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.

Recently, we presented a steady-state analytical hillslope stability model to study rain-induced shallow land-slides. This model is based on kinematic wave dynamics of saturated subsurface storage and the infinite slope stability assumption. Here we apply the model to investigate the effect of neglecting the unsaturated storage on the assessment of slope stability in the steady-state hydrology. For that purpose we extend the hydrological model to compute the soil pore pressure distribution over the entire flow domain. We also apply this model for hillslopes with non-constant soil depth to compare the stability of different hillslopes and to find the critical slip surface in hillslopes with different geometric characteristics. In order to do this, we incorporate more complex approaches to compute slope stability (Janbu's non-circular method and Bishop's simplified method) in the steady-state analytical hillslope stability model. We compare the safety factor (FS) derived from the infinite slope stability method and the more complex approach for two cases: with and without the soil moisture profile in the unsaturated zone. We apply this extended hillslope stability model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). Overall, we find that unsaturated zone storage does not play a critical role in determining the factor of safety for shallow and deep land-slides. As a result, the effect of the unsaturated zone storage on slope stability can be neglected in the steady-state hydrology and one can assume the same bulk specific weight below and above the water table. We find that steep slopes with concave profile and convergent plan shape have the least stability. We also demonstrate that in hillslopes with non-constant soil depth (possible deep landslides), the ones with convex profiles and convergent plan shapes have slip surfaces with the minimum safety factor near the outlet region. In general, when plan shape changes from divergent to convergent, stability decreases for all length profiles. Finally, we show that the applied slope stability methods and steady-state hydrology model based on the relative saturated storage can be used safely to investigate the relation between hillslope geometry and hillslope stability.