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A probabilistic model of rainfall‐triggered shallow landslides in hollows: A long‐term analysis

The long‐term temporal evolution of soil thickness in hollows depends on the processes controlling the rates of colluvium accumulation and erosion. Accumulation is due to soil creep and mass‐wasting processes from the adjacent slopes, while erosion of colluvial deposits is mainly due to debris flow and landsliding. An analysis of the long‐term evolution of colluvial deposits is developed through a stochastic model of soil mass balance at a point accounting for colluvium infilling, expressed as a deterministic function of the deposit thickness, and soil erosion by shallow landslides, modeled as a random (Poisson) process. Landsliding is related to the characteristics of the triggering precipitation through an infinite‐slope stability analysis, a kinematic model of hollow response to rainfall, and the intensity‐duration‐frequency curves characterizing the regime of extreme precipitation. This analysis provides a probabilistic representation of the long‐term dynamics at a point of colluvium thickness as a function of the timescale of hollow infilling and of the frequency of triggering rainfalls. The model is solved both numerically and (under simplified conditions) analytically, showing the existence of different regimes in the temporal evolution of soil thickness. In the case of steep slopes (i.e., with slope angles, β, greater than the soil repose angle, ϕ) the hollow can be either in a supply‐limited state or in event‐limited conditions, depending on whether the dynamics are limited by the supply of sediment from the adjacent slopes or by the occurrence of rainstorms able to trigger landslides. Nevertheless, since the likelihood of landslide occurrence increases with increasing values of deposit thickness, colluvium accretion always leads to conditions favorable to landsliding. Vice versa, in the case of gentle slopes (i.e., β < ϕ) the probability of landsliding decreases with increasing values of soil thickness, and event‐limited conditions may evolve into unconditionally stable states.