Lorenzo Sanavia

CAVITATION MODELLING IN SATURATED GEOMATERIALS WITH APPLICATION TO DYNAMIC STRAIN LOCALIZATION

A model to simulate cavitation phenomena in the pores of saturated porous media is developed. Such phenomena appear in connection with pore water traction, which may be observed during strain localization in dense sand samples or in dynamic fluid–structure interaction problems where the structure is made of geomaterials. The model makes use of an isothermal two‒phase flow approach. Numerical examples relating to strain localization are shown.

Numerical modelling of a slope stability test by means of porous media mechanics

Purpose – The purpose of this paper is to present a finite‐element analysis of the initiation of a slope failure in a small‐scale laboratory test due to pore pressure variation. To this aim, a fully coupled multiphase model for saturated/partially saturated solid porous materials based on porous media mechanics is used.Design/methodology/approach – The slope is described as a three‐phase deforming porous continuum where heat, water and gas flow are taken into account. The gas phase is modelled as an ideal gas composed of dry air and water vapour. Phase changes of water, heat transfer through conduction and convection and latent heat transfer are considered. The independent variables are: solid displacements, capillary pressure, gas pressure and temperature. The effective stress state is limited by Drucker‐Prager yield surface for the sake of simplicity. Small strains and quasi‐static loading conditions are assumed.Findings – The paper shows that the multiphase modelling is able to capture the main experim...

Coupling equations for water saturated and partially saturated geomaterials: A mathematical model for multiphase porous materials: fundamentals and formulation

ABSTRACT A mathematical model for a saturated and partially saturated non-isothermal porous medium is presented. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and gas, which may be either vapour alone or a mixture of dry air and vapour. The governing equations at macroscopic level are derived in a spatial setting using averaging theories. Finite kinematics is included in the model. The solid skeleton of the medium can undergo large elastic or inelastic deformations described in the framework of hyperelastoplasticity. The fluids are assumed to obey Darcys law.

Finite Element Analysis of the Initiation of Landslides with a Non-isothermal Multiphase Model

Finite element analysis of the initiation of landslides due to capillary and water pressure variation is presented in this work. To this aim, a non-isothermal elasto-plastic multiphase material model for soils is used. Soils are modelled as a three-phase deforming porous continuum where heat, water and gas flow are taken into account. In particular, the gas phase is modelled as an ideal gas composed of dry air and water vapor. Phase changes of water, heat transfer through conduction and convection and latent heat transfer are considered. The macroscopic balance equations are discretized in space and time within the finite element method. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The effective stress state is limited by Drucker-Prager yield surface for simplicity. Small strains and quasi-static loading conditions are assumed. Numerical simulation of a slope stability experiment is presented assuming plane strain condition during the computations.

Finite element analysis of strain localization in multiphase materials

ABSTRACT Finite element analysis of strain localization in multiphase materials is presented. The multiphase material is modelled as a deforming porous continuum where heat, water and gas flow are taken into account. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The modified effective stress state is limited by the Drucker-Prager yield surface. Small strains and quasi-static loading conditions are assumed. Numerical results of strain localization in globally undrained samples of dense sand are presented. A biaxial compression test is simulated assuming plane strain condition during the computations. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed.

Geometrical and material non-linear analysis of fully and partially saturated porous media

A formulation for a partially saturated porous medium undergoing large elastic or elasto-plastic deformations is presented. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The elasto-plastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface. The water is assumed to obey Darcy’s law. Numerical examples of the Liakopoulos’ test and of strain localization of dense or loose sand and of clay under undrained conditions conclude the paper.

Some theoretical aspects of strain localization analysis of multiphase porous media with regularized constitutive models

This paper discusses some theoretical aspects of strain localization analysis in multiphase porous media, particularly when regularized constitutive models such as the gradient-dependent and rate-dependent models are used. Stability and hyperbolicity of the governing equations are studied and the relations between permeability and the wave number where a real wave speed exists are investigated numerically. Particular attention is focused on the two cases of wave number K = 0 and K → ∞ of the perturbation waves. The interaction between the different internal length scale parameters during dynamic strain localization in multiphase porous materials is also studied. It is pointed out that the consideration of fluid interaction is necessary for the prediction of the internal length in a multiphase porous medium when regularization through a constitutive model is introduced in the numerical model to overcome mesh dependence in a finite element solution.

A finite element model for water saturated and partially saturated geomaterials Space and time discretisation for a multiphase porous material model

ABSTRACT A finite element formulation for a saturated and partially saturated porous medium undergoing large elastic or inelastic deformations is presented. This model is derived from the general thermo-hydro-mechanical model for porous materials developed in a previous contribution of the authors to this lecture notes. The porous medium is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. The governing equations at macroscopic level are derived in a spatial setting. Solid grains and water are assumed to be incompressible at the microscopic level for simplicity. The consistent linearisation of the fully non linear coupled system of equations is derived. A spatial finite element formulation of the governing equations conclude this contribution of the authors.

Strain localisation simulation in non-isothermal multiphase geomaterials

A coupled finite element formulation for the hydro-thermo-mechanical behaviour of a water saturated and partially saturated porous material has been presented. This model is obtained as a result of a research in progress on the thermo-hydro-mechanical modelling for multiphase geomaterials undergoing inelastic strains. Numerical results of strain localisation in globally undrained samples of dense and medium dense sands have been presented. Vapour pressure below the saturation water pressure (i.e. water cavitation) develops at localisation in case of dense sands, as experimentally observed. A case of strain localisation induced by a thermal load in a sample where the displacements are constrained and evaporation takes place is also analysed.

Modelling of Localisation at Finite Inelastic Strains in Fluid Saturated Porous Media

Quasi-static finite strain localisation phenomena in fluid saturated soils are studied. The governing equations at the macroscopic level arc derived in a spatial and a material setting. The constituents arc assumed to be materially incompressible. The elasto-plastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an clastic and a plastic part. The effective stress state is limited by the Druckcr-Prager yield surface. A particular “apex formulation” is advocated. The fluid is assumed to obey Darcy’s law. Numerical examples highlight the developments. Negative water pressures, which are important for strain localisation analysis of undraiued water saturated dense sands, arc obtained and their values arc critically discussed.