Gravitational stability of three-dimensional stratovolcano edifices

Catastrophic flank collapses have occurred at many stratovolcanoes worldwide. We present a three-dimensional (3-D) slope stability analysis for assessing and quantifying both the locations of minimum edifice stability and the expected volumes of potential failure. Our approach can search the materials underlying a topographic surface, represented as a digital elevation model (DEM), and determine the relative stability of all parts of the edifice. Our 3-D extension of Bishop's [1955] simplified limit-equilibrium analysis incorporates spherical failure surfaces, variable material properties, pore fluid pressures, and earthquake shaking. Although a variety of processes can trigger collapse, we focus here on gravitationally induced instability. Even homogeneous rock properties strongly influence the depth and volume of the least stable potential failure. For large failures in complex topography, patterns of potential instability do not mimic local ground surface slope alone. The May 18, 1980, catastrophic failure of the north flank of Mount St. Helens provides the best documented case history to test our method. Using the undeformed edifice topography of Mount St. Helens in an analysis of dry, static slope stability with homogeneous materials, as might be conducted in a precollapse hazard analysis, our method identified the northwest flank as the least stable region, although the north flank stability was within 5% of the minimum. Using estimates of the conditions that existed 2 days prior to collapse, including deformed topography with a north flank bulge and combined pore pressure and earthquake shaking effects, we obtained good estimates of the actual failure location and volume. Our method can provide estimates of initial failure volume and location to aid in assessing downslope or downstream hazards.