About Darcy's law in non-Galilean frame

This paper is aimed towards investigating the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium (e.g. a porous medium placed in a centrifuge basket). The filtration law is obtained by upscaling the flow equations at the pore scale. The upscaling technique is the homogenization method of multiple scale expansions which rigorously gives the macroscopic behaviour and the effective properties without any prerequisite on the form of the macroscopic equations. The derived filtration law is similar to Darcy's law, but the tensor of permeability presents the following remarkable properties: it depends upon the angular velocity of the porous matrix, it verifies Hall–Onsager's relationship and it is a non-symmetric tensor. We thus deduce that, under rotation, an isotropic porous medium leads to a non-isotropic effective permeability. In this paper, we present the results of numerical simulations of the flow through rotating porous media. This allows us to highlight the deviations of the flow due to Coriolis effects at both the microscopic scale (i.e. the pore scale), and the macroscopic scale (i.e. the sample scale). The above results confirm that for an isotropic medium, phenomenological laws already proposed in the literature fails at reproducing three-dimensional Coriolis effects in all types of pores geometry. We show that Coriolis effects may lead to significant variations of the permeability measured during centrifuge tests when the inverse Ekman number Ek⁻¹ is 𝒪(1). These variations are estimated to be less than 5% if Ek⁻¹<0.2, which is the case of classical geotechnical centrifuge tests. We finally conclude by showing that available experimental data from tests carried out in centrifuges are not sufficient to determining the effective tensor of permeability of rotating porous media. Copyright © 2004 John Wiley & Sons, Ltd.     

Characterization of contact properties in biocemented sand using 3D X-ray micro-tomography

The mechanical efficiency of the biocementation process is directly related to the microstructural properties of the biocemented sand, such as the volume fraction of calcite, its distribution within the pore space (localized at the contact between grains, over the grain surfaces) and the contact properties: coordination number, contact surface area, contacts orientation and types of contact. In the present work, all these micromechanical properties are computed, for the first time, from 3D images obtained by X-ray tomography of intact biocemented sand samples. The evolution of all these properties with respect to the volume fraction of calcite is analyzed and compared between each other (from untreated sand to highly cemented sand). Whatever the volume fraction of calcite, it is shown that the precipitation of the calcite is localized at the contacts between grains. These results are confirmed by comparing our numerical results with analytical estimates assuming that the granular medium is made of periodic simple cubic arrangements of grains and by considering two extreme cases of precipitation: (1) The calcite is localized at the contact, and (2) the grains are covered by a uniform layer of calcite. In overall, the obtained results show that a small percentage of calcite is sufficient to get a large amount of cohesive contacts.

     

Characterization of microstructural and physical properties changes in biocemented sand using 3D X-ray microtomography

An experimental study has been performed to investigate the effect of the biocalcification process on the microstructural and the physical properties of biocemented Fontainebleau sand samples. The microstructural properties (porosity, volume fraction of calcite, total specific surface area, specific surface area of calcite, etc.) and the physical properties (permeability, effective diffusion) of the biocemented samples were computed for the first time from 3D images with a high-resolution images obtained by X-ray synchrotron microtomography. The evolution of all these properties with respect to the volume fraction of calcite is analysed and compared with success to experimental data, when it is possible. In general, our results point out that all the properties are strongly affected by the biocalcification process. Finally, all these numerical results from 3D images and experimental data were compared to numerical values or analytical estimates computed on idealized microstructures constituted of periodic overlapping and random non-overlapping arrangements of coated spheres. These comparisons show that these simple microstructures are sufficient to capture and to predict the main evolution of both microstructural and physical properties of biocemented sands for the whole range of volume fraction of calcite investigated.     

Influence of the microstructural properties of biocemented sand on its mechanical behavior

The mechanical efficiency of the biocementation process is directly related to the microstructural properties of the biocemented sand, such as the volume fraction of calcite, its distribution within the pore space, coordination number, contact surface area, and types of contact. In the present work, some of these microscopic properties are computed, from 3D images obtained by X-ray tomography of biocemented sand. These properties are then used as an input in current analytical models to estimate the elastic properties (Young and shear moduli) and the strength properties (Coulomb cohesion). For the elastic properties, the analytical estimates (contact cement theory model) are compared with classical bounds, self-consistent estimate and numerical results obtained by direct computation (FEM computation) on the same 3D images. Concerning the cohesion, an analytical model initially developed to estimate the cohesion due to suction in unsaturated soils is modified to evaluate the macroscopic cohesion of biocemented sands. Such analytical model is calibrated on experimental data obtained from triaxial tests performed on the same biocemented sand. In overall, the presented results point out the important role of some microstructural parameters, notably those related to the contact, on such effective parameters.