Flow And Transport In Geo-materials:from Pore-scale To Darcy-scale

Geo-materials (e.g., sands, clays, and rocks) are recognized as a typical heterogeneous porous material with its widespread all over the world. The disordered distribution between solid particle and pore space basically makes up this type of heterogeneity. Flow and transport in geo-materials is always one of fundamental topical areas in geotechnical engineering. At present, the main methodology to this topic is based on the so-called phenomenological approach, which is featured by only considering the homogeneous property at the Darcy-scale rather than the heterogeneous one at the pore-scale. Nevertheless, in principle, the numerous properties at the Darcy-scale are essentially determined by all kinds of physical phenomena occurring at the pore-scale. Thus, to more scientifically study those flow and transport properties in heterogeneous porous materials, a sufficient consideration with heterogeneities is required. More specially, the needed pore-scale information including geometry, and physical phenomenon is supposed to be fully incorporated in the flow and transport properties at the Darcy-scale.Motivated by the scientific sense above, this thesis mostly aims at an application of mathematical methodology of up-scaling in flow and transport in geo-materials. More specially, we focus on how to extend to the Darcy-scales for the three principal phenomena below:fluid flow in response to single hydraulic gradient, mass transport in response to hydraulic and concentration gradients, and electrokinetic phenomenon in a clayey soil-aqueous solution. To this end, some theoretical derivations as well as numerical computations are both carried out in this thesis.Fluid flow in response to single hydraulic gradient.1) Through the up-scaling process for fluid flow, the multi-scale computation of permeability for porous media is proposed, and the parametric analysis is numerically conducted to estimate the effects of fabric, particle size, and void ratio on the permeability. Through the parametric analysis, we can conclude that the effect of fabric on the isotropic permeability, to some extent, can be neglected with comparison to those of particle size and void ratio.2) An easy-to-implement multi-scale computation of permeability for geo-materials is proposed. In particular, a conceptual unit cell with characteristic radius is suggested to account for the complexity of the pore network; the determination of this unit cell is an inverse optimization process:to find the characteristic radius that yields a single laboratory permeability test data; using the determined characteristic radius, the permeability can be computed for various void ratios. Such an approach is applied to sands and clays. An agreement between the computed and measured values of the permeability is found.Mass transport in response to hydraulic and concentration gradients.1) Through the up-scaling processes for diffusion and dispersion transport patterns, the theoretical thresholds distinguishing them are quantified.2) Parametric analysis is numerically conducted to estimate the influences of fabric, particle size, and void ratio on the effective diffusivity. Through the parametric analysis, we can conclude that the influence of particle size, to some extent, can be neglected with comparison to those of fabric and void ratio.3) A multi-scale computation of effective diffusivity for geo-materials is proposed. In particular, a conceptual unit cell with characteristic triangle is suggested to account for the fabric factor in the pore network; the determination of this unit cell is an inverse optimization process:to find the characteristic triangle that yields a single laboratory effective diffusivity test data; using the determined characteristic triangle, the effective diffusivity can be computed for various void ratios. Such an approach is applied to clays. An agreement between the computed and measured values of the effective diffusivity is found.Electrokinetic phenomenon in a clayey soil-aqueous solution.1) Through the up-scaling processes for the electrokinetic phenomenon in a clayey soil-aqueous solution, the general formulas are derived to quantify streaming potential gradient and electroviscous effect, respectively, both of which are physically a key to understanding the essence of flow in a clayey soil-aqueous solution system.2) By the formulas, a parametric analysis is numerically conducted to estimate the possible effects of electrokinetic diameter and the surface charge density on streaming potential gradient and electroviscous effect, respectively. For the results obtained in the parametric analysis, some seem normal, which definitely conform to the general physical principle, but the others seem anomalous, which superficially do not conform to the general physical principle. However, with the aid of the so-called synchronous analysis between streaming potential gradient and electroviscous effect, all results including normal and anomalous ones, can be explained well in a physical sense.3) Use of a one-dimensional conceptual unit cell with characteristic particle width, a multi-scale computation of permeability that can account for the electric double layers effect is proposed and also can be successfully applied to clays.