Regulation of landslide motion by dilatancy and pore pressure feedback

[ 1] A new mathematical model clarifies how diverse styles and rates of landslide motion can result from regulation of Coulomb friction by dilation or contraction of water-saturated basal shear zones. Normalization of the model equations shows that feedback due to coupling between landslide motion, shear zone volume change, and pore pressure change depends on a single dimensionless parameter alpha, which, in turn, depends on the dilatancy angle psi and the intrinsic timescales for pore pressure generation and dissipation. If shear zone soil contracts during slope failure, then alpha < 0, and positive pore pressure feedback and runaway acceleration are inevitable. If the shear zone dilates, then alpha > 0, and negative feedback permits slow, steady landslide motion to occur while positive pore pressure is supplied by rain infiltration. Steady state slip velocities nu(0) obey nu(0) = -( K/psi) p(*e), where K is the hydraulic conductivity and p(*e) is the normalized ( dimensionless) negative pore pressure generated by dilation. If rain infiltration and attendant pore pressure growth continue unabated, however, their influence ultimately overwhelms the stabilizing influence of negative p(e)(*). Then, unbounded landslide acceleration occurs, accentuated by an instability that develops if y diminishes as landslide motion proceeds. Nonetheless, numerical solutions of the model equations show that slow, nearly steady motion of a clay-rich landslide may persist for many months as a result of negative pore pressure feedback that regulates basal Coulomb friction. Similarly stabilized motion is less likely to occur in sand-rich landslides that are characterized by weaker negative feedback.