Sedimentation-consolidation of a double porosity material

This paper studies the sedimentation-consolidation of a double porosity material, such as lumpy clay. Large displacements and finite strains are accounted for in a multidimensional setting. Fundamental equations are derived using a phenomenological approach and non-equilibrium thermodynamics, as set out by Coussy [Coussy, Poromechanics, Wiley, Chichester, 2004]. These equations particularise to three non-linear partial differential equations in one dimensional context. Numerical implementation in a finite element code is currently being undertaken

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

On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics

The fixed-stress split method has been widely used as solution method in the coupling of flow and geomechanics. In this work, we analyze the behavior of an inexact version of this algorithm as smoother within a geometric multigrid method, in order to obtain an efficient monolithic solver for Biot's problem. This solver combines the advantages of being a fully coupled method, with the benefit of decoupling the flow and the mechanics part in the smoothing algorithm. Moreover, the fixed-stress split smoother is based on the physics of the problem, and therefore all parameters involved in the relaxation are based on the physical properties of the medium and are given a priori. A local Fourier analysis is applied to study the convergence of the multigrid method and to support the good convergence results obtained. The proposed geometric multigrid algorithm is used to solve several tests in semi-structured triangular grids, in order to show the good behavior of the method and its practical utility

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)

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