Numerical modelling of the propagation of fast landslides using the finite element method

Abstract

SUMMARYThis paper proposes a two-dimensional (2D) model for the analysis of the propagation of fast landslides involving a fluidized material such as debris and mud flows, flowslides and avalanching flows. The model is based on the Navier-Stokes depth-integrated equations. To incorporate the effect of steep slopes and centrifugal forces due to the high velocities characterizing the flowslides and the bed curvature, a curvilinear system of reference is used. The corresponding equations of motion are complemented by depth-averaged constitutive equations and bed friction laws.The resulting set of differential equations are solved using the two-step Taylor-Galerkin algorithm. This algorithm has been used by the authors to solve hydraulic and dam-break problems using the finite element method. Owing to the importance of the source term compared to the advection component, the proposed algorithm follows a splitting scheme using a fourth-order Runge-Kutta method for integrating the friction and slope components.The performance of the overall approach has been checked in a number of examples. The analysis of the results provides insights into the key elements of the model and shows the adequacy of the method to solve real problems where merging and splitting of the flow occur.

Recommendations for the quantitative analysis of landslide risk

“…As the geometry is rather complex, there is no analytical solution and it is necessary to discretise the equations using a suitable numerical model. These models are very expensive in terms of computing time, but must be used in situations where 3D effects are important, as in the case of waves generated by landslides or the impact of the flowing material with structures and buildings (Quecedo et al 2004). This kind of model can be applied to all types of movement, with the exception of those where the granularity of the mixture is an important influence.…”

“…Moreover, pressures and forces over structures are hydrostatic. Therefore, if this information is needed, it is necessary to couple the 2D Quecedo et al (2004) depth-integrated model with the full 3D model in the proximity of the obstacle. Depth-integrated models represent an excellent compromise between computer time and accuracy.…”

“…Depth-integrated models represent an excellent compromise between computer time and accuracy. They have been used to describe rock avalanches, lahars, mudflows, debris flows and flowslides Hungr 1995;McDougall and Hungr 2004;Pastor et al 2002Pastor et al , 2009Quecedo et al 2004;Savage and Hutter 1991;Sosio et al 2008, Laigle andCoussot 1997). (d) Depth-integrated models can be simplified still further, as in the case of so-called infinite landslide approaches.…”

Wave propagation and localization problems in saturated viscoplastic geomaterials

“…The authors have shown in a previous work [29] that the best choice to maintain the accuracy is the use of the fourth-order Runge-Kutta splitting scheme. Therefore, in order to solve the limitations of the two-step Taylor-Galerkin algorithm, we will apply this splitting scheme to solve Equations (17).…”

Aznalcóllar dam failure. Part 3: Dynamics of the motion

“…In recent studies (Hungr, 1995;McDougall & Hungr, 2004;Quecedo et al, 2004) the slide is idealised as a fluidised mass of soil, and the Navier-Stokes equations are integrated in depth, adapted to the curved geometry of the surface and solved for some rheological models adopted for the moving mass. In other approaches, conceived for rockslides, discrete element approaches and hybrid continuum-discontinuum models have been developed (Eberhardt et al, 2004).…”