Intermittent slipping of landslide regulated by dilatancy evolution and velocity-weakening friction law: an efficient numerical scheme

When a block of dense sandy soil moves downhill, the shear-induced soil dilatancy along the basal shear boundary produces a negative value of excess pore pressure that increases the basal frictional resistance. Dilatancy angle, Ψ, the degree to which the basal soil dilates due to the shear, normally evolves during slope failure. A study by other researchers shows that if Ψ is constant, the block of dense soil will remain stable (or unstable) sliding when the velocity-weakening rate of the basal friction coefficient of the block is small (or large) enough. Moreover, during unstable sliding processes, the block of dense soil exhibits “periodic” patterns of intermittent slipping. Here, we used a more efficient and accurate numerical scheme to revisit that study. We expanded their model by assuming Ψ evolves during slope failure. Consequently, we acquired completely different results. For instance, even though the velocity-weakening rate of the friction coefficient is fixed at the same smaller (or larger) value that those researchers use, the stable (or unstable) steady states of landslide they predict will inversely change to unstable (or stable) when Ψ decreases (or increases) with the increase of slide displacement to a value small (or large) enough. Particularly, in unstable processes, the soil block exhibits “aperiodic” styles of intermittent slipping, instead of “periodic”. We found out that the stick states appearing later last longer (or shorter) in the case of decreasing (or increasing) Ψ. Moreover, because the basic states of landslides with impacts of dilatancy evolution are not steady nor periodic, traditional stability-analysis methods cannot be “directly” used to analyze the stability of such landslides. Here, we broke through this technical problem to a degree. We showed that combining a concept called “quasi-steady-state approximation” with a traditional stability-analysis technique can qualitatively predict the instability onset of the landslides. Through this study, we demonstrated that the combination of Chebyshev collocation (CC) and 4th-order Runge-Kutta methods is more accurate and efficient than the numerical scheme those researchers use.