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.

SUMMARYThe damage caused by impulse waves generated in water bodies by fast landslides can be very high in terms of human lives and economic losses. The complex phenomena taking place in this highly unsteady process are difficult to model because three interacting phases: air, water and soil are involved. Solutions currently available are based on either closed form equations supported experimentally or the depth integrated Navier-Stokes equations. The latter, although of more general applicability, requires knowledge of the evolution of the bathimetry and slide drag forces and their applicability may be restricted by the steep slopes existing in most real cases.To avoid these limitations, the authors propose the solution of the full Navier-Stokes equations, using indicator functions to assign the material properties to each spatial point in the domain. The method performance is illustrated by comparison against the experimental results obtained in a physical model of an actual case.

This paper presents a depth-integrated model that can be used to simulate the flowslides, mudflows and debris flows that are caused by the failure of tailing dams, mining waste dumps and other similar structures. The sliding mass is first determined using a coupled elastoplastic finite element code and a suitable constitutive equation. Once failure has been triggered, propagation of the mobilised material is analysed considering flow properties averaged over depth. A simple law of pore pressure dissipation is postulated for cases in which the consolidation and propagation times are of the same order of magnitude.

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The accurate prediction of the behaviour of geostructures is based on the strong coupling between the pore fluid and the solid skeleton. If the relative acceleration of the fluid phase relative to the skeleton is neglected, the equations describing the problem can be written in terms of skeleton displacements (or velocities) and pore pressures. This mixed problem is similar to others found in solid and fluid dynamics. In the limit case of zero permeability and incompressibility of the fluid phase, the restrictions on the shape functions used to approximate displacements and pressures imposed by Babuska–Brezzi conditions or the Zienkiewicz–Taylor patch test hold. As a consequence, it is not possible to use directly elements with the same order of interpolation for the field variables. This paper proposes a generalization of the fractional‐step method introduced by Chorin for fluid dynamics problems, which allows to circumvent BB restrictions in the incompressibility limit, thus making it possible to use elements with the same order of interpolation. Copyright © 2000 John Wiley & Sons, Ltd.