Effects of the foot evolution on the behaviour of slow-moving landslides A. Ferrari a,b , A. Ledesma c, ⁎, D.A. González c , J. Corominas c a Laboratory of Soil Mechanics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland b Formerly Technical University of Catalonia, UPC, Spain c Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, UPC, Jordi Girona 1-3, D-2 Building E-08034 Barcelona, Spain abstract article info Article history: Received 19 January 2010 Received in revised form 3 November 2010 Accepted 7 November 2010 Available online 20 November 2010 Keywords: Translational slide Block model Toe erosion Motion analysis Viscosity The paper presents a time-dependent 2D numerical model which has been developed with the purpose of highlighting the effects of the slope foot evolution on the behaviour of slow-moving landslides. The model allows to quantitatively analyse how foot mass variations can influence the stability and the movement rates of the landslide. The landslide body is modelled as composed of two rigid blocks sliding on two different planes and interacting through a common boundary, which position is assumed fixed during the analysis. A finite difference approach is used to discretize the time. For each time increment, changes in model parameters are allowed, including variations in shearing resistances, groundwater level and block masses (in order to simulate foot erosion). During each iteration, the overall stability of the system is checked computing the safety factor, assuming that the percentage of mobilized shear strength is the same for the three surfaces. If the system is not stable or if it is not at rest, the velocity of the system is computed solving the momentum equations for the two blocks taking into account destabilising and resisting forces, the mechanical interaction between the blocks and viscous components. Computed velocities are iteratively used to compute mass accumulation at the foot, which in turn results in a change of the stability condition of the system. Examples are provided in order to highlight the roles of the model parameters. Finally, the application to a real landslide (Vallcebre, Spain) is presented which shows the advantage of considering the foot mass in the analysis of the displacement trends and the possibility to take into account the foot erosion in the long-term behaviour of the slope. © 2010 Elsevier B.V. All rights reserved. 1. Introduction The ability to predict accelerations and the long-term behaviour for slow-moving landslides is a crucial requirement in the hazard management process and, in particular, in the establishment of early warning systems. Variation of pore water pressure within the slope is frequently recognized as the main cause for accelerations to occur and quantitative relationships among groundwater level and landslide velocity are pursued. However, most of the traditional analyses of landslides refer to failure under static or quasistatic conditions and landslide motion is seldom considered in engineering practice. This is probably due to the complexity of the dynamics of a mass movement. Several models have been developed for the analysis of rapid mass propagation (e.g. debris flows) that simulate the slide as a fluidised mass of soil and allow to consider the time variables of the landslide by adopting usually a fluid mechanics approach (i.e., Hungr, 1995, Pastor et al., 2002). When the sliding mass keeps its basic shape, the analysis is much simpler and the motion of a rigid block can be simulated using a single dynamic equation. The initial model was proposed by Heim (1932), but there are many recent examples involving further developments: a viscous term was incorporated by Angeli et al. (1996) and Corominas et al. (2005), and also an interaction between two blocks was considered in a particular case by Alonso and Gens (2006). In fact, the idealization of a landslide as a set of several interacting blocks was proposed by Picarelli et al (2004) and seems to be a promising modelling strategy. Obviously this type of numerical models can provide realistic predictions only if the involved physical processes are correctly taken into account and distinctive features are well reproduced, such as the evolution of the sliding masses. To this regard, the paper presents a mechanical model that has been set up to analyze the effects of the slope foot evolution on the behaviour of slow-moving landslides. The model applies for translational land- slides in which the slip surface presents a simple geometry and the sliding mass can be treated as composed of two interacting blocks sliding on two different planes (Fig. 1). The balance of momentum for each block is considered including viscous terms. Groundwater fluctuation effects are taken into account in the momentum balances and therefore, the time evolution of the landslide can be followed in the simulation. Computed velocities are obtained as a result of the analysis at a particular time step and they are used to transfer mass between the Engineering Geology 117 (2011) 217–228 ⁎ Corresponding author. Tel.: +34 93 401 6864; fax: +34 93 401 7251. E-mail address: alberto.ledesma@upc.edu (A. Ledesma). 0013-7952/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2010.11.001 Contents lists available at ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo