A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis
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Abstract
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, m, 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, vs. 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 ∇⋅vs. Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to m−meq, where meq is the value of m 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 m−meq 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 m. A companion paper presents a suite of model predictions and tests.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis |
| Series title | Proceedings of the Royal Society A |
| DOI | 10.1098/rspa.2013.0819 |
| Volume | 471 |
| Issue | 2170 |
| Publication Date | October 08, 2014 |
| Year Published | 2014 |
| Language | English |
| Publisher | The Royal Society |
| Contributing office(s) | Volcano Hazards Program, Volcano Science Center |
| Description | 31 p. |
| Online Only (Y/N) | N |
| Additional Online Files (Y/N) | N |