A rate- and state-dependent friction model to describe the seasonal motion of slow-moving earthflows and quantify their potential for catastrophic failure

Abstract:

Slow-moving earthflows regularly exhibit seasonal velocity patterns driven by transient perturbations in effective normal stress that alter the frictional resistance along the sliding surface. These annual velocity patterns are ubiquitous in slow-moving landslides throughout the world, with individual landslides often displaying complex spatial patterns of acceleration that can vary from year to year. Here, we model landslide motion using a rate- and state-dependent frictional treatment that incorporates variations in effective normal stress and material properties, including both velocity-weakening (VW) and velocity-strengthening (VS) patches, along the sliding surface. We calculate changes in effective stress by allowing rainfall-induced changes in pore-water pressure to diffuse vertically from the ground surface to the landslide base. We then solve for changes in frictional strength and velocity along a 1D slip surface that extends the length of the landslide. Model parameters are calibrated using measurements from laboratory tests, field instruments, and satellite InSAR. Our model is able to produce seasonal variations in sliding rate that mimic the patterns commonly displayed by these slope failures. We use our model to identify the conditions under which these slides can transition from non-catastrophic motion to catastrophic failure. We find that non-catastrophic motion occurs if the landslides are comprised of entirely VS material or if their spatial dimensions do not exceed a critical nucleation length, which is determined by the ratio of VW to VS material and the effective stress. Furthermore, this modeling framework suggests that landslides that exhibit spatially varying motion (i.e. consisting of an ensemble of smaller slip patches) may be less likely to fail catastrophically when compared to landslides that exhibit spatially uniform motion if differences in the timing of motion along the landslide reflect the presence of temporary slip barriers (i.e. strong patches). Our rate and state friction model provides a new way to view the evolution of slow-moving earthflows and to predict their behavior. Future work would benefit from additional laboratory tests on materials from a broad (i.e. worldwide) distribution of earthflows to better constrain their frictional properties.