Catastrophic flank collapses have occurred at many stratovolcanoes worldwid
e. We present a three-dimensional (3-D) slope stability analysis for assess
ing and quantifying both the locations of minimum edifice stability and the
expected volumes of potential failure. Our approach can search the materia
ls underlying a topographic surface, represented as a digital elevation mod
el (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, por
e 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 o
f the least stable potential failure. For large failures in complex topogra
phy, patterns of potential instability do not mimic local ground surface sl
ope alone. The May 18, 1980, catastrophic failure of the north flank of Mou
nt 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 con
ducted in a precollapse hazard analysis, our method identified the northwes
t 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 bu
lge and combined pore pressure and earthquake shaking effects, we obtained
good estimates of the actual failure location and volume. Our method can pr
ovide estimates of initial failure volume and location to aid in assessing
downslope or downstream hazards.