A low‐dimensional physically based model of hydrologic control of shallow landsliding on complex hillslopes

Abstract

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 hillslopestorage 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.* This parameter has been calculated for a slope angle β = 15° (β/φ = 0·5). 1968A. Talebi, R. Uijlenhoet and P. A. Troch Figure 3. Variations of the safety factor on hillslopes with different plan shapes computed using the original HSB model (solid line) and the coupled HSB model (dashed line), assuming β = 0·5φ and N = 20 mm d −1 . Top panel, convergent; middle panel, parallel; bottom panel, divergent hillslope (profile curvature is constant).quickly. In contrast, in the divergent hillslopes (Figure 4, nos 3, ...

Quantification of the influence of preferential flow on slope stability using a numerical modelling approach

“…The limit equilibrium method or infinite slope stability approach is frequently integrated with Richards' equation (Lanni et al, 2013;Ng and Shi, 1998;Godt et al, 2008;Shuin et al, 2012;Wilkinson et al, 2002;Talebi et al, 2008;Greco et al, 2013) or conceptual models (Arnone et al, 2011;Simoni et al, 2008;Qiu et al, 2007) for landslide hazard evaluation. The limit equilibrium method and infinite slope approach assume or search for a potential failure surface.…”

“…Lanni et al, 2013;Lu et al, 2012). Although the underlying assumptions of the slope failure mechanism have limitations (Huang and Jia, 2009;Griffiths et al, 2011), the simplified slope stability analysis method has low computational demand and is widely used for geotechnical analyses at the slope scale (Talebi et al, 2008;Tsai and Yang, 2006;Abramson, 2002), watershed scale, and catchment scale (Borga et al, 2002a, b;Baum et al, 2010;Wilkinson et al, 2002).…”

A steady-state saturation model to determine the subsurface travel time (STT) in complex hillslopes

“…Troch et al (2003) and Talebi et al (2008b) have used the unsteady-state hsB model in their researches. The main aim of the present study is to benefit from its results for the modeling saturation zone extension in unsteady-state condition based on temporal distributions of rainfall during storms in hillslopes in future studies.…”

Seepage and slope stability modelling of rainfall-induced slope failures in topographic hollows

“…Therefore, hydro-mechanical phenomena occurring on topographic hollow are considered to be three-dimensional in nature (Dietrich et al 1987). The three-dimensional modelling programmes of dynamic hydrology and stability, like Hillslope-storage Bossinesq-Stability Model (HSB-SM) , Integrated Hydrological-Stability Model (InH-SM) (VanderKwaak 1999), and GEOtop-FS (Rigon et al 2006), have been applied to simulate hillslope hydrologic response to rainfall and instability in a few case studies, like Loague et al 2005, Talebi et al 2008a, and Simoni et al 2008. However, these programmes require not only the high amount of accurate data but also the solution of extremely large systems of equations even to analyse small instability problems .…”