left;" data-mce-style="text-align: left;"><span>To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, two-phase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid mechanics. The model's balance equations describe coupled evolution of the solid volume fraction,<span class="Apple-converted-space"> </span></span><i>m</i><span>, basal pore-fluid pressure, flow thickness and two components of flow velocity. Basal friction is evaluated using a generalized Coulomb rule, and fluid motion is evaluated in a frame of reference that translates with the velocity of the granular phase,<span class="Apple-converted-space"> </span></span><i>v</i><sub>s</sub><span>. Source terms in each of the depth-averaged balance equations account for the influence of the granular dilation rate, defined as the depth integral of ∇⋅</span><i>v</i><sub>s</sub><span>. Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to<span class="Apple-converted-space"> </span></span><i>m</i><span>−</span><i>m</i><sub>eq</sub><span>, where<span class="Apple-converted-space"> </span></span><i>m</i><sub>eq</sub><span><span class="Apple-converted-space"> </span>is the value of<span class="Apple-converted-space"> </span></span><i>m</i><span><span class="Apple-converted-space"> </span>in equilibrium with the ambient stress state and flow rate. Normalization of the model equations shows that predicted debris-flow behaviour depends principally on the initial value of<span class="Apple-converted-space"> </span></span><i>m</i><span>−</span><i>m</i><sub>eq</sub><span><span class="Apple-converted-space"> </span>and on the ratio of two fundamental timescales. One of these timescales governs downslope debris-flow motion, and the other governs pore-pressure relaxation that modifies Coulomb friction and regulates evolution of<span class="Apple-converted-space"> </span></span><i>m</i><span>. A companion paper presents a suite of model predictions and tests.</span></p>
application/pdf
10.1098/rspa.2013.0819
en
The Royal Society
A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis
article