A smoothed particle hydrodynamics model for droplet and film flow on smooth and rough fracture surfaces

Flow on fracture surfaces has been identified by many authors as an important flow process in unsaturated fractured rock formations. Given the complexity of flow dynamics on such small scales, robust numerical methods have to be employed in order to capture the highly dynamic interfaces and flow intermittency. In this work we use a three-dimensional multiphase Smoothed Particle Hydrodynamics (SPH) model to simulate surface tension dominated flow on smooth fracture surfaces. We model droplet and film flow over a wide range of contact angles and Reynolds numbers encountered in such flows on rock surfaces. We validate our model via comparison with existing empirical and semi-analytical solutions for droplet flow. We use the SPH model to investigate the occurrence of adsorbed trailing films left behind droplets under various flow conditions and its importance for the flow dynamics when films and droplets coexist. It is shown that flow velocities are higher on prewetted surfaces covered by a thin film which is qualitatively attributed to the enhanced dynamic wetting and dewetting at the trailing and advancing contact lines. Finally, we demonstrate that the SPH model can be used to study flow on rough surfaces.     

Unsaturated hydro-mechanical-chemo coupled constitutive model with consideration of osmotic flow

Since low permeability rock has the potential to behave as an actual semi-permeable osmotic membrane, chemical osmosis may have an effect on water flow and needs to be accounted for in analysis. Hence, an advanced fully coupled formulation for modelling unsaturated hydro, chemical and mechanical effects is here presented based on modified mixture theory. Firstly, the classical Darcy’s law has been modified to include the chemical potential. Secondly, the mechanical deformation, which affects the permeability, has been coupled with the water and chemical flows by using Helmholtz free energy and the Gibbs–Duhem equation. Finally, an illustrative numerical example with relevance to radioactive waste disposal has been analysed to investigate the performance of the coupled formulation and the relative influence of parameters.     

A comparative modeling study of a dual tracer experiment in a large lysimeter under atmospheric conditions

In this paper, five model approaches with different physical and mathematical concepts varying in their model complexity and requirements were applied to identify the transport processes in the unsaturated zone. The applicability of these model approaches were compared and evaluated investigating two tracer breakthrough curves (bromide, deuterium) in a cropped, free-draining lysimeter experiment under natural atmospheric boundary conditions. The data set consisted of time series of water balance, depth resolved water contents, pressure heads and resident concentrations measured during 800 days. The tracer transport parameters were determined using a simple stochastic (stream tube model), three lumped parameter (constant water content model, multi-flow dispersion model, variable flow dispersion model) and a transient model approach. All of them were able to fit the tracer breakthrough curves. The identified transport parameters of each model approach were compared. Despite the differing physical and mathematical concepts the resulting parameters (mean water contents, mean water flux, dispersivities) of the five model approaches were all in the same range. The results indicate that the flow processes are also describable assuming steady state conditions. Homogeneous matrix flow is dominant and a small pore volume with enhanced flow velocities near saturation was identified with variable saturation flow and transport approach. The multi-flow dispersion model also identified preferential flow and additionally suggested a third less mobile flow component. Due to high fitting accuracy and parameter similarity all model approaches indicated reliable results.     

A Methodology for Simulating Radionuclide Diffusion in Unsaturated Soils

In this paper, a methodology that can be employed to simulate radionuclide migration through unsaturated soils, under laboratory conditions, has been developed and reported. This was achieved with the help of a specially designed half-cell setup to study diffusion characteristics of inactive forms of Cs⁺, Sr⁺² and Co⁺² in two different types of soils, corresponding to their different compaction states. It has been noted that the apparent diffusion coefficient strongly depends on the volumetric water content of the soil. However, increase of the apparent diffusion coefficient for higher volumetric water contents is found to be much less as compared to the lower volumetric water contents.     

The role of uncertainty in bedrock depth and hydraulic properties on the stability of a variably-saturated slope

We investigate the uncertainty in bedrock depth and soil hydraulic parameters on the stability of a variably-saturated slope in Rio de Janeiro, Brazil. We couple Monte Carlo simulation of a three-dimensional flow model with numerical limit analysis to calculate confidence intervals of the safety factor using a 22-day rainfall record. We evaluate the marginal and joint impact of bedrock depth and soil hydraulic uncertainty. The mean safety factor and its 95% confidence interval evolve rapidly in response to the storm events. Explicit recognition of uncertainty in the hydraulic properties and depth to bedrock increases significantly the probability of failure.     

Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary

This paper presents semi-analytical solutions to Fredlund and Hasan’s one-dimensional consolidation for unsaturated soils under symmetric semi-permeable drainage boundary conditions. Two variables are introduced to transform two coupled governing equations of pore-air and pore-water pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. Then, the pore-air and pore-water pressures, and soil settlement are obtained in the Laplace domain. Crump’s method is adopted to perform the inverse Laplace transform in order to obtain semi-analytical solutions in time domain. It is shown that the present solution is more applicable to various types of drainage boundary conditions, and in a good agreement with existing solutions from the literature. Furthermore, several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with traditional drainage boundary (single or double), and single-sided and double-sided semi-permeable drainage boundaries. Finally, it illustrates the changes in pore-air and pore-water pressures and soil settlement with time at different values of symmetric semi-permeable drainage boundary conditions parameters. In addition, parametric studies are conducted by the variations of pore-air and pore-water pressures at different ratios of air-water permeability coefficient and the depth.     

Rapid imbibition of water in fractures within unsaturated sedimentary rock

The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated porous media is important in a variety of engineering and geological contexts. However, surprisingly few studies have investigated this phenomenon. We present a theoretical framework for predicting the 1-dimensional movement of water into air-filled fractures within a porous medium based on early-time capillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimation of sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifies the extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water in unsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with different permeability classes ranging from 50 to 500 mD and were fractured using the Brazilian method. Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at the Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Water uptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrix sorptivities ranged from 2.9 to 4.6 mm s^−0.5, and increased linearly as the permeability class increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 mm s^−0.5, and increased linearly with increasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7 mm² s⁻¹ and increased linearly with increasing fracture aperture width and damage zone width. Both theory and observations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sedimentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increase the dispersion of the wetting front. Further research is needed to investigate this phenomenon in other natural and engineered porous media.     

Adaptive multi-scale parameterization for one-dimensional flow in unsaturated porous media

In the analysis of the unsaturated zone, one of the most challenging problems is to use inverse theory in the search for an optimal parameterization of the porous media. Adaptative multi-scale parameterization consists in solving the problem through successive approximations by refining the parameter at the next finer scale all over the domain and stopping the process when the refinement does not induce significant decrease of the objective function any more. In this context, the refinement indicators algorithm provides an adaptive parameterization technique that opens the degrees of freedom in an iterative way driven at first order by the model to locate the discontinuities of the sought parameters. We present a refinement indicators algorithm for adaptive multi-scale parameterization that is applicable to the estimation of multi-dimensional hydraulic parameters in unsaturated soil water flow. Numerical examples are presented which show the efficiency of the algorithm in case of noisy data and missing data.     

Chemical evolution of acid precipitation in the unsaturated zone of the Pennsylvanian siltstones and shale of central Ohio

The North Appalachian Experimental Watershed in Coshocton, Ohio, USA has recorded average pH of precipitation of 4.7 over a 30-year period. The area lies within the Pennsylvanian siltstones and shale, dominated by aluminosilicates and <5% calcite. A study was conducted to determine the evolution of acid deposition through an unsaturated to saturated zone composed of siltstone and shale in an isolated hill, precluding lateral flow and seepage. The results from water–rock chemical reactions modeled using PHREEQM demonstrate the percolating precipitation water is neutralized to pH 7.5 within the top 1.5 m. The model suggests that, along with calcite, dissolution of albite, illite, and kaolinite are the dominant mechanisms of neutralization. The cation exchange capacity of the siltstone and shale, in the range 54.6–386 meq/100 g, appears to be a function of high organic carbon content of 2.0–3.2%. While cation exchange is responsible for some of the Na⁺ in solution, it is not the primary source of Ca²⁺, Mg²⁺, or K⁺ ions. Exchange onto clays is occurring, but is secondary to exchange on organic matter. Chemical composition of groundwater perched within a coal seam is controlled by oxidation and dissolution of pyrite, returning pH to approximately 4.0.     

非饱和黏性土抗剪强度的温度效应试验研究

为了系统地了解温度对黏性土工程性质的影响,本文采用南京地区三种不同矿物成分的黏性土,制成不同含水量和干密度的试样,在5～45℃条件下,开展了抗剪强度试验,获得了三种土的非饱和重塑试样的抗剪强度与温度的关系.试验结果表明:黏性土的黏聚力随温度升高呈线性变化;亲水矿物含量较高的黏性土抗剪强度对温度变化较敏感,黏聚力随着温度...