Modelling plasticity of unsaturated soils in a thermodynamically consistent framework

Constitutive equations of unsaturated soils are often derived in a thermodynamically consistent framework through the use a unique 'effective' interstitial pressure. This later is naturally chosen as the space averaged interstitial pressure. However, experimental observations have revealed that two stress state variables were needed to describe the stress-strain-strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the retention properties of the soil and two effective stresses, which are required to describe the soil deformation at water saturation held constant. Actually, it is shown that a simple assumption related to internal deformation leads to the need of a unique effective stress to formulate the stress-strain constitutive equation describing the soil deformation. An elastoplastic framework is then presented and it is finally shown that the Barcelona Basic Model, a commonly accepted model for unsaturated soils, as well as all models deriving from it, appear as special extreme cases of the thermodynamic framework proposed here

Wave motion in elastic cracked composites

We study the scattering of elastic waves by fiber reinforced composites with interface cracks . In the long wave approximation, by means of a perturbation method, we derived in a closed foi-in the scattering section for an isolated fiber, partially debonded from the matrix, Using a homogenization procedure we extend the analysis to random distributions of inclusions and cracks . We show that the cracked composite behaves like an anisotropic viscoelastic material.On étudie la diffraction des ondes élastiques par des composites fibrés fissurés aux interfaces . Dans l'approximation des ondes longues, par une méthode de perturbation, on détermine analytiquement la section efficace pour une fibre isolée, partiellement désolidarisée de la matrice . Par une technique d'homogénéisation, on étend l'analyse à des distributions aléatoires d'inclusions et de fissures . On montre alors que le matériau composite fissuré se comporte comme un matériau viscoélastique anisotrope

Fracture Propagation Driven by Fluid Outflow from a Low-permeability Aquifer

Deep saline aquifers are promising geological reservoirs for CO2 sequestration if they do not leak. The absence of leakage is provided by the caprock integrity. However, CO2 injection operations may change the geomechanical stresses and cause fracturing of the caprock. We present a model for the propagation of a fracture in the caprock driven by the outflow of fluid from a low-permeability aquifer. We show that to describe the fracture propagation, it is necessary to solve the pressure diffusion problem in the aquifer. We solve the problem numerically for the two-dimensional domain and show that, after a relatively short time, the solution is close to that of one-dimensional problem, which can be solved analytically. We use the relations derived in the hydraulic fracture literature to relate the the width of the fracture to its length and the flux into it, which allows us to obtain an analytical expression for the fracture length as a function of time. Using these results we predict the propagation of a hypothetical fracture at the In Salah CO2 injection site to be as fast as a typical hydraulic fracture. We also show that the hydrostatic and geostatic effects cause the increase of the driving force for the fracture propagation and, therefore, our solution serves as an estimate from below. Numerical estimates show that if a fracture appears, it is likely that it will become a pathway for CO2 leakage.Comment: 21 page

Phase coexistence in consolidating porous media

The appearence of the fluid-rich phase in saturated porous media under the effect of an external pressure is investigated. For this purpose we introduce a two field second gradient model allowing the complete description of the phenomenon. We study the coexistence profile between poor and rich fluid phases and we show that for a suitable choice of the parameters non-monotonic interfaces show-up at coexistence

A large-strain radial consolidation theory for soft clays improved by vertical drains

A system of vertical drains with combined vacuum and surcharge preloading is an effective solution for promoting radial flow, accelerating consolidation. However, when a mixture of soil and water is deposited at a low initial density, a significant amount of deformation or surface settlement occurs. Therefore, it is necessary to introduce large-strain theory, which has been widely used to manage dredged disposal sites in one-dimensional theory, into radial consolidation theory. A governing equation based on Gibson's large-strain theory and Barron's free-strain theory incorporating the radial and vertical flows, the weight of the soil, variable hydraulic conductivity and compressibility during the consolidation process is therefore presented

Recursive double-size fixed precision arithmetic

International audienceThis work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture)

Numerical study of nonlinear heat transfer from a wavy surface to a high permeability medium with pseudo-spectral and smoothed particle methods

Motivated by petro-chemical geological systems, we consider the natural convection boundary layer flow from a vertical isothermal wavy surface adjacent to a saturated non-Darcian high permeability porous medium. High permeability is considered to represent geologically sparsely packed porous media. Both Darcian drag and Forchheimer inertial drag terms are included in the velocity boundary layer equation. A high permeability medium is considered. We employ a sinusoidal relation for the wavy surface. Using a set of transformations, the momentum and heat conservation equations are converted from an (x, y) coordinate system to an (x,η) dimensionless system. The two-point boundary value problem is then solved numerically with a pseudo-spectral method based on combining the Bellman–Kalaba quasi linearization method with the Chebyschev spectral collocation technique (SQLM). The SQLM computations are demonstrated to achieve excellent correlation with smoothed particle hydrodynamic (SPH) Lagrangian solutions. We study the effect of Darcy number (Da), Forchheimer number (Fs), amplitude wavelength (A) and Prandtl number (Pr) on the velocity and temperature distributions in the regime. Local Nusselt number is also computed for selected cases. The study finds important applications in petroleum engineering and also energy systems exploiting porous media and undulating (wavy) surface geometry. The SQLM algorithm is shown to be exceptionally robust and achieves fast convergence and excellent accuracy in nonlinear heat transfer simulations