岩土介质渗流以及输运从孔隙尺度到达西尺度的研究
摘要
岩土介质是一种遍及于自然界的非均质多孔材料。实体颗粒与孔隙空间的无序分布构成了岩土介质非均质特性的典型要素。与岩土介质相关的渗流以及输运现象是岩土工程学科研究的基础课题之一。目前针对这一课题的主要研究手段是基于唯象的方法论,而唯象研究方法的主要特点是放弃孔隙尺度上的非均质性,单考虑达西尺度上的均质特性。但是从认识事物的本质规律出发,非均质多孔材料在达西尺度上所表现出来的各种特性必定是孔隙尺度上的各种物理过程的本质反映。所以,针对岩土介质渗流以及输运的研究课题,从更为科学的角度出发,应该充分考虑孔隙尺度上的非均质性。这就要求,必须将孔隙的几何结构,以及孔隙空间内发生的物理过程,与达西尺度上的渗流以及输运的均质特性紧密的联系起来。
源于上述研究动机,本文以岩土介质为研究对象,借助尺度扩展的数学方法,针对水力梯度驱动下的流体渗流,水力、浓度梯度驱动下的物质输运,以及粘土-水溶液体系的电动现象,展开了从孔隙到达西的尺度扩展的理论和计算工作。
针对水力梯度驱动下的流体渗流问题：1)通过对渗流问题的尺度扩展,给出了渗透率的多尺度计算方法,并数值考察了渗透率的影响因素。结果表明,组构对于各向同性渗透率的影响并不显著,而颗粒大小以及孔隙比的影响却是显著的正相关。2)借助一个持有特征半径以及相关孔隙比定义的概念性单胞,同时结合反演优化技术,提出一个简单易于操作的岩土介质渗透率的多尺度计算方法,并将该计算方法应用于砂土以及粘土的各向同性(异性)渗透率的计算。
针对水力、浓度梯度驱动下的物质输运问题：1)通过对扩散型和弥散型传输的尺度扩展,量化了两者界限的理论阀值标准。2)数值考察了有效扩散系数的影响因素。结果表明,颗粒大小对于有效扩散系数影响不显著,而组构以及孔隙比的影响显著。3)借助特征底角的概念来考虑组构的影响,给出了岩土介质有效扩散系数的多尺度计算方法,并将之应用于粘土的有效扩散系数的计算。
针对粘土-水溶液体系的电动现象问题：1)通过对粘土-水溶液体系电动现象的尺度扩展,量化了流动电势梯度以及电粘效应的一般计算公式,从而揭示了粘土渗流的胶体科学本质。2)数值考察了电动直径,表面带电密度各自对于流动电势梯度以及电粘效应的影响,得到了一系列“直观朴素”或者“反直观朴素”的结果,并且借助流动电势梯度和电粘效应的协同分析,在物理上合理的解释了上述“直观朴素”以及“反直观朴素”的结果。3)借助持有颗粒宽度的一维概念性单胞,同样较好的应用于考虑双电层效应的粘土渗透率的计算。
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.
源于上述研究动机,本文以岩土介质为研究对象,借助尺度扩展的数学方法,针对水力梯度驱动下的流体渗流,水力、浓度梯度驱动下的物质输运,以及粘土-水溶液体系的电动现象,展开了从孔隙到达西的尺度扩展的理论和计算工作。
针对水力梯度驱动下的流体渗流问题：1)通过对渗流问题的尺度扩展,给出了渗透率的多尺度计算方法,并数值考察了渗透率的影响因素。结果表明,组构对于各向同性渗透率的影响并不显著,而颗粒大小以及孔隙比的影响却是显著的正相关。2)借助一个持有特征半径以及相关孔隙比定义的概念性单胞,同时结合反演优化技术,提出一个简单易于操作的岩土介质渗透率的多尺度计算方法,并将该计算方法应用于砂土以及粘土的各向同性(异性)渗透率的计算。
针对水力、浓度梯度驱动下的物质输运问题：1)通过对扩散型和弥散型传输的尺度扩展,量化了两者界限的理论阀值标准。2)数值考察了有效扩散系数的影响因素。结果表明,颗粒大小对于有效扩散系数影响不显著,而组构以及孔隙比的影响显著。3)借助特征底角的概念来考虑组构的影响,给出了岩土介质有效扩散系数的多尺度计算方法,并将之应用于粘土的有效扩散系数的计算。
针对粘土-水溶液体系的电动现象问题：1)通过对粘土-水溶液体系电动现象的尺度扩展,量化了流动电势梯度以及电粘效应的一般计算公式,从而揭示了粘土渗流的胶体科学本质。2)数值考察了电动直径,表面带电密度各自对于流动电势梯度以及电粘效应的影响,得到了一系列“直观朴素”或者“反直观朴素”的结果,并且借助流动电势梯度和电粘效应的协同分析,在物理上合理的解释了上述“直观朴素”以及“反直观朴素”的结果。3)借助持有颗粒宽度的一维概念性单胞,同样较好的应用于考虑双电层效应的粘土渗透率的计算。
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.
引文
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