Nucleation of slip‐weakening rupture instability in landslides by localized increase of pore pressure

Abstract

[1] We model landslide initiation as slip surface growth driven by locally elevated pore pressure, with particular reference to submarine slides. Assuming an elastic medium and friction that weakens with slip, solutions exist in which the slip surface may dynamically grow, without further pore pressure increases, at a rate of the order of the sediment shear wave speed, a situation comparable to earthquake nucleation. The size of the rupture at this transition point depends weakly on the imposed pore pressure profile; however, the amount of slip at the transition depends strongly on whether the pore pressure was broadly or sharply elevated. Sharper profiles may result in pore pressures reaching the total slope-normal stress before dynamic rupture is nucleated. While we do not account for modes of failure other than pure slip on a failure surface, this may be an indication that additional modes involving liquefaction or hydraulic cracking may be factors in the initiation of shallow slope failure. We identify two length scales, one geometrical (h, depth below the free surface) and one material (', determined by the frictional weakening rate) and a transition in nucleation behavior between effectively "deep" and "shallow" limits dependent on their ratio. Whether dynamic propagation of failure is indefinite or arresting depends largely on whether the background shear stress is closer to nominal peak or residual frictional strength. This is determined in part by background pore pressures, and to consider the submarine case we simplify a common sedimentation/consolidation approach to reflect interest in near-seafloor conditions. Citation: Viesca, R. C., and J. R. Rice (2012), Nucleation of slip-weakening rupture instability in landslides by localized increase of pore pressure,

Rate-weakening friction characterizes both slow sliding and catastrophic failure of landslides

“…However, elastic deformation can be significant for small displacement and strain over short timescales. Several studies have accounted for these effects to quantify key features of landslides, including landslide depth (17) and incipient motion (15,16). Because our model simulations describe small displacements and gradients in slip rate over short distances, the incorporation of elastic effects is both reasonable and appropriate.…”

“…One potential scenario involves a decrease in the characteristic slip distance d c for the evolution of frictional contacts as a result of shear localization (35,37), which in turn decreases h * relative to L. Alternatively, we hypothesize that the spatial dimensions of the landslide, or slip patch, may evolve in time until L > h * . Landslides tend to grow until they span from hilltops to channel bottoms (16,37,38). Furthermore, landslides can display distinct kinematic elements that are defined empirically by differences in the timing of motion along the landslide body (39).…”

“…3 to account for changes in shear and normal stress that arise from slip near a free surface (see equations 21-25 in ref. 16). Studies that have incorporated the free surface into their model simulations in other contexts have found that these effects produce fairly minor differences in the overall model predictions (12,16).…”

“…16). Studies that have incorporated the free surface into their model simulations in other contexts have found that these effects produce fairly minor differences in the overall model predictions (12,16). Similar to the results of these studies, our preliminary calculations with a more computationally challenging elastic formulation that imposes stress-free boundary conditions at the free surface result in changes to the predicted behavior that are of secondary importance to the overall displacement patterns that are our focus here.…”

“…a free surface). Although it is generally accepted that the weathered rock and soil that overlies the landslide slip surface does not behave elastically over long timescales or for large displacements, elastic deformation can be significant for small displacement and strain over short timescales (i.e., transient motion) (15)(16)(17).…”