P. Mira

A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems

Abstract In order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid. Classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible. This type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met. There are two classical approaches to this problem. The first is usually known as the Zienkiewicz–Taylor patch test for mixed formulations. As a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field. Mathematically speaking this is a necessary condition for stability. The second approach, mathematically more involved, is usually known as the Babŭska–Brezzi inf–sup condition and constitutes a sufficient condition for stability. However it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so-called stabilization techniques. These techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics. This article presents a new formulation in which stabilization is achieved through an approach based on the Simo–Rifai enhanced strain element.

Modelling of Landslides: (II) Propagation

This paper presents a numerical model wich can be used to simulate phenomena such as flowslides, avalanches, mudflows and debris flows. The proposed approach is eulerian, and balance of mass and momentum equations are integrated on depht. Depending on the material involved, the model can implement rheological models such as Bingham or frictional fluids. A simple dissipation law allows the approximation of pore pressure dissipation in the sliding mass. Finally some applications are presented.

Modelling of Landslides: (I) Failure Mechanisms

This paper presents a theoretical and numerical framework to model the initiation mechanisms of catastrophic landslides. The equations describing the coupling between the solid skeleton and the pore fluids are presented following an eulerian approach based on the mixture theory that can provide a unified formulation for both initiation and propagation phases. The system of Partial Differential Equations is then discretized using the classical Galerkin Finite Element Method and neglecting the convective terms. Some applications to localized and diffuse failure will be presented.

Application of a New Rheological Model to Rock Avalanches: An SPH Approach

AbstractRock avalanches move large volumes of material causing a highly destructive power over large areas. In these events, it is possible to monitor the evolution of slopes but failure cannot be always prevented. For this reason, modelling of the propagation phase provides engineers with fundamental information regarding speed, track, runout and depth. From these data, it is possible to perform a better risk assessment and propose mitigation measures to reduce the potential hazard of specific area. The purpose of this paper is to present a depth integrated, SPH model, which can be used to simulate real rock avalanches and to assess the influence of the rheology on the avalanche properties. The paper compares the performance of different rheological models to reproduce the track, runout and depth of the final deposit for both, scale test and real events such as Frank and Thurwiesier rock avalanches. These sets of benchmarks provide information on the proposed model accuracy and limitations.

Modelling of debris flows and flow slides

ABSTRACT This paper presents a numerical model which can be used to simulate phenomena such as flowslides, avalanches, mudflows and debris flows. The proposed approach is la- grangian, and balance of mass and momentum equations are integrated on depth. Depending on the material involved, the model can implement rheological models such as Bingham orfrictional fluids. A simple dissipation law allows the approximation of pore pressure dissipation in the sliding mass. Finally, some applications are presented.

Practical aspects of the finite element method

ABSTRACT This paper deals with practical aspects of the use and implementation of the finite element method. These aspects frequently cause serious difficulties specially to new comers to finite element practice and may even be the source of important error on the final results of computations. The aspects that will be analyzed are:—the computational aspects of bending—the reduced integration—the volumetric locking of incompressible situations—the patch test for mixed formulations—the solver of the system of equations.

An eulerian model for soil dynamics: application to fast slope movements

ABSTRACT This paper presents a theoretical framework to model soil behaviour under dynamic conditions. The equations describing the coupling between the solid skeleton and the pore fluids are presented following an eulerian approach based on the mixture theory that can provide an unified formulation for both initiation and propagation phases of fast landslides, such as avalanches of rocks and granular materials, flowslides and debris flows.

Fast Landslide Propagation: Alternative Modelling Techniques

We model debris flows using two sets of nodes, describing the water and the solid phases, which can move relative to each other. We present first the mathematical model which will be used, deriving it from Zienkiewicz-Shiomi model, and arriving to the depth integrated model proposed by Pitman and Le. Then, we present the rheological models describing solid, fluid and their interaction. Next, the SPH model for two phases will be described. Finally, we present some application cases where we will compare the results provided by the proposed model against those obtained using more simplified models.

An eulerian model for soil dynamics: application to fast slope movements: (III) Rheological models

ABSTRACT This paper presents some useful rheological models that can be used to characterize the soil behaviour in fast landslides. The approach followed is based on a general formulation of the stress tensor in terms of I, D and D 2 where D is the rate of deformation tensor. Then we particularize it to simple shear flow conditions and compare it to some simple rheological laws. From here, expressions valid for general flow conditions are proposed.

An eulerian model for soil dynamics: application to fast slope movements: (II) A simple velocity-pore pressure formulation

ABSTRACT This paper presents an eulerian approach that can be used to model the propagation phase of catastrophic landslides. In the case of material composed by a solid skeleton and pore fluids, two physical phenomena must be considered: i) the propagation and, ii) the consolidation and dissipation of pore pressures. The PDEs are integrated in depth and solved with the Finite Element Method using the Taylor-Galerkin algorithm. Its possible to take into account the curvature effect of the bed of the slide using a curvilinear reference system or adding the contribution of the centrifuge force to the bottom friction force. A simple frictional fluid flow example shows the influence of the curvature effect. Role of pore pressure dissipation is analyzed modelling the Aberfan flowslide (1966).