Soil creep facilitated by cyclic variations of environmental conditions

Abstract

Sloped terrains tend to creep downward over time, even when their slope is below the nominal angle of repose. This behavior can result from periodic variations in environmental conditions, such as daily or seasonal fluctuations in temperature and humidity. We study this process by considering a model of an athermal yield stress material under an applied stress lower than the critical yield stress value $\sigma_c$. Normally, in such a situation the material does not flow at all. However, under cyclic temporal variation of system parameters a finite amount of irreversible deformation can remain after each cycle, and a long term steady-state flow of the whole system can be induced. In our model, we cycle the strength of internal elastic interactions to mimic the effect of cyclic variation of environmental conditions in the real soils. We find that the amount of deformation per cycle increases if $\sigma_c$ is approached from below, and it decreases and even vanishes at a novel critical stress $\sigma_0<\sigma_c$ when this, in turn, is reached from above. Interestingly, $\sigma_0$ plays a role similar to the endurance limit in the context of fatigue damage propagation. Despite the model's simplicity, our results offer a fresh perspective on subcritical landform evolution, with implications for the creep of hill slopes over long periods and the precursors to runaway landslides.