A computer model for the movement of gravity flows calculates the velocities and simulated flow paths over digital topographic models. The nonuniform flow movements are determined from initial conditions, gravitational accelerations, and resistance to motion (tr) described by the general equation τr = α0 + α1ν + α2ν2, where ν is velocity. Although empirical, the terms α0, α1 and α2 may be related to Coulomb, viscous, and turbulent resistance, respectively. The energy-line model is used by setting α0 proportional to a coefficient of friction and setting α1 and α2 to zero. Use of the terms α0 and α1 results in a Bingham-like model. The models were tested against the reported velocities and distributions of the pyroclastic flows, rockslide-avalanche, lahars, and blast of the 1980 eruptions of Mount St. Helens, Washington. The energy-line model, which has been widely used for this type of effort, generally predicts velocities that are too high, resulting in flow paths that are not sufficiently responsive to the topography. Use of the α1 or α2 term usually results in better matches to the observed velocities and flow paths. An August 7th pyroclastic flow was modeled in detail for comparison with the velocities acquired from a timed sequence of photographs. Both the energy-line model and a Bingham model based on measured rheologic properties result in model velocities that are much too high. The Reynolds and Bingham numbers indicate that local turbulence was likely, which is consistent with the presence of plane-parallel and cross-bedded deposits on the steep northern flanks of Mount St. Helens. Addition of turbulent resistance to the Bingham model results in a much better match to the measured velocities. A similar model best matches the distribution of deposits from the more voluminous May 18th pyroclastic flows. Our best result for the rockslide-avalanche in the North Fork Toutle River is a Bingham model with a viscosity of 3 × 104 Pa s and a yield strength of 104 Pa. For the lahars, viscous models gives the best results, but model viscosities range from 103-104 Pa s near the flanks of the volcano and in relatively dry creeks and canyons to 101-102 Pa s where the lahars entered river channels and were significantly diluted. For the blast, each of the three basic types of resistance models compares reasonably well with the observed distribution and velocities, provided the resistance is small. However, the expected resistances from both boundary-layer turbulence and air drag are substantial; in order to account for the blast's travel distance of 20-30 km, some process in addition to the initial momentum and gravity must have operated, such as continued decompression far from the vent.
ASJC Scopus subject areas
- Geochemistry and Petrology