A low-dimensional physically based model of hydrologic control of shallow landslinding on complex hillslopes
Talebi, A. ; Uijlenhoet, R. ; Troch, P.A. - \ 2008
Earth Surface Processes and Landforms 33 (2008)13. - ISSN 0197-9337 - p. 1964 - 1976.
storage boussinesq model - subsurface flow - debris flows - rainfall - slope - stability - soils
Hillslopes have complex three-dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslope-storage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three-dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr-Coulomb failure law. The resulting hillslope-storage Boussinesq stability model (HSB-SM) is able to simulate rain-induced shallow landsliding on hillslopes with non-constant bedrock slope and non-parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB-SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes
Application of a probabilistic model of rainfall-induced shallow landslides to complex hollows
Talebi, A. ; Uijlenhoet, R. ; Troch, P.A. - \ 2008
Natural Hazards and Earth System Sciences 8 (2008)4. - ISSN 1561-8633 - p. 733 - 744.
storage boussinesq model - physically-based model - slope stability model - hydrologic response - hillslope stability - subsurface flow - soil production - steep - catchment - valley
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
A steady-state analytical slope stability model for complex hillslopes
Talebi, A. ; Troch, P.A. ; Uijlenhoet, R. - \ 2008
Hydrological Processes 22 (2008)4. - ISSN 0885-6087 - p. 546 - 553.
storage boussinesq model - physically-based model - subsurface flow - scale
This paper presents a steady-state analytical hillslope stability model to study the role of topography on rain-induced shallow landslides. We combine a bivariate continuous function of the topographic surface, a steady-state hydrological model of hillslope saturated storage, and the infinite slope stability assumption to investigate the interplay between terrain characteristics, saturated storage within hillslopes and soil mechanics. We demonstrate the model by examining the stability of nine characteristic hillslope types (landform elements) with three different profile curvatures (concave, straight and convex) and three different plan shapes (convergent, parallel and divergent). For each hillslope type, the steady-state saturated storage corresponding to given recharge rates is computed for three different average bedrock slope angles. On the basis of the infinite slope stability method, the factor of safety (FS) along the hillslopes is determined. Our results demonstrate that in the steep slopes, the least stable situation occurs in hillslopes with convergent plan shapes and concave length profiles, while the convex ones are more stable. In addition to testing our method for nine characteristic hillslope types, a general relationship between plan shape and profile curvature of landform elements and the factor of safety is derived for a pre-defined hillslope length scale. Our results show that slope stability increases when profile curvature changes from concave to convex. In terms of plan shapes, changing from convergent to divergent, slope stability increases for all length profiles. However, we find that the effect of plan shape is more pronounced for convex length profiles. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan shape and profile curvature is an important control on hillslope stability.
Similarity analysis of subsurface flow response of hillslopes with complex geometry
Berne, A.D. ; Uijlenhoet, R. ; Troch, P.A.A. - \ 2005
Water Resources Research 41 (2005). - ISSN 0043-1397 - 10 p.
generating surface runoff - storage boussinesq model - hydrologic similarity - groundwater outflow - unit response - source areas - saturation - equation
The matter of the efficient and parsimonious parameterization of hillslope subsurface flow remains an important issue in catchment hydrological studies (Brutsaert, 1995). Insights into the influence of the shape and hydraulic characteristics of hillslopes is required to further our understanding and our ability to model catchment hydrological processes. Recently, Troch et al. (2003) introduced the hillslope-storage Boussinesq (HSB) equation to describe subsurface flow and saturation along geometrically complex hillslopes. The HSB equation can be linearized and further reduced to an advection-diffusion equation for subsurface flow in hillslopes with constant bedrock slopes and exponential width functions. This paper presents a dimensional analysis of the latter equation in order to study the moments of the characteristic response function (CRF), corresponding to the free drainage of this type of hillslope. These moments, in a dimensionless form, can be expressed as functions of a similarity parameter, hereafter called the hillslope Péclet number, and a group of dimensionless numbers accounting for the effects of the boundary and initial conditions. The analytical expressions for the first four central CRF moments are derived for two types of initial conditions. The analysis of their respective influences shows that the hillslope Péclet number is an efficient similarity parameter to describe the hillslope subsurface flow response. Moreover, comparison between the CRF moments predicted by means of our similarity analysis and empirical moments derived from outflow measurements for different types of laboratory hillslopes shows good agreement