In this study, I develop a Gaussian Closure method to simulate steady state unsaturated flow in randomly heterogeneous soils. I predict pressure heads and fluxes and evaluate uncertainties associated with these predictions, without resorting to Monte Carlo simulation, upscaling, or linearization of the governing flow equations and the constitutive relationship between unsaturated hydraulic conductivity and pressure head. Upon treating dimensionless pressure head as a multivariate Gaussian function in the manner of Amir and Neuman [2001], I obtain a closed system of coupled non-linear differential equations for the first and second moments of pressure head and flux for both spatially uncorrelated Y (log saturated hydraulic conductivity) and spatially correlated Y. Computational examples for unsaturated flow in a vertical plane, subject to deterministic forcing terms including a point source, show a good agreement between my Gaussian closure solution and a more general Monte Carlo solution. The computational examples include a uniform domain, eight subdomains, spatially uncorrelated non-uniform Y cases, spatially correlated Y cases, and conditional Y cases. Though the computational examples treat the random pore size parameter a as being uniform across the entire flow domain, I show theoretically that the Gaussian closure method could apply to spatially variable a statistics.

Conventional disposal of waste rock results in the construction of benches with interbedded fine and coarse layers dipping at the angle of repose. The waste rock benches are typically 20-meters in height and are constructed in a vertical sequence to form waste rock dumps commonly greater than 100-meters high. The interbedded structure influences the flow pathways for infiltration water within the waste rock profile. Preferential flow pathways develop when one material becomes more conductive than the surrounding material. The flow of meteoric waters through the interbedded waste rock structure is difficult to describe since the dumps are constructed above natural topography and are generally unsaturated. Two previous research studies were undertaken at the University of Saskatchewan to study end dumped waste rock piles and the relationship to preferential flow for unsaturated conditions. The first study was conducted during the excavation of a large waste rock pile at Golden Sunlight Mine in Montana (Herasymuik, 1996). Field observations showed that the waste rock pile consisted of steeply dipping fine and coarse-grained layers. The results of further laboratory analysis indicated the potential for preferential flow through the fine-grained material under conditions with negative pore-water pressures and unsaturated flow. The second study investigated the mechanism for preferential flow in vertically layered, unsaturated soil systems (Newman, 1999). The investigation included a vertical two-layer column study and a subsequent numerical modelling program showing that water prefers to flow in the finer-grained material. The preferential flow path was determined to be a function of the applied surface flux rates and the unsaturated hydraulic conductivity of the fine-grained material layer. A numerical modelling program to evaluate preferential flow was conducted for the present study in an inclined four-layer system consisting of alternating fine and coarse-grained waste rock. The numerical modelling program was undertaken using the commercial seepage software package, Seep/W, that is commonly used by geotechnical engineers. The result obtained using Seep/W showed preferential flow to occur in the fine-grained layer. However, difficulties with respect to convergence under low flow conditions with steep hydraulic conductivity functions were encountered. A comprehensive sensitivity analysis was completed to investigate the factors that influence convergence in the Seep/W model including: convergence criteria, mesh design and material properties. It was found that the hydraulic conductivity function used for the coarse-grained material was the most important factor. The problem of the steep slope for the hydraulic conductivity function specified for the coarse-grained material was solved by progressively decreasing the slope of the hydraulic conductivity function at 10-8 m/s (for applied fluxes of 10-7 m/s or less). The sensitivity analysis showed that the manipulation of the hydraulic conductivity function had insignificant changes in the flux distribution between the waste rock layers and great significance for achieving convergence. Based on the discoveries of the sensitivity analysis, a 20-meter high multi-layer waste rock profile inclined at 50º with an applied flux of 7.7e10-9 m/s equal to the annual precipitation at the Golden Sunlight Mine was successfully simulated. A parametric study was subsequently conducted for an applied flux rate of 10-5 m/s for slope heights of 1-meter to 20 meters with slope angles varying between 45º and 90º. The parametric study demonstrated that flow in a multi-layered waste rock dump is a function of inclination, contact length between the layers, and the coarse and fine-grained hydraulic properties for the waste rock. An alternative numerical modelling technique based on a modified Kisch solution was also used to investigate preferential flow. The Kisch method helped to verify and simplify the numerical problem as well as to illustrate the mechanics of preferential flow in a two-layered system. In general, commercial seepage modeling packages are powerful and useful tools that are designed to adequately accommodate a wide range of geotechnical problems. The results of this research study indicate that Seep/W may not be the best-suited tool to analyze unsaturated seepage through sloped waste rock layers. However, numerical modelling is a process and working through the process helps to enhance engineering judgment. The Seep/W model provided an adequate solution for a simplified simulation of unsaturated seepage through waste rock layers. The modified Kisch solution independently verified the solution and provided additional confidence for the results of Seep/W model.

Conventional disposal of waste rock results in the construction of benches with interbedded fine and coarse layers dipping at the angle of repose. The waste rock benches are typically 20-meters in height and are constructed in a vertical sequence to form waste rock dumps commonly greater than 100-meters high. The interbedded structure influences the flow pathways for infiltration water within the waste rock profile. Preferential flow pathways develop when one material becomes more conductive than the surrounding material. The flow of meteoric waters through the interbedded waste rock structure is difficult to describe since the dumps are constructed above natural topography and are generally unsaturated. Two previous research studies were undertaken at the University of Saskatchewan to study end dumped waste rock piles and the relationship to preferential flow for unsaturated conditions. The first study was conducted during the excavation of a large waste rock pile at Golden Sunlight Mine in Montana (Herasymuik, 1996). Field observations showed that the waste rock pile consisted of steeply dipping fine and coarse-grained layers. The results of further laboratory analysis indicated the potential for preferential flow through the fine-grained material under conditions with negative pore-water pressures and unsaturated flow. The second study investigated the mechanism for preferential flow in vertically layered, unsaturated soil systems (Newman, 1999). The investigation included a vertical two-layer column study and a subsequent numerical modelling program showing that water prefers to flow in the finer-grained material. The preferential flow path was determined to be a function of the applied surface flux rates and the unsaturated hydraulic conductivity of the fine-grained material layer. A numerical modelling program to evaluate preferential flow was conducted for the present study in an inclined four-layer system consisting of alternating fine and coarse-grained waste rock. The numerical modelling program was undertaken using the commercial seepage software package, Seep/W, that is commonly used by geotechnical engineers. The result obtained using Seep/W showed preferential flow to occur in the fine-grained layer. However, difficulties with respect to convergence under low flow conditions with steep hydraulic conductivity functions were encountered. A comprehensive sensitivity analysis was completed to investigate the factors that influence convergence in the Seep/W model including: convergence criteria, mesh design and material properties. It was found that the hydraulic conductivity function used for the coarse-grained material was the most important factor. The problem of the steep slope for the hydraulic conductivity function specified for the coarse-grained material was solved by progressively decreasing the slope of the hydraulic conductivity function at 10-8 m/s (for applied fluxes of 10-7 m/s or less). The sensitivity analysis showed that the manipulation of the hydraulic conductivity function had insignificant changes in the flux distribution between the waste rock layers and great significance for achieving convergence. Based on the discoveries of the sensitivity analysis, a 20-meter high multi-layer waste rock profile inclined at 50º with an applied flux of 7.7e10-9 m/s equal to the annual precipitation at the Golden Sunlight Mine was successfully simulated. A parametric study was subsequently conducted for an applied flux rate of 10-5 m/s for slope heights of 1-meter to 20 meters with slope angles varying between 45º and 90º. The parametric study demonstrated that flow in a multi-layered waste rock dump is a function of inclination, contact length between the layers, and the coarse and fine-grained hydraulic properties for the waste rock. An alternative numerical modelling technique based on a modified Kisch solution was also used to investigate preferential flow. The Kisch method helped to verify and simplify the numerical problem as well as to illustrate the mechanics of preferential flow in a two-layered system. In general, commercial seepage modeling packages are powerful and useful tools that are designed to adequately accommodate a wide range of geotechnical problems. The results of this research study indicate that Seep/W may not be the best-suited tool to analyze unsaturated seepage through sloped waste rock layers. However, numerical modelling is a process and working through the process helps to enhance engineering judgment. The Seep/W model provided an adequate solution for a simplified simulation of unsaturated seepage through waste rock layers. The modified Kisch solution independently verified the solution and provided additional confidence for the results of Seep/W model.

Cílem této práce bylo orientačně otestovat, do jaké míry je rozpad díky vzduchu stlačovanému kapilární vodou nasávanou do sedimentu (kapilárně-pneumatický rozpad, KP rozpad) významným procesem při erozi různých sedimentů, jako jsou písky až slabě cementované pískovce, spraše, jíly, jílovce a případně i jílovité půdy. Dílčím cílem bylo především vytvořit a na několika vybraných materiálech otestovat jednoduchou metodiku, prokazující, zda sediment podlehne KP rozpadu, dále vypočítat destrukční tlak daný KP rozpadem v pórech sedimentu a porovnat ho s tahovou pevností materiálu a konečně posoudit vliv mineralogie a porosity sedimentů na KP rozpad. Pro odlišení KP rozpadu od jiných destrukčních procesů jsem zvolila pozorování rozpadu dvojic vzorků, kdy jeden byl saturován za běžného atmosférického tlaku vzduchu a druhý ve vakuu. Tato metoda je schopná odlišit KP působení od jiných erozních procesů a zároveň je přiměřeně rychlá a vhodná pro různé sedimenty a zeminy. Pozorování potvrzuje, že KP působení je schopno rozložit různé sedimenty a zeminy na jemné částice, jedná se o velmi důležitý proces rozpadu, který probíhá i ve stojaté vodě, může být iniciátorem pipingu a měl by být proto intenzivně studován. Srovnání vypočtených hodnot pórového tlaku s tahovou pevností ukázala, že vypočtené pórové tlaky...

abstract: The primary objective of this study is to understand the effect of soil cracking on foundation performance for expansive soil profiles. Two major effects of cracks were studied to assess the effect of cracks on foundation performance. First, the effect of cracks on soil volume change response was studied. Second, the effect of cracks on unsaturated flow properties and extent and degree of wetting were evaluated. Multiple oedometer-type pressure plate tests were conducted to evaluate the effect of cracks on soil properties commonly used in volume change (heave) analyses, such as swell pressure, soil water characteristic curve (SWCC), and swell potential. Additionally, the effect of cracks on saturated and unsaturated hydraulic conductivity was studied experimentally to assess the impact of cracks on properties critical to evaluation of extent and degree of wetting. Laboratory experiments were performed on both intact and cracked specimen so that the effect of cracks on behavior could be benchmarked against intact soil response. Based on laboratory observations, the SWCC of a cracked soil is bimodal. However, this bimodal behavior is only observed in the very low suction ranges. Because the bimodal nature of the SWCC of cracked clays is only distinguishable at extremely low suctions, the bimodal behavior is unlikely to have engineering significance when soils remain unsaturated. A "lumped mass" parameter approach has been studied as a practical approach for modeling of cracked soils for both fluid flow and volume change determination. Laboratory unsaturated flow experiments were simulated using a saturated-unsaturated flow finite element code, SVFlux, to back-analyze unsaturated hydraulic conductivity functions for the subject soils. These back-analyzed results were compared to the results from traditionally-applied analyses of the laboratory instantaneous profile tests on intact and cracked specimens. Based on this comparison, empirical adjustments were suggested for modeling "lumped mass" cracked soil behavior in numerical codes for fluid flow through cracked soils. Using the empirically adjusted flow parameters for unsaturated flow modeling, example analyses were performed for slab-on-grade problems to demonstrate the impact of cracks on degree and extent of wetting under unsaturated and saturated flow conditions for different surface flux boundary conditions. / Dissertation/Thesis / Ph.D. Civil and Environmental Engineering 2011

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The percolation of water through waste rock dumps at mine sites can lead to the production of a leachate with high concentrations of dissolved metals, sulfate and nitrogen compounds. It is important to understand how water flows in waste rock dumps in order to predict the environmental impact of this leachate on recipients. The dynamics of percolation and leachate discharge are controlled by climatological conditions at the site, where relatively large flows in northern Sweden correspond to snowmelt during late Spring. Rock dumps are often tens of meters in height, resulting in an unsaturated water flow system through heterogeneous material. Hence, the simulation of leachate generation requires an accurate representation of the subsurface materials as well as the flow processes, where water flow in waste rock dumps is dominated by matrix flow with macropore flow being of secondary importance. Matrix flow is rather slow and may thus potentially yield relatively high concentrations of contaminants in the leachate, in response to precipitation and snow melt. This study uses Hydrus-1D to predict leachate generation from a small-scale waste rock dump in Kiruna in terms of discharge magnitude and timing. The 3-dimensional geometry of the waste rock dump is approximated by summing simulations from 1225 one-dimensional columns of different length, with a surface area of 1 m2 each. There are four output parameters that are compared between the model results and measured data: snow accumulation, water content, temperature, and discharge. There are some discrepancies between the model results and field measurements, most likely due to uncertainties in the input parameters (especially waste rock properties), limitations in the Hydrus-1D model (i.e. freeze-thaw dynamics), and assumptions that are used in constructing the conceptual model. For better agreement between model results and measured data, a new modelling approach is recommended, potentially using a different program than Hydrus-1D.

Seawater intrusion (SWI) is a widespread environmental problem, particularly in arid and semi-arid coastal areas. Unplanned prolonged over-pumping of groundwater is the most important factor in SWI that could result in severe deterioration of groundwater quality. Therefore, appropriate management strategies should be implemented in coastal aquifers to control SWI with acceptable limits of economic and environmental costs. This PhD project presents the development and application of a simulation-optimization (S/O) model to assess different management methods of controlling saltwater intrusion while satisfying water demands, and with acceptable limits of economic and environmental costs, in confined and unconfined coastal aquifers. The first S/O model (FE-GA) is developed by direct linking of an FE simulation model with a multi-objective Genetic Algorithm (GA) to optimize the efficiency of a wide range of SWI management scenarios. However, in this S/O framework, several multiple calls of the simulation model by the population-based optimization model, evaluating best individual candidate solutions resulted in a considerable computational burden. To solve this problem the numerical simulation model is replaced by an Evolutionary Polynomial Regression (EPR)-based surrogate model in the next S/O model (EPR-GA). Through these S/O approaches (FE-GA and EPR-GA) the optimal coordinates and rates of the both abstraction and recharge barriers are determined in the studied management scenarios. As a result, a new combined methodology, so far called ADRTWW, is proposed to control SWI. The ADRTWW model consists of deep Abstraction of saline water near the coast followed by Desalination of the abstracted water to a potable level for public uses and simultaneously Recharging the aquifer using a more economic source of water such as treated wastewater (TWW). In accordance to the available recharge options (injection through well or infiltration from surface pond), the general performance of ADRTWW is evaluated in different hydro-geological settings of the aquifers indicating that it offers the least cost and least salinity in comparison with other scenarios. The great capabilities of both developed S/O models in identification of the best management solutions and the optimal coordinates and rates of the abstraction well and recharge well/pond are discussed. Both FE-GA and EPR-GA can be successfully employed by a robust decision support system. In the next phase of the study, the general impacts of sea level rise (SLR), associated with its transgression nature along the coastline surface on the saltwater intrusion mechanism are investigated in different hypothetical and real case studies of coastal aquifer systems. The results show that the rate and the amount of SWI are considerably greater in aquifers with flat shoreline slopes compared with those with steep slopes. The SWI process is followed by a significant depletion in quantity of freshwater resources at the end of the century. The situation is exacerbated with combined action of SLR and groundwater withdrawals. This finding is also confirmed by 3D simulation of SWI in a regional coastal aquifer (Wadi Ham aquifer) in the UAE subjected to the coupled actions of SLR and pumping.

[pt] O estudo de fluxo saturado - não saturado em solos exige o conhecimento das funções de relação, como a curva característica (q x h) e a curva de condutividade hidráulica (K x h). Para determinar estas relações o presente trabalho utiliza o modelo de van Genuchten- Mualem, o qual está implementado numa ferramenta numérica que permite a utilização da retroanálise como método para determinação dos parâmetros do modelo. O principal objetivo deste trabalho é a avaliação de um método que permita a estimativa dos parâmetros do modelo de van Genuchten-Mualem, a partir de dados coletados em campo ou laboratório para, então, realizar-se a análise de fluxo saturado - não saturado e a estimativa dos parametros de van Genuchtem-Mualem. Finalmente, a as condições de fluxo saturado - não saturado em duas encostas foram simuladas, em duas e três dimensões, a fim de verificar a variação de fluxo nestes casos. / [en] The study of saturated and non saturated flow in soils requires the knowledge of relation functions, as water retention curve (q vs. h) and hydraulic conductivity curve (K vs. h).In order to determine these relations, this research uses van Genuchten-Mualem`s model, which is implemented on a numerical based method. This tool allows the inverse solution as a method to determine the parameters of the model. The main objective of this research is the evaluation of a method which allows the estimative of the required parameters by the chosen model, determined based on field or laboratory data, so then, based on these parameters, saturated and non- saturated flow analysis were carried out and the estimative of parameters of van Genuchten-Mualem`s model. Finally, saturated and non-saturated simulations were made on two slopes. These simulations were followed by 2D and 3D models, in order to verify the flow variation on these cases.