MODELING LANDSLIDE AND DEBRIS-FLOW MOTION: CONFRONTING THE DIRTY LITTLE SECRET

Nearly all published models of landslide, debris-flow, and avalanche dynamics simulate onset of motion by using dam-break initial conditions. In other words, models specify a large initial force imbalance, but artificially restrain motion until the modeler issues a command. In extreme cases, models use basal friction angles <10º to simulate motion, whereas values >30º may be necessary to balance forces at steeply sloping initiation sites. Despite the lack of physical justification for this mismatch, publications commonly disregard its significance and instead gauge the predictive power of a model by whether its output can be fitted to observed distributions of deposits. This "dirty little secret" may be hidden from those outside the modeling coterie, leading to widespread misunderstanding of predictive capabilities.

In an effort to seamlessly simulate landslide and debris-flow evolution from static to dynamic states, without invoking changes in parameter values, we have developed a model that includes feedback resulting from interaction between downslope motion and evolution of porosity and pore-fluid pressure. Such feedback allows an infinitesimal force imbalance to evolve naturally toward a larger one -- or to a newly balanced state -- thereby eliminating the need to use unrealistic initial conditions or parameter values. Our depth-integrated one-dimensional model includes four coupled differential equations describing spatial and temporal evolution of the mass thickness h, depth-averaged downslope velocity v, depth-averaged solid volume fraction m, and basal pore-fluid pressure p. All of the evolution equations include terms that contain the local, depth-averaged dilation rate, D = (h/m)(dm/dt), which in turn depends on v and the evolving dilatancy angle and effective stress. At steady state the dilatancy angle is zero, D is zero, p is hydrostatic, and m is equilibrated to v and the effective stress. True steady states are unlikely to occur in nature, but our numerical results demonstrate that coevolution of h, v, m, and p can lead to stable transient states similar to those measured in reproducible experiments at the USGS debris-flow flume.