Application of a probabilistic model of rainfall-induced shallow landslides to complex hollows

Recently, D'Odorico and Fagherazzi (2003) proposed "A probabilistic model of rainfall-triggered shallow landslides in hollows" (Water Resour. Res., 39, 2003). Their model describes the long-term evolution of colluvial deposits through a probabilistic soil mass balance at a point. Further building blocks of the model are: an infinite-slope stability analysis; a steady-state kinematic wave model (KW) of hollow groundwater hydrology; and a statistical model relating intensity, duration, and frequency of extreme precipitation. Here we extend the work of D'Odorico and Fagherazzi (2003) by incorporating a more realistic description of hollow hydrology (hillslope storage Boussinesq model, HSB) such that this model can also be applied to more gentle slopes and hollows with different plan shapes. We show that results obtained using the KW and HSB models are significantly different as in the KW model the diffusion term is ignored. We generalize our results by examining the stability of several hollow types with different plan shapes (different convergence degree). For each hollow type, the minimum value of the landslide-triggering saturated depth corresponding to the triggering precipitation (critical recharge rate) is computed for steep and gentle hollows. Long term analysis of shallow landslides by the presented model illustrates that all hollows show a quite different behavior from the stability view point. In hollows with more convergence, landslide occurrence is limited by the supply of deposits (supply limited regime) or rainfall events (event limited regime) while hollows with low convergence degree are unconditionally stable regardless of the soil thickness or rainfall intensity. Overall, our results show that in addition to the effect of slope angle, plan shape (convergence degree) also controls the subsurface flow and this process affects the probability distribution of landslide occurrence in different hollows. Finally, we conclude that incorporating a more realistic description of hollow hydrology (instead of the KW model) in landslide probability models is necessary, especially for hollows with high convergence degree which are more susceptible to landsliding.