Slip-weakening zone sizes at nucleation of catastrophic subaerial and submarine landslides by gradually increasing pore pressure

We address the nucleation of dynamic landslide rupture in response to gradual pore pressure increases. Nucleation marks the onset of acceleration of the overlying slope mass due to the suddenly rapid enlargement of a sub-surface zone of shear failure, previously deforming quasi-statically. We model that zone as a planar surface undergoing initially linear slip-weakening frictional failure within a bordering linear-elastic medium. The results are also relevant to earthquake nucleation. The sub-surface rupture zone considered runs parallel to the free surface of a uniform slope, under a 2D plane-strain deformation state. We show results for ruptures with friction coefficients following linear slip weakening (i.e., the residual friction is not yet reached). For spatially broad increases in pore pressure, the nucleation length depends on a ratio of depth to a cohesive zone length scale. In the very broad-increase limit, a direct numerical solution for nucleation lengths compares well with solutions to a corresponding eigenvalue problem (similar to Uenishi and Rice [JGR '03]), in which spatial variations in normal stress are neglected. We estimate nucleation lengths for subaerial and submarine conditions using data [e.g., Bishop et al., Géotech. '71; Stark et al., JGGE '05] from ring-shear tests on sediments (peak friction f_p = 0.5, frictional slip-weakening rate within the range w = -df/d(slip) = 0.1/cm-1/cm). We assume that only pre-stresses, and not material properties, vary with depth. With such f_p and w, we find for a range of subsurface depths and shear moduli μ that nucleation lengths are typically several hundred meters long for shallow undersea slopes, and up to an order of magnitude less for steeper slopes on the Earth's surface. In the submarine case, this puts nucleation lengths in a size range comparable to observed pore-pressure-generated seafloor disturbances as pockmarks [e.g., Gay et al., MG '06].