A Study On Flow And Mass Transport In Soils By Asymptotic Expansion Theory

Geo-materials, such as soils exist widely as a typical heterogeneous porous media in the nature. The shape and the size of the solid particle, the distribution of the pore space and the inner complicated component constitute the character of heterogeneity of geo-materials. Flow, adsorption and transport in them are always one of fundamental topics in geotechnical engineering. Nowadays, the main thought and methodology to the topic are on the macro-scale, which is based on the phenomenological approach. However, the feather shown from the macro-sample is determined by the physical phenomenon of the pore scale. Hence, we thought that the research of the topic will be more essential if micro-scale and macro-scale can be combined. From this thought, it is necessary to focus on the pore character of micro-scale, and combine the particle, pore distribution, the physical and chemical phenomenon with the flow and transport of the macro-sample.Motivated by the consideration above, with the theory of double-scale asymptotic expansion, the thesis aims at different kinds of soils. Especially, we focus on the intrinsic feature of porous media, fluid flow in response to single hydraulic gradient and mass transport in response to hydraulic and concentration gradients. What’s more, some theoretical derivations and numerical calculation are carried out.(1)Tortuosity of porous media with quadrate and circular particles is calculated, respectively, with the geometrical line method.In the process, the occurrence of interaction between the molecule and the particle, weight factor are taken into consideration. On the other hand, the relationship between tortuosity and porosity is modeled by the numerical computation. The focus is also on the porous media with quadrate or circular particles. Models differ from the coefficient, the minimum value of which to sand is0.357while the minimum value to clay is0.613. The models are contracted with the experimental data from the porous media with glass particles. They have a good agreement, which shows that the method proposed is reliable. However, the soil is more complicated. It’s analyzed and actually calculated from three impact factors:arrangment of particles, physical adsorption (hygroscopic water) and chemical adsorption.(2) Navier-Stokes equation is analyzed forward, through the double-scale asymptotic expansion theory. And the double-scale computation of permeability for porous materials is proposed, which is verified by the numerical example. The parametric analysis indicates that permeability is affected by the particle shape and size, the porosity, not the distribution of the pore. And the larger porosity indicates the larger permeability. What’s more, it’s proposed an inversion method of calculating the permeability with the double-scale asymptotic expansion theory, which is applied to sands, kaolins, illites and sea clays.(3) Three concepts of the average velocity in the pore space, the axial average velocity in the pore space and the average velocity of the sample have totally different physical significance. On the base of them, the Hagen-Poiseulle model is analyzed, which is shown that tortuosity has an important impact on the field of flow. The equation achieved has the same form as Blake-Kozeny eqation. What’s more, with the tortuosity model got, Bruschke and Advani theoretical model can be revised. The revised model is not so different from the one before, but can simulate the multi-scale answer better.(4) Through the process of the up-scaling for dispersion patterns, the thresholds which can distinguish different transport model, including significant diffusion, insignificant diffusion, dispersion and not homogeneous model are quantified. Also a computation of effective diffusion coefficient for soil is proposed. The parametric analysis indicates that the effective diffusion coefficient is affected by the particle shape and the porosity, not the distribution of the pore and the size of the particle. On the other hand, an inverse computation is achieved to calculate the effective diffusivity. The conceptual REVs with quadrate and circular particle are for sand and clay, respectively. Because of the special feature of clays, hygroscopic water should be taken into consideration. An agreement between the measured and computed values is found.(5) Three concepts of the average flux in the pore space, the axial average flux in the pore space and the average flux of the solute have totally different physical significance. On the base of them, the equation including the effective diffusion coefficient, porosity, and molecule diffusion coefficient are derived, which is used widely to calculate the effective diffusivity. And it shows that the tortuosity has an important impact on the field of diffusion.